News <2010>

December 2010

December 31, 2010

Serge Batalov proved 1 near-repdigit-related prime by PFGW and CHG.

Proven near-repdigit-related primes (except ru/nr/pd/qr)
	digits	flabel	wlabel	expression	when	who
160	4718		34w11	(31·10⁴⁷¹⁷-301)/9	December 31, 2010	Serge Batalov

Maksym Voznyy proved 1 near-repdigit prime by Primo 3.0.9 and PFGW 3.4.4.

Proven near-repdigit primes
	digits	flabel	wlabel	expression	when	who
279	4809	11101	1w01	(10⁴⁸⁰⁹-91)/9	December 31, 2010	Maksym Voznyy

December 30, 2010

Maksym Voznyy proved 6 near-repdigit primes by Primo 3.0.9.

Proven near-repdigit primes
	digits	flabel	wlabel	expression	when	who
318	3308	97777	97w	(88·10³³⁰⁷-7)/9	December 30, 2010	Maksym Voznyy
321	3247	88881	8w1	(8·10³²⁴⁷-71)/9	December 30, 2010	Maksym Voznyy
329	2998	81111	81w	(73·10²⁹⁹⁷-1)/9	December 30, 2010	Maksym Voznyy
333	2968	33337	3w7	(10²⁹⁶⁸+11)/3	December 30, 2010	Maksym Voznyy
338	2906	88883	8w3	(8·10²⁹⁰⁶-53)/9	December 30, 2010	Maksym Voznyy
342	2811	33337	3w7	(10²⁸¹¹+11)/3	December 30, 2010	Maksym Voznyy

Maksym Voznyy proved 1 prime by Primo 3.0.9 and PFGW.

Proven near-repdigit-related primes (except ru/nr/pd/qr)
	digits	flabel	wlabel	expression	when	who
141	5737	80081	80w81	8·10⁵⁷³⁶+81	December 30, 2010	Maksym Voznyy

December 29, 2010

Thanks to Ray Chandler, obsolete links from our tables of the form AABAA to OEIS were corrected.

December 27, 2010

Bob Price found 5 near-repdigit-related PRPs by PFGW.

Unprovable near-repdigit-related PRPs (except ru/nr/pd/qr)
	digits	flabel	wlabel	expression	when	who
4	47027	10051	10w51	10⁴⁷⁰²⁶+51	December 27, 2010	Bob Price
5	42458	10019	10w19	10⁴²⁴⁵⁷+19	December 27, 2010	Bob Price
6	42082	10081	10w81	10⁴²⁰⁸¹+81	December 27, 2010	Bob Price
7	41457	10049	10w49	10⁴¹⁴⁵⁶+49	December 27, 2010	Bob Price
8	40930	10019	10w19	10⁴⁰⁹²⁹+19	December 27, 2010	Bob Price

December 26, 2010

Ray Chandler found 30 primes and 181 PRPs by srsieve and PFGW.

Proven near-repdigit primes
	digits	flabel	wlabel	expression	when	who
114	29126		999999959w	99999996·10²⁹¹¹⁸-1	December 26, 2010	Ray Chandler
120	26200		99999919w	9999992·10²⁶¹⁹³-1	December 26, 2010	Ray Chandler

Proven quasi-repdigit primes
	digits	flabel	wlabel	expression	when	who
11	29791	34999	349w	35·10²⁹⁷⁸⁹-1	December 26, 2010	Ray Chandler
12	29551	68999	689w	69·10²⁹⁵⁴⁹-1	December 26, 2010	Ray Chandler
13	29334	32999	329w	33·10²⁹³³²-1	December 26, 2010	Ray Chandler
14	28460	16999	169w	17·10²⁸⁴⁵⁸-1	December 26, 2010	Ray Chandler
15	28109	46999	469w	47·10²⁸¹⁰⁷-1	December 26, 2010	Ray Chandler
16	28094	83999	839w	84·10²⁸⁰⁹²-1	December 26, 2010	Ray Chandler
18	27638	34999	349w	35·10²⁷⁶³⁶-1	December 26, 2010	Ray Chandler
19	27577	62999	629w	63·10²⁷⁵⁷⁵-1	December 26, 2010	Ray Chandler
20	27491	46999	469w	47·10²⁷⁴⁸⁹-1	December 26, 2010	Ray Chandler
21	27250	20999	209w	21·10²⁷²⁴⁸-1	December 26, 2010	Ray Chandler
22	27036	65999	659w	66·10²⁷⁰³⁴-1	December 26, 2010	Ray Chandler
23	26783	25999	259w	26·10²⁶⁷⁸¹-1	December 26, 2010	Ray Chandler
24	26576	38999	389w	39·10²⁶⁵⁷⁴-1	December 26, 2010	Ray Chandler
25	26415		779w	78·10²⁶⁴¹³-1	December 26, 2010	Ray Chandler
26	26342	50999	509w	51·10²⁶³⁴⁰-1	December 26, 2010	Ray Chandler
27	26238	14999	149w	15·10²⁶²³⁶-1	December 26, 2010	Ray Chandler
28	26034	23999	239w	24·10²⁶⁰³²-1	December 26, 2010	Ray Chandler
30	25672	85999	859w	86·10²⁵⁶⁷⁰-1	December 26, 2010	Ray Chandler
31	25546	26999	269w	27·10²⁵⁵⁴⁴-1	December 26, 2010	Ray Chandler
32	25246	62999	629w	63·10²⁵²⁴⁴-1	December 26, 2010	Ray Chandler
33	25121	65999	659w	66·10²⁵¹¹⁹-1	December 26, 2010	Ray Chandler
34	25056	76999	769w	77·10²⁵⁰⁵⁴-1	December 26, 2010	Ray Chandler
35	24947	65999	659w	66·10²⁴⁹⁴⁵-1	December 26, 2010	Ray Chandler
36	24357	47999	479w	48·10²⁴³⁵⁵-1	December 26, 2010	Ray Chandler
37	24310	70999	709w	71·10²⁴³⁰⁸-1	December 26, 2010	Ray Chandler
38	24112	16999	169w	17·10²⁴¹¹⁰-1	December 26, 2010	Ray Chandler
39	23277	13999	139w	14·10²³²⁷⁵-1	December 26, 2010	Ray Chandler
40	23225	46999	469w	47·10²³²²³-1	December 26, 2010	Ray Chandler

Unprovable quasi-repdigit PRPs
	digits	flabel	wlabel	expression	when	who
106	29913	69959	69w59	7·10²⁹⁹¹²-41	December 26, 2010	Ray Chandler
107	29628	49979	49w79	5·10²⁹⁶²⁷-21	December 26, 2010	Ray Chandler
108	29538	79969	79w69	8·10²⁹⁵³⁷-31	December 26, 2010	Ray Chandler
119	29091	97991	979w1	98·10²⁹⁰⁸⁹-9	December 26, 2010	Ray Chandler
127	28528	19909	19w09	2·10²⁸⁵²⁷-91	December 26, 2010	Ray Chandler
129	28351	79969	79w69	8·10²⁸³⁵⁰-31	December 26, 2010	Ray Chandler
130	28346	59909	59w09	6·10²⁸³⁴⁵-91	December 26, 2010	Ray Chandler
133	28073	29959	29w59	3·10²⁸⁰⁷²-41	December 26, 2010	Ray Chandler
138	27749	89959	89w59	9·10²⁷⁷⁴⁸-41	December 26, 2010	Ray Chandler
143	27407	94993	949w3	95·10²⁷⁴⁰⁵-7	December 26, 2010	Ray Chandler
157	26566	79919	79w19	8·10²⁶⁵⁶⁵-81	December 26, 2010	Ray Chandler
164	26183	19979	19w79	2·10²⁶¹⁸²-21	December 26, 2010	Ray Chandler
177	25641	59969	59w69	6·10²⁵⁶⁴⁰-31	December 26, 2010	Ray Chandler
178	25575	79939	79w39	8·10²⁵⁵⁷⁴-61	December 26, 2010	Ray Chandler
180	25243	19909	19w09	2·10²⁵²⁴²-91	December 26, 2010	Ray Chandler
185	25023	49949	49w49	5·10²⁵⁰²²-51	December 26, 2010	Ray Chandler
193	24745	59909	59w09	6·10²⁴⁷⁴⁴-91	December 26, 2010	Ray Chandler
195	24599	79969	79w69	8·10²⁴⁵⁹⁸-31	December 26, 2010	Ray Chandler
196	24589	19909	19w09	2·10²⁴⁵⁸⁸-91	December 26, 2010	Ray Chandler
199	24200	39989	39w89	4·10²⁴¹⁹⁹-11	December 26, 2010	Ray Chandler
200	24160	93991	939w1	94·10²⁴¹⁵⁸-9	December 26, 2010	Ray Chandler
201	24146	99947	9w47	10²⁴¹⁴⁶-53	December 26, 2010	Ray Chandler
204	23837	29989	29w89	3·10²³⁸³⁶-11	December 26, 2010	Ray Chandler
207	23680	49919	49w19	5·10²³⁶⁷⁹-81	December 26, 2010	Ray Chandler
216	23071	89989	89w89	9·10²³⁰⁷⁰-11	December 26, 2010	Ray Chandler

Unprovable near-repdigit-related PRPs (except ru/nr/pd/qr)
	digits	flabel	wlabel	expression	when	who
10	30000	19963	19w63	2·10²⁹⁹⁹⁹-37	December 26, 2010	Ray Chandler
11	29994		559w7	56·10²⁹⁹⁹²-3	December 26, 2010	Ray Chandler
12	29959	39917	39w17	4·10²⁹⁹⁵⁸-83	December 26, 2010	Ray Chandler
13	29941	29947	29w47	3·10²⁹⁹⁴⁰-53	December 26, 2010	Ray Chandler
14	29928		20w77	2·10²⁹⁹²⁷+77	December 26, 2010	Ray Chandler
16	29604	60037	60w37	6·10²⁹⁶⁰³+37	December 26, 2010	Ray Chandler
17	29596	50081	50w81	5·10²⁹⁵⁹⁵+81	December 26, 2010	Ray Chandler
18	29589		80w11	8·10²⁹⁵⁸⁸+11	December 26, 2010	Ray Chandler
19	29547	40039	40w39	4·10²⁹⁵⁴⁶+39	December 26, 2010	Ray Chandler
20	29507		19w33	2·10²⁹⁵⁰⁶-67	December 26, 2010	Ray Chandler
22	29388	89947	89w47	9·10²⁹³⁸⁷-53	December 26, 2010	Ray Chandler
23	29339	60017	60w17	6·10²⁹³³⁸+17	December 26, 2010	Ray Chandler
24	29303		70w33	7·10²⁹³⁰²+33	December 26, 2010	Ray Chandler
25	29293		779w3	78·10²⁹²⁹¹-7	December 26, 2010	Ray Chandler
26	29254		49w33	5·10²⁹²⁵³-67	December 26, 2010	Ray Chandler
27	29222	49907	49w07	5·10²⁹²²¹-93	December 26, 2010	Ray Chandler
28	29206	80039	80w39	8·10²⁹²⁰⁵+39	December 26, 2010	Ray Chandler
30	29181	69931	69w31	7·10²⁹¹⁸⁰-69	December 26, 2010	Ray Chandler
31	29164	19951	19w51	2·10²⁹¹⁶³-49	December 26, 2010	Ray Chandler
33	29133	70039	70w39	7·10²⁹¹³²+39	December 26, 2010	Ray Chandler
34	29096	40061	40w61	4·10²⁹⁰⁹⁵+61	December 26, 2010	Ray Chandler
35	29089	90041	90w41	9·10²⁹⁰⁸⁸+41	December 26, 2010	Ray Chandler
36	29069	20071	20w71	2·10²⁹⁰⁶⁸+71	December 26, 2010	Ray Chandler
37	29063	40031	40w31	4·10²⁹⁰⁶²+31	December 26, 2010	Ray Chandler
38	29063	20093	20w93	2·10²⁹⁰⁶²+93	December 26, 2010	Ray Chandler
40	29027	29947	29w47	3·10²⁹⁰²⁶-53	December 26, 2010	Ray Chandler
41	29008	69973	69w73	7·10²⁹⁰⁰⁷-27	December 26, 2010	Ray Chandler
42	28974	30043	30w43	3·10²⁸⁹⁷³+43	December 26, 2010	Ray Chandler
43	28923	39953	39w53	4·10²⁸⁹²²-47	December 26, 2010	Ray Chandler
44	28890	89953	89w53	9·10²⁸⁸⁸⁹-47	December 26, 2010	Ray Chandler
45	28882		220w7	22·10²⁸⁸⁸⁰+7	December 26, 2010	Ray Chandler
46	28861		39w11	4·10²⁸⁸⁶⁰-89	December 26, 2010	Ray Chandler
47	28819		119w3	12·10²⁸⁸¹⁷-7	December 26, 2010	Ray Chandler
48	28732	20081	20w81	2·10²⁸⁷³¹+81	December 26, 2010	Ray Chandler
51	28471	50053	50w53	5·10²⁸⁴⁷⁰+53	December 26, 2010	Ray Chandler
52	28455	79943	79w43	8·10²⁸⁴⁵⁴-57	December 26, 2010	Ray Chandler
53	28349	30031	30w31	3·10²⁸³⁴⁸+31	December 26, 2010	Ray Chandler
54	28319	30031	30w31	3·10²⁸³¹⁸+31	December 26, 2010	Ray Chandler
55	28275	90043	90w43	9·10²⁸²⁷⁴+43	December 26, 2010	Ray Chandler
56	28271	70061	70w61	7·10²⁸²⁷⁰+61	December 26, 2010	Ray Chandler
58	28220	79961	79w61	8·10²⁸²¹⁹-39	December 26, 2010	Ray Chandler
59	28162	30067	30w67	3·10²⁸¹⁶¹+67	December 26, 2010	Ray Chandler
60	28074	60097	60w97	6·10²⁸⁰⁷³+97	December 26, 2010	Ray Chandler
61	28064	69971	69w71	7·10²⁸⁰⁶³-29	December 26, 2010	Ray Chandler
62	27868		339w7	34·10²⁷⁸⁶⁶-3	December 26, 2010	Ray Chandler
63	27714	80053	80w53	8·10²⁷⁷¹³+53	December 26, 2010	Ray Chandler
64	27670	39923	39w23	4·10²⁷⁶⁶⁹-77	December 26, 2010	Ray Chandler
65	27649	30059	30w59	3·10²⁷⁶⁴⁸+59	December 26, 2010	Ray Chandler
66	27624	30029	30w29	3·10²⁷⁶²³+29	December 26, 2010	Ray Chandler
67	27607	30029	30w29	3·10²⁷⁶⁰⁶+29	December 26, 2010	Ray Chandler
68	27532	90029	90w29	9·10²⁷⁵³¹+29	December 26, 2010	Ray Chandler
69	27503	30073	30w73	3·10²⁷⁵⁰²+73	December 26, 2010	Ray Chandler
70	27441	79961	79w61	8·10²⁷⁴⁴⁰-39	December 26, 2010	Ray Chandler
71	27419	50047	50w47	5·10²⁷⁴¹⁸+47	December 26, 2010	Ray Chandler
72	27403	20083	20w83	2·10²⁷⁴⁰²+83	December 26, 2010	Ray Chandler
73	27346	29917	29w17	3·10²⁷³⁴⁵-83	December 26, 2010	Ray Chandler
74	27319	20039	20w39	2·10²⁷³¹⁸+39	December 26, 2010	Ray Chandler
75	27208	30037	30w37	3·10²⁷²⁰⁷+37	December 26, 2010	Ray Chandler
76	27051	90061	90w61	9·10²⁷⁰⁵⁰+61	December 26, 2010	Ray Chandler
77	27003	89987	89w87	9·10²⁷⁰⁰²-13	December 26, 2010	Ray Chandler
80	26745		79w33	8·10²⁶⁷⁴⁴-67	December 26, 2010	Ray Chandler
81	26668	89903	89w03	9·10²⁶⁶⁶⁷-97	December 26, 2010	Ray Chandler
82	26663	80051	80w51	8·10²⁶⁶⁶²+51	December 26, 2010	Ray Chandler
83	26611	70057	70w57	7·10²⁶⁶¹⁰+57	December 26, 2010	Ray Chandler
84	26565	80063	80w63	8·10²⁶⁵⁶⁴+63	December 26, 2010	Ray Chandler
85	26490	69973	69w73	7·10²⁶⁴⁸⁹-27	December 26, 2010	Ray Chandler
87	26400	40067	40w67	4·10²⁶³⁹⁹+67	December 26, 2010	Ray Chandler
88	26378	59971	59w71	6·10²⁶³⁷⁷-29	December 26, 2010	Ray Chandler
89	26361	20063	20w63	2·10²⁶³⁶⁰+63	December 26, 2010	Ray Chandler
90	26294	30043	30w43	3·10²⁶²⁹³+43	December 26, 2010	Ray Chandler
91	26253	80087	80w87	8·10²⁶²⁵²+87	December 26, 2010	Ray Chandler
92	26201		440w3	44·10²⁶¹⁹⁹+3	December 26, 2010	Ray Chandler
93	26198	90083	90w83	9·10²⁶¹⁹⁷+83	December 26, 2010	Ray Chandler
94	26126		40w99	4·10²⁶¹²⁵+99	December 26, 2010	Ray Chandler
95	26123	89963	89w63	9·10²⁶¹²²-37	December 26, 2010	Ray Chandler
96	26085	79913	79w13	8·10²⁶⁰⁸⁴-87	December 26, 2010	Ray Chandler
97	25986	39941	39w41	4·10²⁵⁹⁸⁵-59	December 26, 2010	Ray Chandler
98	25963		110w9	11·10²⁵⁹⁶¹+9	December 26, 2010	Ray Chandler
99	25882	90043	90w43	9·10²⁵⁸⁸¹+43	December 26, 2010	Ray Chandler
100	25825	30037	30w37	3·10²⁵⁸²⁴+37	December 26, 2010	Ray Chandler
101	25762		339w1	34·10²⁵⁷⁶⁰-9	December 26, 2010	Ray Chandler
102	25738		339w7	34·10²⁵⁷³⁶-3	December 26, 2010	Ray Chandler
103	25733		40w99	4·10²⁵⁷³²+99	December 26, 2010	Ray Chandler
104	25727	40097	40w97	4·10²⁵⁷²⁶+97	December 26, 2010	Ray Chandler
105	25716		29w33	3·10²⁵⁷¹⁵-67	December 26, 2010	Ray Chandler
106	25686	90019	90w19	9·10²⁵⁶⁸⁵+19	December 26, 2010	Ray Chandler
108	25526	40097	40w97	4·10²⁵⁵²⁵+97	December 26, 2010	Ray Chandler
109	25475	30097	30w97	3·10²⁵⁴⁷⁴+97	December 26, 2010	Ray Chandler
110	25452		19w33	2·10²⁵⁴⁵¹-67	December 26, 2010	Ray Chandler
111	25438	70027	70w27	7·10²⁵⁴³⁷+27	December 26, 2010	Ray Chandler
112	25428		50w77	5·10²⁵⁴²⁷+77	December 26, 2010	Ray Chandler
113	25419	19903	19w03	2·10²⁵⁴¹⁸-97	December 26, 2010	Ray Chandler
114	25408		50w99	5·10²⁵⁴⁰⁷+99	December 26, 2010	Ray Chandler
115	25393	30013	30w13	3·10²⁵³⁹²+13	December 26, 2010	Ray Chandler
116	25304	50063	50w63	5·10²⁵³⁰³+63	December 26, 2010	Ray Chandler
117	25257		20w11	2·10²⁵²⁵⁶+11	December 26, 2010	Ray Chandler
118	25233	50069	50w69	5·10²⁵²³²+69	December 26, 2010	Ray Chandler
119	25212	40063	40w63	4·10²⁵²¹¹+63	December 26, 2010	Ray Chandler
120	25206	59927	59w27	6·10²⁵²⁰⁵-73	December 26, 2010	Ray Chandler
121	25194	89953	89w53	9·10²⁵¹⁹³-47	December 26, 2010	Ray Chandler
122	25187	89981	89w81	9·10²⁵¹⁸⁶-19	December 26, 2010	Ray Chandler
123	25180	30061	30w61	3·10²⁵¹⁷⁹+61	December 26, 2010	Ray Chandler
124	25179		220w9	22·10²⁵¹⁷⁷+9	December 26, 2010	Ray Chandler
125	25173	59951	59w51	6·10²⁵¹⁷²-49	December 26, 2010	Ray Chandler
126	25104		889w1	89·10²⁵¹⁰²-9	December 26, 2010	Ray Chandler
127	25043	50053	50w53	5·10²⁵⁰⁴²+53	December 26, 2010	Ray Chandler
128	25019		339w7	34·10²⁵⁰¹⁷-3	December 26, 2010	Ray Chandler
129	24957		79w33	8·10²⁴⁹⁵⁶-67	December 26, 2010	Ray Chandler
130	24949	20081	20w81	2·10²⁴⁹⁴⁸+81	December 26, 2010	Ray Chandler
132	24935	39901	39w01	4·10²⁴⁹³⁴-99	December 26, 2010	Ray Chandler
133	24909	80027	80w27	8·10²⁴⁹⁰⁸+27	December 26, 2010	Ray Chandler
134	24843	49987	49w87	5·10²⁴⁸⁴²-13	December 26, 2010	Ray Chandler
135	24842	20087	20w87	2·10²⁴⁸⁴¹+87	December 26, 2010	Ray Chandler
136	24818		20w33	2·10²⁴⁸¹⁷+33	December 26, 2010	Ray Chandler
138	24775	90049	90w49	9·10²⁴⁷⁷⁴+49	December 26, 2010	Ray Chandler
139	24757	30089	30w89	3·10²⁴⁷⁵⁶+89	December 26, 2010	Ray Chandler
140	24746		990w7	99·10²⁴⁷⁴⁴+7	December 26, 2010	Ray Chandler
141	24713	79907	79w07	8·10²⁴⁷¹²-93	December 26, 2010	Ray Chandler
144	24565	50081	50w81	5·10²⁴⁵⁶⁴+81	December 26, 2010	Ray Chandler
145	24498	79921	79w21	8·10²⁴⁴⁹⁷-79	December 26, 2010	Ray Chandler
146	24413	30049	30w49	3·10²⁴⁴¹²+49	December 26, 2010	Ray Chandler
147	24373	49961	49w61	5·10²⁴³⁷²-39	December 26, 2010	Ray Chandler
148	24353	50093	50w93	5·10²⁴³⁵²+93	December 26, 2010	Ray Chandler
149	24338	60079	60w79	6·10²⁴³³⁷+79	December 26, 2010	Ray Chandler
150	24327	79987	79w87	8·10²⁴³²⁶-13	December 26, 2010	Ray Chandler
151	24290	70061	70w61	7·10²⁴²⁸⁹+61	December 26, 2010	Ray Chandler
152	24286	69967	69w67	7·10²⁴²⁸⁵-33	December 26, 2010	Ray Chandler
153	24214	89951	89w51	9·10²⁴²¹³-49	December 26, 2010	Ray Chandler
154	24175	90053	90w53	9·10²⁴¹⁷⁴+53	December 26, 2010	Ray Chandler
155	24097	59953	59w53	6·10²⁴⁰⁹⁶-47	December 26, 2010	Ray Chandler
157	24073	40063	40w63	4·10²⁴⁰⁷²+63	December 26, 2010	Ray Chandler
158	24064	60029	60w29	6·10²⁴⁰⁶³+29	December 26, 2010	Ray Chandler
159	24042	40087	40w87	4·10²⁴⁰⁴¹+87	December 26, 2010	Ray Chandler
160	23947		550w7	55·10²³⁹⁴⁵+7	December 26, 2010	Ray Chandler
161	23930	40069	40w69	4·10²³⁹²⁹+69	December 26, 2010	Ray Chandler
162	23901	50041	50w41	5·10²³⁹⁰⁰+41	December 26, 2010	Ray Chandler
163	23898	79943	79w43	8·10²³⁸⁹⁷-57	December 26, 2010	Ray Chandler
164	23894	90067	90w67	9·10²³⁸⁹³+67	December 26, 2010	Ray Chandler
166	23829	30037	30w37	3·10²³⁸²⁸+37	December 26, 2010	Ray Chandler
167	23813	60013	60w13	6·10²³⁸¹²+13	December 26, 2010	Ray Chandler
168	23813	30061	30w61	3·10²³⁸¹²+61	December 26, 2010	Ray Chandler
169	23783	30013	30w13	3·10²³⁷⁸²+13	December 26, 2010	Ray Chandler
170	23740	40061	40w61	4·10²³⁷³⁹+61	December 26, 2010	Ray Chandler
171	23733		20w33	2·10²³⁷³²+33	December 26, 2010	Ray Chandler
173	23680	50041	50w41	5·10²³⁶⁷⁹+41	December 26, 2010	Ray Chandler
174	23642	70081	70w81	7·10²³⁶⁴¹+81	December 26, 2010	Ray Chandler
175	23567	49927	49w27	5·10²³⁵⁶⁶-73	December 26, 2010	Ray Chandler
177	23374		559w1	56·10²³³⁷²-9	December 26, 2010	Ray Chandler
178	23366	70097	70w97	7·10²³³⁶⁵+97	December 26, 2010	Ray Chandler
180	23328		50w77	5·10²³³²⁷+77	December 26, 2010	Ray Chandler
182	23239	40039	40w39	4·10²³²³⁸+39	December 26, 2010	Ray Chandler
183	23218	40057	40w57	4·10²³²¹⁷+57	December 26, 2010	Ray Chandler
184	23168	60023	60w23	6·10²³¹⁶⁷+23	December 26, 2010	Ray Chandler
185	23165	40091	40w91	4·10²³¹⁶⁴+91	December 26, 2010	Ray Chandler
186	23125	60017	60w17	6·10²³¹²⁴+17	December 26, 2010	Ray Chandler
187	23030	59963	59w63	6·10²³⁰²⁹-37	December 26, 2010	Ray Chandler

Bob Price proved 1 prime by Primo.

Proven near-repdigit-related primes (except ru/nr/pd/qr)
	digits	flabel	wlabel	expression	when	who
461	1180	10097	10w97	10¹¹⁷⁹+97	December 26, 2010	Bob Price

December 25, 2010

Bob Price found 13 primes and 36 PRPs by PFGW and Primo.

Proven near-repdigit-related primes (except ru/nr/pd/qr)
	digits	flabel	wlabel	expression	when	who
278	1943	10067	10w67	10¹⁹⁴²+67	December 25, 2010	Bob Price
282	1924	10039	10w39	10¹⁹²³+39	December 25, 2010	Bob Price
312	1765	10061	10w61	10¹⁷⁶⁴+61	December 25, 2010	Bob Price
319	1732	10051	10w51	10¹⁷³¹+51	December 25, 2010	Bob Price
366	1529	10039	10w39	10¹⁵²⁸+39	December 25, 2010	Bob Price
368	1524	10069	10w69	10¹⁵²³+69	December 25, 2010	Bob Price
434	1244	10087	10w87	10¹²⁴³+87	December 25, 2010	Bob Price
459	1185	10093	10w93	10¹¹⁸⁴+93	December 25, 2010	Bob Price
469	1152	10097	10w97	10¹¹⁵¹+97	December 25, 2010	Bob Price
485	1100	10073	10w73	10¹⁰⁹⁹+73	December 25, 2010	Bob Price
496	1071	10051	10w51	10¹⁰⁷⁰+51	December 25, 2010	Bob Price
525	1010	10051	10w51	10¹⁰⁰⁹+51	December 25, 2010	Bob Price
528	1004	10069	10w69	10¹⁰⁰³+69	December 25, 2010	Bob Price

Unprovable near-repdigit PRPs
	digits	flabel	wlabel	expression	when	who
29	37169	99959	9w59	10³⁷¹⁶⁹-41	December 25, 2010	Bob Price
31	36271	99929	9w29	10³⁶²⁷¹-71	December 25, 2010	Bob Price
34	35371	99989	9w89	10³⁵³⁷¹-11	December 25, 2010	Bob Price
35	35316	99959	9w59	10³⁵³¹⁶-41	December 25, 2010	Bob Price
47	27312	99959	9w59	10²⁷³¹²-41	December 25, 2010	Bob Price
62	23932	99959	9w59	10²³⁹³²-41	December 25, 2010	Bob Price

Unprovable quasi-repdigit PRPs
	digits	flabel	wlabel	expression	when	who
64	39922	99943	9w43	10³⁹⁹²²-57	December 25, 2010	Bob Price
77	37344	99941	9w41	10³⁷³⁴⁴-59	December 25, 2010	Bob Price
90	34399	99943	9w43	10³⁴³⁹⁹-57	December 25, 2010	Bob Price
91	34313		9w77	10³⁴³¹³-23	December 25, 2010	Bob Price
93	32909	99907	9w07	10³²⁹⁰⁹-93	December 25, 2010	Bob Price
101	31123	99907	9w07	10³¹¹²³-93	December 25, 2010	Bob Price
102	30791	99973	9w73	10³⁰⁷⁹¹-27	December 25, 2010	Bob Price
107	29455		9w11	10²⁹⁴⁵⁵-89	December 25, 2010	Bob Price
115	29091	99971	9w71	10²⁹⁰⁹¹-29	December 25, 2010	Bob Price
123	28437	99907	9w07	10²⁸⁴³⁷-93	December 25, 2010	Bob Price
133	27681		9w77	10²⁷⁶⁸¹-23	December 25, 2010	Bob Price
162	25727	99947	9w47	10²⁵⁷²⁷-53	December 25, 2010	Bob Price
177	24693	99907	9w07	10²⁴⁶⁹³-93	December 25, 2010	Bob Price
180	23936	99961	9w61	10²³⁹³⁶-39	December 25, 2010	Bob Price
181	23854	99901	9w01	10²³⁸⁵⁴-99	December 25, 2010	Bob Price

Unprovable near-repdigit-related PRPs (except ru/nr/pd/qr)
	digits	flabel	wlabel	expression	when	who
4	39584	10091	10w91	10³⁹⁵⁸³+91	December 25, 2010	Bob Price
5	39188	10049	10w49	10³⁹¹⁸⁷+49	December 25, 2010	Bob Price
7	35394	10043	10w43	10³⁵³⁹³+43	December 25, 2010	Bob Price
8	34624	10063	10w63	10³⁴⁶²³+63	December 25, 2010	Bob Price
9	32646	10057	10w57	10³²⁶⁴⁵+57	December 25, 2010	Bob Price
10	29885	10057	10w57	10²⁹⁸⁸⁴+57	December 25, 2010	Bob Price
11	29472	10049	10w49	10²⁹⁴⁷¹+49	December 25, 2010	Bob Price
15	28700	10051	10w51	10²⁸⁶⁹⁹+51	December 25, 2010	Bob Price
17	28221	10063	10w63	10²⁸²²⁰+63	December 25, 2010	Bob Price
19	26780	10087	10w87	10²⁶⁷⁷⁹+87	December 25, 2010	Bob Price
20	26426	10097	10w97	10²⁶⁴²⁵+97	December 25, 2010	Bob Price
21	25672	10021	10w21	10²⁵⁶⁷¹+21	December 25, 2010	Bob Price
26	24095	10081	10w81	10²⁴⁰⁹⁴+81	December 25, 2010	Bob Price
29	23500	10091	10w91	10²³⁴⁹⁹+91	December 25, 2010	Bob Price
8796	1180	10097	10w97	10¹¹⁷⁹+97	December 25, 2010	Bob Price

Factorizations of 100...009 have been extended up to n=250. Composite numbers that appeared newly got through ECM 118 times at level 35. Most unknown factors are supposed to be greater than 10³⁰.

Ray Chandler's research found some inconsistencies between Henri & Renaud Lifchitz's PRP Top records and primesize.txt. The following records were corrected or added.

Unprovable near-repdigit PRPs
	digits	flabel	wlabel	expression	when	who
90	18236	11131	1w31	(10¹⁸²³⁶+179)/9	August 2007	Paul Bourdelais
103	16922	11101	1w01	(10¹⁶⁹²²-91)/9	August 2007	Paul Bourdelais
107	16401	11191	1w91	(10¹⁶⁴⁰¹+719)/9	August 2007	Paul Bourdelais
125	15189	11191	1w91	(10¹⁵¹⁸⁹+719)/9	August 2007	Paul Bourdelais
130	14724	11121	1w21	(10¹⁴⁷²⁴+89)/9	May 2004	Donovan Johnson
135	14549	11171	1w71	(10¹⁴⁵⁴⁹+539)/9	August 2007	Paul Bourdelais
153	13290	11121	1w21	(10¹³²⁹⁰+89)/9	May 2004	Donovan Johnson
156	13224	11151	1w51	(10¹³²²⁴+359)/9	August 2007	Paul Bourdelais
157	13222	11181	1w81	(10¹³²²²+629)/9	August 2007	Paul Bourdelais
161	13151	11161	1w61	(10¹³¹⁵¹+449)/9	August 2007	Paul Bourdelais
167	12685	11171	1w71	(10¹²⁶⁸⁵+539)/9	August 2007	Paul Bourdelais
169	12626	11161	1w61	(10¹²⁶²⁶+449)/9	August 2007	Paul Bourdelais
190	11254	11151	1w51	(10¹¹²⁵⁴+359)/9	August 2007	Paul Bourdelais
206	10555	11171	1w71	(10¹⁰⁵⁵⁵+539)/9	August 2007	Paul Bourdelais

Unprovable quasi-repdigit PRPs
	digits	flabel	wlabel	expression	when	who
224	20818	11193	1w93	(10²⁰⁸¹⁸+737)/9	August 2007	Paul Bourdelais
247	19920	11143	1w43	(10¹⁹⁹²⁰+287)/9	October 2007	Paul Bourdelais
283	19530	11157	1w57	(10¹⁹⁵³⁰+413)/9	October 2007	Paul Bourdelais
291	19380	11103	1w03	(10¹⁹³⁸⁰-73)/9	October 2007	Paul Bourdelais
446	17314	11129	1w29	(10¹⁷³¹⁴+161)/9	August 2007	Paul Bourdelais
508	16749	11163	1w63	(10¹⁶⁷⁴⁹+467)/9	August 2007	Paul Bourdelais
535	16471		1w99	(10¹⁶⁴⁷¹+791)/9	August 2007	Paul Bourdelais
627	15584	11147	1w47	(10¹⁵⁵⁸⁴+323)/9	August 2007	Paul Bourdelais
680	15060	11127	1w27	(10¹⁵⁰⁶⁰+143)/9	August 2007	Paul Bourdelais
738	14440	11129	1w29	(10¹⁴⁴⁴⁰+161)/9	August 2007	Paul Bourdelais
764	14181	11127	1w27	(10¹⁴¹⁸¹+143)/9	August 2007	Paul Bourdelais
786	14004	11179	1w79	(10¹⁴⁰⁰⁴+611)/9	August 2007	Paul Bourdelais
789	13963	11193	1w93	(10¹³⁹⁶³+737)/9	August 2007	Paul Bourdelais
932	12549	11179	1w79	(10¹²⁵⁴⁹+611)/9	August 2007	Paul Bourdelais
981	12107	11147	1w47	(10¹²¹⁰⁷+323)/9	August 2007	Paul Bourdelais
1058	11582	11197	1w97	(10¹¹⁵⁸²+773)/9	August 2007	Paul Bourdelais
1119	10981	11127	1w27	(10¹⁰⁹⁸¹+143)/9	August 2007	Paul Bourdelais
1135	10894	11103	1w03	(10¹⁰⁸⁹⁴-73)/9	August 2007	Paul Bourdelais
1186	10591	11189	1w89	(10¹⁰⁵⁹¹+701)/9	August 2007	Paul Bourdelais
1192	10550	11147	1w47	(10¹⁰⁵⁵⁰+323)/9	August 2007	Paul Bourdelais
1226	10271	11149	1w49	(10¹⁰²⁷¹+341)/9	August 2007	Paul Bourdelais

Unprovable near-repdigit-related PRPs (except ru/nr/pd/qr)
	digits	flabel	wlabel	expression	when	who
12	24676		226w9	(68·10²⁴⁶⁷⁴+7)/3	October 2010	Ray Chandler
13	24589	53327	53w27	(16·10²⁴⁵⁸⁸-19)/3	October 2010	Ray Chandler
2076	10979	10063	10w63	10¹⁰⁹⁷⁸+63	April 2010	Patrick De Geest

December 23, 2010

Giovanni Di Maria's website: http://www.elektrosoft.it/matematica/repunit/repunit.htm

December 22, 2010

Maksym Voznyy proved 1 near-repdigit prime and 1 near-repdigit-related prime by Primo 3.0.9, PFGW 3.4.4, CHG.GP and chgcertd.gp.

Proven near-repdigit primes
	digits	flabel	wlabel	expression	when	who
333	2874	21111	21w	(19·10²⁸⁷³-1)/9	December 22, 2010	Maksym Voznyy

Proven near-repdigit-related primes (except ru/nr/pd/qr)
	digits	flabel	wlabel	expression	when	who
147	5437	53327	53w27	(16·10⁵⁴³⁶-19)/3	December 22, 2010	Maksym Voznyy

December 21, 2010

Maksym Voznyy proved 1 near-repdigit prime, 2 quasi-repdigit primes and 1 near-repdigit-related prime by Primo 3.0.9, PFGW 3.4.4, CHG.GP and chgcertd.gp.

Proven near-repdigit primes
	digits	flabel	wlabel	expression	when	who
334	2811	21111	21w	(19·10²⁸¹⁰-1)/9	December 21, 2010	Maksym Voznyy

Proven quasi-repdigit primes
	digits	flabel	wlabel	expression	when	who
160	4881	11109	1w09	(10⁴⁸⁸¹-19)/9	December 21, 2010	Maksym Voznyy
170	4229	48883	48w3	(44·10⁴²²⁸-53)/9	December 21, 2010	Maksym Voznyy

Proven near-repdigit-related primes (except ru/nr/pd/qr)
	digits	flabel	wlabel	expression	when	who
153	5089	71103	71w03	(64·10⁵⁰⁸⁸-73)/9	December 21, 2010	Maksym Voznyy

December 20, 2010

Maksym Voznyy proved 2 near-repdigit primes, 1 quasi-repdigit prime and 2 near-repdigit-related primes by Primo 3.0.9, PFGW 3.4.4, CHG.GP and chgcertd.gp.

Proven near-repdigit primes
	digits	flabel	wlabel	expression	when	who
343	2744	55559	5w9	(5·10²⁷⁴⁴+31)/9	December 20, 2010	Maksym Voznyy
345	2720	77773	7w3	(7·10²⁷²⁰-43)/9	December 20, 2010	Maksym Voznyy

Proven quasi-repdigit primes
	digits	flabel	wlabel	expression	when	who
185	3757	11109	1w09	(10³⁷⁵⁷-19)/9	December 20, 2010	Maksym Voznyy

Proven near-repdigit-related primes (except ru/nr/pd/qr)
	digits	flabel	wlabel	expression	when	who
177	3758	57721	57w21	(52·10³⁷⁵⁷-511)/9	December 20, 2010	Maksym Voznyy
184	3593	57721	57w21	(52·10³⁵⁹²-511)/9	December 20, 2010	Maksym Voznyy

Factorizations of 66...661 have been extended up to n=250. Composite numbers that appeared newly got through ECM 118 times at level 35. Most unknown factors are supposed to be greater than 10³⁰.

December 19, 2010

David Broadhurst found the largest known near-repdigit prime. Congratulations!

Proven near-repdigit primes
	digits	flabel	wlabel	expression	when	who
1	364522	89999	89w	9·10³⁶⁴⁵²¹-1	December 19, 2010	David Broadhurst

Maksym Voznyy proved 1 near-repdigit prime by Primo 3.0.9.

Proven near-repdigit primes
	digits	flabel	wlabel	expression	when	who
342	2691	88887	8w7	(8·10²⁶⁹¹-17)/9	December 19, 2010	Maksym Voznyy

December 18, 2010

Maksym Voznyy proved 1 near-repdigit prime by Primo 3.0.9.

Proven near-repdigit primes
	digits	flabel	wlabel	expression	when	who
348	2586	33337	3w7	(10²⁵⁸⁶+11)/3	December 18, 2010	Maksym Voznyy

December 17, 2010

Maksym Voznyy proved 2 near-repdigit primes by Primo 3.0.9.

Proven near-repdigit primes
	digits	flabel	wlabel	expression	when	who
364	2380	73333	73w	(22·10²³⁷⁹-1)/3	December 17, 2010	Maksym Voznyy
366	2356	57777	57w	(52·10²³⁵⁵-7)/9	December 17, 2010	Maksym Voznyy

Maksym Voznyy proved 1 near-repdigit-palindrome prime by Primo 3.0.9.

Proven near-repdigit-palindrome primes
	digits	flabel	wlabel	expression	when	who
23	3089	11411	1w41w	(10³⁰⁸⁹+27·10¹⁵⁴⁴-1)/9	December 17, 2010	Maksym Voznyy

Ray Chander found 3 near-repdigit primes, 9 quasi-repdigit primes, 2 near-repdigit PRPs, 19 quasi-repdigit PRPs and 85 near-repdigit-related PRPs (except ru/nr/pd/qr) by srsieve and PFGW.

Proven near-repdigit primes
	digits	wlabel	expression	when	who
115	22592	999999959w	99999996·10²²⁵⁸⁴-1	December 17, 2010	Ray Chandler
119	21761	999999929w	99999993·10²¹⁷⁵³-1	December 17, 2010	Ray Chandler
127	20112	999999949w	99999995·10²⁰¹⁰⁴-1	December 17, 2010	Ray Chandler

Proven quasi-repdigit primes
	digits	flabel	wlabel	expression	when	who
14	22805	32999	329w	33·10²²⁸⁰³-1	December 17, 2010	Ray Chandler
15	22745	25999	259w	26·10²²⁷⁴³-1	December 17, 2010	Ray Chandler
16	22221	37999	379w	38·10²²²¹⁹-1	December 17, 2010	Ray Chandler
17	22024	50999	509w	51·10²²⁰²²-1	December 17, 2010	Ray Chandler
18	21608	83999	839w	84·10²¹⁶⁰⁶-1	December 17, 2010	Ray Chandler
19	21515	13999	139w	14·10²¹⁵¹³-1	December 17, 2010	Ray Chandler
20	21034	37999	379w	38·10²¹⁰³²-1	December 17, 2010	Ray Chandler
22	20570	85999	859w	86·10²⁰⁵⁶⁸-1	December 17, 2010	Ray Chandler
25	20246	41999	419w	42·10²⁰²⁴⁴-1	December 17, 2010	Ray Chandler

December 16, 2010

Maksym Voznyy proved 1 near-repdigit prime, 1 quasi-repdigit prime and 5 near-repdigit-related primes (except ru/nr/pd/qr) by Promo 3.0.9.

Proven near-repdigit primes
	digits	flabel	wlabel	expression	when	who
359	1949	11101	1w01	(10¹⁹⁴⁹-91)/9	December 16, 2010	Maksym Voznyy

Proven quasi-repdigit primes
	digits	flabel	wlabel	expression	when	who
327	2069	49919	49w19	5·10²⁰⁶⁸-81	December 16, 2010	Maksym Voznyy

Proven near-repdigit-related primes (except ru/nr/pd/qr)
	digits	flabel	wlabel	expression	when	who
210	3392	49951	49w51	5·10³³⁹¹-49	December 16, 2010	Maksym Voznyy
286	2061	10031	10w31	10²⁰⁶⁰+31	December 16, 2010	Maksym Voznyy
291	2038	83329	83w29	(25·10²⁰³⁷-13)/3	December 16, 2010	Maksym Voznyy
294	2001	26657	26w57	(8·10²⁰⁰⁰-29)/3	December 16, 2010	Maksym Voznyy
296	1979	38851	38w51	(35·10¹⁹⁷⁸-341)/9	December 16, 2010	Maksym Voznyy

December 15, 2010

Maksym Voznyy proved 3 quasi-repdigit primes and 4 near-repdigit-related primes (except ru/nr/pd/qr) by Primo 3.0.9.

Proven quasi-repdigit primes
	digits	flabel	wlabel	expression	when	who
356	1935	99961	9w61	10¹⁹³⁵-39	December 15, 2010	Maksym Voznyy
357	1932	99983	9w83	10¹⁹³²-17	December 15, 2010	Maksym Voznyy
361	1916	44417	4w17	(4·10¹⁹¹⁶-247)/9	December 15, 2010	Maksym Voznyy

Proven near-repdigit-related primes (except ru/nr/pd/qr)
	digits	flabel	wlabel	expression	when	who
297	1948	37739	37w39	(34·10¹⁹⁴⁷-349)/9	December 15, 2010	Maksym Voznyy
300	1931	13327	13w27	(4·10¹⁹³⁰-19)/3	December 15, 2010	Maksym Voznyy
301	1924	26689	26w89	(8·10¹⁹²³+67)/3	December 15, 2010	Maksym Voznyy
302	1923	63307	63w07	(19·10¹⁹²²-79)/3	December 15, 2010	Maksym Voznyy

Gary Barnes's 61 near-repdigit primes were imported from his page.

Proven near-repdigit primes
	digits	flabel	wlabel	expression	when	who
28	98740	95999	959w	96·10⁹⁸⁷³⁸-1	November 2010	Gary Barnes
29	95299		9919w	992·10⁹⁵²⁹⁶-1	November 2010	Gary Barnes
35	80772		9999919w	999992·10⁸⁰⁷⁶⁶-1	November 2010	Gary Barnes
36	80730		9989w	999·10⁸⁰⁷²⁷-1	November 2010	Gary Barnes
38	78719		999919w	99992·10⁷⁸⁷¹⁴-1	November 2010	Gary Barnes
39	74980		9929w	993·10⁷⁴⁹⁷⁷-1	November 2010	Gary Barnes
42	72631		99919w	9992·10⁷²⁶²⁷-1	November 2010	Gary Barnes
45	67870		9979w	998·10⁶⁷⁸⁶⁷-1	November 2010	Gary Barnes
46	67770		9999979w	999998·10⁶⁷⁷⁶⁴-1	November 2010	Gary Barnes
47	66851		9929w	993·10⁶⁶⁸⁴⁸-1	November 2010	Gary Barnes
48	66686		9989w	999·10⁶⁶⁶⁸³-1	November 2010	Gary Barnes
50	63337		9999989w	999999·10⁶³³³¹-1	November 2010	Gary Barnes
51	62469		99949w	9995·10⁶²⁴⁶⁵-1	November 2010	Gary Barnes
53	61254		99959w	9996·10⁶¹²⁵⁰-1	November 2010	Gary Barnes
54	59475		9979w	998·10⁵⁹⁴⁷²-1	November 2010	Gary Barnes
56	55540		9999919w	999992·10⁵⁵⁵³⁴-1	November 2010	Gary Barnes
58	54593		9999919w	999992·10⁵⁴⁵⁸⁷-1	November 2010	Gary Barnes
59	54548		99919w	9992·10⁵⁴⁵⁴⁴-1	November 2010	Gary Barnes
60	54464		9999949w	999995·10⁵⁴⁴⁵⁸-1	November 2010	Gary Barnes
61	54065		999949w	99995·10⁵⁴⁰⁶⁰-1	November 2010	Gary Barnes
62	53717		9989w	999·10⁵³⁷¹⁴-1	November 2010	Gary Barnes
63	53583		9999949w	999995·10⁵³⁵⁷⁷-1	November 2010	Gary Barnes
66	50217		9999929w	999993·10⁵⁰²¹¹-1	November 2010	Gary Barnes
67	50103		9999959w	999996·10⁵⁰⁰⁹⁷-1	November 2010	Gary Barnes
71	48894		9949w	995·10⁴⁸⁸⁹¹-1	November 2010	Gary Barnes
74	46849		9999929w	999993·10⁴⁶⁸⁴³-1	November 2010	Gary Barnes
76	45820		9999959w	999996·10⁴⁵⁸¹⁴-1	November 2010	Gary Barnes
78	44868		9919w	992·10⁴⁴⁸⁶⁵-1	November 2010	Gary Barnes
79	44278		99959w	9996·10⁴⁴²⁷⁴-1	November 2010	Gary Barnes
80	42636		9989w	999·10⁴²⁶³³-1	November 2010	Gary Barnes
82	41686		999919w	99992·10⁴¹⁶⁸¹-1	November 2010	Gary Barnes
83	41497		999959w	99996·10⁴¹⁴⁹²-1	November 2010	Gary Barnes
85	40227		99959w	9996·10⁴⁰²²³-1	November 2010	Gary Barnes
86	38403		9959w	996·10³⁸⁴⁰⁰-1	November 2010	Gary Barnes
89	35899		999979w	99998·10³⁵⁸⁹⁴-1	November 2010	Gary Barnes
90	35881		9999989w	999999·10³⁵⁸⁷⁵-1	November 2010	Gary Barnes
91	35215		9949w	995·10³⁵²¹²-1	November 2010	Gary Barnes
93	34923		9999929w	999993·10³⁴⁹¹⁷-1	November 2010	Gary Barnes
95	33090		999959w	99996·10³³⁰⁸⁵-1	November 2010	Gary Barnes
98	32192		9949w	995·10³²¹⁸⁹-1	November 2010	Gary Barnes
101	30848		9999949w	999995·10³⁰⁸⁴²-1	November 2010	Gary Barnes
103	29005		9919w	992·10²⁹⁰⁰²-1	October 2010	Gary Barnes
104	28861		9999959w	999996·10²⁸⁸⁵⁵-1	October 2010	Gary Barnes
105	28360		9929w	993·10²⁸³⁵⁷-1	October 2010	Gary Barnes
106	27482		999929w	99993·10²⁷⁴⁷⁷-1	October 2010	Gary Barnes
107	26781		9919w	992·10²⁶⁷⁷⁸-1	October 2010	Gary Barnes
110	25982		9989w	999·10²⁵⁹⁷⁹-1	October 2010	Gary Barnes
111	25821		9929w	993·10²⁵⁸¹⁸-1	October 2010	Gary Barnes
112	25644		999949w	99995·10²⁵⁶³⁹-1	October 2010	Gary Barnes
113	25058		9999919w	999992·10²⁵⁰⁵²-1	October 2010	Gary Barnes
114	24692		999989w	99999·10²⁴⁶⁸⁷-1	October 2010	Gary Barnes
115	22482		999989w	99999·10²²⁴⁷⁷-1	October 2010	Gary Barnes
116	22180		999989w	99999·10²²¹⁷⁵-1	October 2010	Gary Barnes
117	22014		9959w	996·10²²⁰¹¹-1	October 2010	Gary Barnes
118	21574		999949w	99995·10²¹⁵⁶⁹-1	October 2010	Gary Barnes
121	20614		9929w	993·10²⁰⁶¹¹-1	October 2010	Gary Barnes
122	20608		999989w	99999·10²⁰⁶⁰³-1	October 2010	Gary Barnes
123	20546		99949w	9995·10²⁰⁵⁴²-1	October 2010	Gary Barnes
124	20360		9919w	992·10²⁰³⁵⁷-1	October 2010	Gary Barnes
558	767		999989w	99999·10⁷⁶²-1	October 2010	Gary Barnes
888	202		999919w	99992·10¹⁹⁷-1	October 2010	Gary Barnes

Serge Batalov proved the second largest known plateau-and-depression prime and a quasi-repdigit prime by CHG.

Proven plateau and depression primes
	digits	flabel	wlabel	expression	when	who
2	5209	37773	37w3	(34·10⁵²⁰⁸-43)/9	December 15, 2010	Serge Batalov

Proven quasi-repdigit primes
	digits	flabel	wlabel	expression	when	who
140	5133	68883	68w3	(62·10⁵¹³²-53)/9	December 15, 2010	Serge Batalov

December 14, 2010

Erik Branger searched near-repdigit prime number of the form 22...221;(2·10ⁿ-11)/9, up to n=100000. No additional (probable) prime number was found.

Stefano D'Urso found the seventh largest known near-repdigit prime number.

Proven near-repdigit primes
	digits	flabel	wlabel	expression	when	who
7	225620	95999	959w	96·10²²⁵⁶¹⁸-1	December 14, 2010	Stefano D'Urso

Maksym Voznyy proved 3 quasi-repdigit primes and 10 near-repdigit-related primes by Primo.

Proven quasi-repdigit primes
	digits	flabel	wlabel	expression	when	who
383	1819	55519	5w19	(5·10¹⁸¹⁹-329)/9	December 14, 2010	Maksym Voznyy
385	1817	37339	373w9	(112·10¹⁸¹⁵+17)/3	December 14, 2010	Maksym Voznyy
387	1811	93323	93w23	(28·10¹⁸¹⁰-31)/3	December 14, 2010	Maksym Voznyy

Proven near-repdigit-related primes (except ru/nr/pd/qr)
	digits	flabel	wlabel	expression	when	who
301	1912	16657	16w57	(5·10¹⁹¹¹-29)/3	December 14, 2010	Maksym Voznyy
305	1888	38851	38w51	(35·10¹⁸⁸⁷-341)/9	December 14, 2010	Maksym Voznyy
306	1884	62217	62w17	(56·10¹⁸⁸³-47)/9	December 14, 2010	Maksym Voznyy
308	1877		23w11	(7·10¹⁸⁷⁶-67)/3	December 14, 2010	Maksym Voznyy
311	1846	64497	64w97	(58·10¹⁸⁴⁵+473)/9	December 14, 2010	Maksym Voznyy
313	1841		83w11	(25·10¹⁸⁴⁰-67)/3	December 14, 2010	Maksym Voznyy
314	1835	27751	27w51	(25·10¹⁸³⁴-241)/9	December 14, 2010	Maksym Voznyy
315	1822	75549	75w49	(68·10¹⁸²¹-59)/9	December 14, 2010	Maksym Voznyy
316	1812	58829	58w29	(53·10¹⁸¹¹-539)/9	December 14, 2010	Maksym Voznyy
318	1805	35513	35w13	(32·10¹⁸⁰⁴-383)/9	December 14, 2010	Maksym Voznyy

December 13, 2010

Ray Chandler found the fourth largest known plateau-and-depression PRP by srsieve and PFGW.

Unprovable plateau and depression PRPs
	digits	flabel	wlabel	expression	when	who
4	80163	37773	37w3	(34·10⁸⁰¹⁶²-43)/9	December 13, 2010	Ray Chandler

Factorizations of 22...223 have been extended up to n=250. Composite numbers that appeared newly got through ECM 118 times at level 35. Most unknown factors are supposed to be greater than 10³⁰.

Ray Chandler found 3 near-repdigit prime numbers, 6 quasi-repdigit prime numbers, 2 near-repdigit PRPs, 53 quasi-repdigit PRPs and 165 near-repdigit-related PRPs by srsieve, PFGW. The upper limit of searched near-repdigit-related prime numbers reached to n=20000.

Proven near-repdigit primes
	digits	wlabel	expression	when	who
65	19614	99999959w	9999996·10¹⁹⁶⁰⁷-1	December 12, 2010	Ray Chandler
66	19560	999999979w	99999998·10¹⁹⁵⁵²-1	December 12, 2010	Ray Chandler
67	19256	999999959w	99999996·10¹⁹²⁴⁸-1	December 12, 2010	Ray Chandler

Proven quasi-repdigit primes
	digits	flabel	wlabel	expression	when	who
17	19773	23999	239w	24·10¹⁹⁷⁷¹-1	December 12, 2010	Ray Chandler
18	19687		889w	89·10¹⁹⁶⁸⁵-1	December 12, 2010	Ray Chandler
19	19447	38999	389w	39·10¹⁹⁴⁴⁵-1	December 12, 2010	Ray Chandler
20	19438	32999	329w	33·10¹⁹⁴³⁶-1	December 12, 2010	Ray Chandler
21	19339	47999	479w	48·10¹⁹³³⁷-1	December 12, 2010	Ray Chandler
22	19247		779w	78·10¹⁹²⁴⁵-1	December 12, 2010	Ray Chandler

Unprovable near-repdigit PRPs
	digits	flabel	wlabel	expression	when	who
61	19908	77757	7w57	(7·10¹⁹⁹⁰⁸-187)/9	December 12, 2010	Ray Chandler
64	19524	77737	7w37	(7·10¹⁹⁵²⁴-367)/9	December 12, 2010	Ray Chandler

Maksym Voznyy proved the primality of 2 quasi-repdigit prime and 9 near-repdigit-related primes by Primo.

Proven quasi-repdigit primes
	digits	flabel	wlabel	expression	when	who
215	2805	46663	46w3	(14·10²⁸⁰⁴-11)/3	December 12, 2010	Maksym Voznyy
395	1741	17757	17w57	(16·10¹⁷⁴⁰-187)/9	December 12, 2010	Maksym Voznyy

Proven near-repdigit-related primes (except ru/nr/pd/qr)
	digits	flabel	wlabel	expression	when	who
230	2873	58831	58w31	(53·10²⁸⁷²-521)/9	December 12, 2010	Maksym Voznyy
234	2777		56w11	(17·10²⁷⁷⁶-167)/3	December 12, 2010	Maksym Voznyy
310	1799	75547	75w47	(68·10¹⁷⁹⁸-77)/9	December 12, 2010	Maksym Voznyy
317	1773	69973	69w73	7·10¹⁷⁷²-27	December 12, 2010	Maksym Voznyy
321	1750	14429	14w29	(13·10¹⁷⁴⁹-139)/9	December 12, 2010	Maksym Voznyy
323	1745		26w33	(8·10¹⁷⁴⁴-101)/3	December 12, 2010	Maksym Voznyy
324	1737		53w99	(16·10¹⁷³⁶+197)/3	December 12, 2010	Maksym Voznyy
328	1717	21129	21w29	(19·10¹⁷¹⁶+161)/9	December 12, 2010	Maksym Voznyy
330	1708	71109	71w09	(64·10¹⁷⁰⁷-19)/9	December 12, 2010	Maksym Voznyy

December 11, 2010

Serge Batalov proved the primality of a 7412-digit near-repdigit-realted prime by CHG.

Proven near-repdigit-related primes (except ru/nr/pd/qr)
	digits	flabel	wlabel	expression	when	who
126	7412	18869	18w69	(17·10⁷⁴¹¹-179)/9	December 11, 2010	Serge Batalov

Serge Batalov proved the primality of a 17877-digit near-repdigit-related prime by Primo, PFGW, CHG.gp and chgcertd.gp. See certifications for details.

Proven near-repdigit-related primes (except ru/nr/pd/qr)
	digits	flabel	wlabel	expression	when	who
39	17877	42219	42w19	(38·10¹⁷⁸⁷⁶-29)/9	December 11, 2010	Serge Batalov

December 10, 2010

Stefano D'Urso found 1 near-repdigit prime.

Proven near-repdigit primes
	digits	flabel	wlabel	expression	when	who
9	211985	95999	959w	96·10²¹¹⁹⁸³-1	December 10, 2010	Stefano D'Urso

Maksym Voznyy proved the primality of 1 quasi-repdigit prime and 3 near-repdigit-related primes by Primo.

Proven quasi-repdigit primes
	digits	flabel	wlabel	expression	when	who
393	1743		4w99	(4·10¹⁷⁴³+491)/9	December 10, 2010	Maksym Voznyy

Proven near-repdigit-related primes (except ru/nr/pd/qr)
	digits	flabel	wlabel	expression	when	who
313	1765	36653	36w53	(11·10¹⁷⁶⁴-41)/3	December 10, 2010	Maksym Voznyy
317	1733		10w99	10¹⁷³²+99	December 10, 2010	Maksym Voznyy
319	1710	86659	86w59	(26·10¹⁷⁰⁹-23)/3	December 10, 2010	Maksym Voznyy

December 9, 2010

Maksym Voznyy proved the primality of 4 quasi-repdigit primes and 10 near-repdigit-related primes by Primo.

Proven quasi-repdigit primes
	digits	flabel	wlabel	expression	when	who
409	1679	55501	5w01	(5·10¹⁶⁷⁹-491)/9	December 9, 2010	Maksym Voznyy
413	1668	71101	71w01	(64·10¹⁶⁶⁷-91)/9	December 9, 2010	Maksym Voznyy
422	1620	22251	2w51	(2·10¹⁶²⁰+259)/9	December 9, 2010	Maksym Voznyy
423	1620	11169	1w69	(10¹⁶²⁰+521)/9	December 9, 2010	Maksym Voznyy

Proven near-repdigit-related primes (except ru/nr/pd/qr)
	digits	flabel	wlabel	expression	when	who
236	2630	18869	18w69	(17·10²⁶²⁹-179)/9	December 9, 2010	Maksym Voznyy
237	2619	62217	62w17	(56·10²⁶¹⁸-47)/9	December 9, 2010	Maksym Voznyy
264	2277	48839	48w39	(44·10²²⁷⁶-449)/9	December 9, 2010	Maksym Voznyy
317	1702	90091	90w91	9·10¹⁷⁰¹+91	December 9, 2010	Maksym Voznyy
318	1697	10063	10w63	10¹⁶⁹⁶+63	December 9, 2010	Maksym Voznyy
319	1690	43369	43w69	(13·10¹⁶⁸⁹+107)/3	December 9, 2010	Maksym Voznyy
320	1688	27751	27w51	(25·10¹⁶⁸⁷-241)/9	December 9, 2010	Maksym Voznyy
324	1668	16601	16w01	(5·10¹⁶⁶⁷-197)/3	December 9, 2010	Maksym Voznyy
328	1639	83329	83w29	(25·10¹⁶³⁸-13)/3	December 9, 2010	Maksym Voznyy
518	1019	35561	35w61	(32·10¹⁰¹⁸+49)/9	December 9, 2010	Maksym Voznyy

December 8, 2010

Bob Price found 1 prime and 3 PRPs.

Proven near-repdigit-related primes (except ru/nr/pd/qr)
	digits	flabel	wlabel	expression	when	who
293	1913	10079	10w79	10¹⁹¹²+79	December 8, 2010	Bob Price

Unprovable near-repdigit-related PRPs (except ru/nr/pd/qr)
	digits	flabel	wlabel	expression	when	who
13	29059	10079	10w79	10²⁹⁰⁵⁸+79	December 8, 2010	Bob Price
16	26990	10037	10w37	10²⁶⁹⁸⁹+37	December 8, 2010	Bob Price
24	23733	10079	10w79	10²³⁷³²+79	December 8, 2010	Bob Price

Maksym Voznyy proved the primality of a quasi-repdigit prime and a near-repdigit-related prime by Primo.

Proven quasi-repdigit primes
	digits	flabel	wlabel	expression	when	who
307	2116	97767	97w67	(88·10²¹¹⁵-97)/9	December 8, 2010	Maksym Voznyy

Proven near-repdigit-related primes (except ru/nr/pd/qr)
	digits	flabel	wlabel	expression	when	who
264	2225	67709	67w09	(61·10²²²⁴-619)/9	December 8, 2010	Maksym Voznyy

Serge Batalov proved the primality of a quasi-repdigit prime number 11103_3258 = (10³²⁵⁸-73)/9 by Primo and PFGW.
11103_3258+1 = (10³²⁵⁸-73)/9+1 = 64·(5·10⁵⁴²+1)/3·(5·10⁵⁴²-1)·(25·10¹⁰⁸⁴-5·10⁵⁴²+1)/3·(25·10¹⁰⁸⁴+5·10⁵⁴²+1) = 64·16667_542·49999_542·83w16w7_542·250w50w1_542.
83w16w7_542 = 7·109·563041·869047141·147372142447·p1057.
p1057 was proved by ECPP and 11103_3258 was proved by N-1/N+1/BLS with factored part 33.82%.

Proven quasi-repdigit primes
	digits	flabel	wlabel	expression	when	who
187	3258	11103	1w03	(10³²⁵⁸-73)/9	December 8, 2010	Serge Batalov

December 7, 2010

Maksym Voznyy proved 3 primes by Primo 3.0.9.

Proven near-repdigit primes
	digits	flabel	wlabel	expression	when	who
241	2894	99989	9w89	10²⁸⁹⁴-11	December 7, 2010	Maksym Voznyy

Proven near-repdigit-related primes (except ru/nr/pd/qr)
	digits	flabel	wlabel	expression	when	who
225	2979	15539	15w39	(14·10²⁹⁷⁸-149)/9	December 7, 2010	Maksym Voznyy
311	1731		23w11	(7·10¹⁷³⁰-67)/3	December 7, 2010	Maksym Voznyy

December 5, 2010

Stefano D'Urso found 4 near-repdigit primes.

Proven near-repdigit primes
	digits	flabel	wlabel	expression	when	who
10	183454	95999	959w	96·10¹⁸³⁴⁵²-1	December 5, 2010	Stefano D'Urso
14	140328	95999	959w	96·10¹⁴⁰³²⁶-1	December 5, 2010	Stefano D'Urso
16	130567	95999	959w	96·10¹³⁰⁵⁶⁵-1	December 5, 2010	Stefano D'Urso
19	118951	95999	959w	96·10¹¹⁸⁹⁴⁹-1	December 5, 2010	Stefano D'Urso

Maksym Voznyy proved 3 primes by Primo 3.0.9.

Proven quasi-repdigit primes
	digits	flabel	wlabel	expression	when	who
214	2789	93323	93w23	(28·10²⁷⁸⁸-31)/3	December 5, 2010	Maksym Voznyy

Proven near-repdigit-related primes (except ru/nr/pd/qr)
	digits	flabel	wlabel	expression	when	who
250	2415		34w11	(31·10²⁴¹⁴-301)/9	December 5, 2010	Maksym Voznyy
267	2153	80081	80w81	8·10²¹⁵²+81	December 5, 2010	Maksym Voznyy

Ray Chandler found 5 primes and 231 PRPs by PFGW.

Proven near-repdigit primes
	digits	wlabel	expression	when	who
61	18841	999979w	99998·10¹⁸⁸³⁶-1	December 5, 2010	Ray Chandler
63	18604	9999989w	999999·10¹⁸⁵⁹⁸-1	December 5, 2010	Ray Chandler
64	18212	99959w	9996·10¹⁸²⁰⁸-1	December 5, 2010	Ray Chandler

Proven quasi-repdigit primes
	digits	flabel	wlabel	expression	when	who
17	18820	74999	749w	75·10¹⁸⁸¹⁸-1	December 5, 2010	Ray Chandler
18	18025	56999	569w	57·10¹⁸⁰²³-1	December 5, 2010	Ray Chandler

Unprovable near-repdigit PRPs
	digits	flabel	wlabel	expression	when	who
66	18580	99949	9w49	10¹⁸⁵⁸⁰-51	December 5, 2010	Ray Chandler
70	18236	11131	1w31	(10¹⁸²³⁶+179)/9	December 5, 2010	Ray Chandler
71	18211	99929	9w29	10¹⁸²¹¹-71	December 5, 2010	Ray Chandler
74	18134	33383	3w83	(10¹⁸¹³⁴+149)/3	December 5, 2010	Ray Chandler

Unprovable near-repdigit-related PRPs (except ru/nr/pd/qr)
	digits	flabel	wlabel	expression	when	who
42	18987	42201	42w01	(38·10¹⁸⁹⁸⁶-191)/9	December 5, 2010	Ray Chandler
43	18987	30053	30w53	3·10¹⁸⁹⁸⁶+53	December 5, 2010	Ray Chandler
44	18985	50087	50w87	5·10¹⁸⁹⁸⁴+87	December 5, 2010	Ray Chandler
45	18982		35w11	(32·10¹⁸⁹⁸¹-401)/9	December 5, 2010	Ray Chandler
46	18979	14451	14w51	(13·10¹⁸⁹⁷⁸+59)/9	December 5, 2010	Ray Chandler
47	18978	15527	15w27	(14·10¹⁸⁹⁷⁷-257)/9	December 5, 2010	Ray Chandler
48	18977	31153	31w53	(28·10¹⁸⁹⁷⁶+377)/9	December 5, 2010	Ray Chandler
49	18974		886w7	(266·10¹⁸⁹⁷²+1)/3	December 5, 2010	Ray Chandler
50	18973	92203	92w03	(83·10¹⁸⁹⁷²-173)/9	December 5, 2010	Ray Chandler
51	18948	84489	84w89	(76·10¹⁸⁹⁴⁷+401)/9	December 5, 2010	Ray Chandler
52	18942	56641	56w41	(17·10¹⁸⁹⁴¹-77)/3	December 5, 2010	Ray Chandler
53	18935	32251	32w51	(29·10¹⁸⁹³⁴+259)/9	December 5, 2010	Ray Chandler
54	18924	58857	58w57	(53·10¹⁸⁹²³-287)/9	December 5, 2010	Ray Chandler
55	18923	61153	61w53	(55·10¹⁸⁹²²+377)/9	December 5, 2010	Ray Chandler
56	18897	57709	57w09	(52·10¹⁸⁸⁹⁶-619)/9	December 5, 2010	Ray Chandler
57	18888	78897	78w97	(71·10¹⁸⁸⁸⁷+73)/9	December 5, 2010	Ray Chandler
58	18885	78827	78w27	(71·10¹⁸⁸⁸⁴-557)/9	December 5, 2010	Ray Chandler
59	18876	82293	82w93	(74·10¹⁸⁸⁷⁵+637)/9	December 5, 2010	Ray Chandler
60	18865	61137	61w37	(55·10¹⁸⁸⁶⁴+233)/9	December 5, 2010	Ray Chandler
61	18859	81107	81w07	(73·10¹⁸⁸⁵⁸-37)/9	December 5, 2010	Ray Chandler
62	18858	48821	48w21	(44·10¹⁸⁸⁵⁷-611)/9	December 5, 2010	Ray Chandler
63	18857	27721	27w21	(25·10¹⁸⁸⁵⁶-511)/9	December 5, 2010	Ray Chandler
64	18845	38879	38w79	(35·10¹⁸⁸⁴⁴-89)/9	December 5, 2010	Ray Chandler
65	18844	20069	20w69	2·10¹⁸⁸⁴³+69	December 5, 2010	Ray Chandler
66	18838	18817	18w17	(17·10¹⁸⁸³⁷-647)/9	December 5, 2010	Ray Chandler
67	18835		221w3	(199·10¹⁸⁸³³+17)/9	December 5, 2010	Ray Chandler
68	18829	93347	93w47	(28·10¹⁸⁸²⁸+41)/3	December 5, 2010	Ray Chandler
69	18829		89w11	9·10¹⁸⁸²⁸-89	December 5, 2010	Ray Chandler
70	18825	18839	18w39	(17·10¹⁸⁸²⁴-449)/9	December 5, 2010	Ray Chandler
71	18818	13319	13w19	(4·10¹⁸⁸¹⁷-43)/3	December 5, 2010	Ray Chandler
72	18810	47749	47w49	(43·10¹⁸⁸⁰⁹-259)/9	December 5, 2010	Ray Chandler
73	18809	95531	95w31	(86·10¹⁸⁸⁰⁸-221)/9	December 5, 2010	Ray Chandler
74	18808	42259	42w59	(38·10¹⁸⁸⁰⁷+331)/9	December 5, 2010	Ray Chandler
75	18791	38893	38w93	(35·10¹⁸⁷⁹⁰+37)/9	December 5, 2010	Ray Chandler
76	18786	53317	53w17	(16·10¹⁸⁷⁸⁵-49)/3	December 5, 2010	Ray Chandler
77	18785	20081	20w81	2·10¹⁸⁷⁸⁴+81	December 5, 2010	Ray Chandler
78	18781	13351	13w51	(4·10¹⁸⁷⁸⁰+53)/3	December 5, 2010	Ray Chandler
79	18778	70013	70w13	7·10¹⁸⁷⁷⁷+13	December 5, 2010	Ray Chandler
80	18777	52263	52w63	(47·10¹⁸⁷⁷⁶+367)/9	December 5, 2010	Ray Chandler
81	18771	45521	45w21	(41·10¹⁸⁷⁷⁰-311)/9	December 5, 2010	Ray Chandler
82	18769		991w7	(892·10¹⁸⁷⁶⁷+53)/9	December 5, 2010	Ray Chandler
83	18768		30w77	3·10¹⁸⁷⁶⁷+77	December 5, 2010	Ray Chandler
84	18762		990w7	99·10¹⁸⁷⁶⁰+7	December 5, 2010	Ray Chandler
85	18760	64469	64w69	(58·10¹⁸⁷⁵⁹+221)/9	December 5, 2010	Ray Chandler
86	18757	50081	50w81	5·10¹⁸⁷⁵⁶+81	December 5, 2010	Ray Chandler
87	18747	57709	57w09	(52·10¹⁸⁷⁴⁶-619)/9	December 5, 2010	Ray Chandler
88	18742	82257	82w57	(74·10¹⁸⁷⁴¹+313)/9	December 5, 2010	Ray Chandler
89	18721		227w3	(205·10¹⁸⁷¹⁹-43)/9	December 5, 2010	Ray Chandler
90	18715		50w77	5·10¹⁸⁷¹⁴+77	December 5, 2010	Ray Chandler
91	18712	73367	73w67	(22·10¹⁸⁷¹¹+101)/3	December 5, 2010	Ray Chandler
92	18701	31183	31w83	(28·10¹⁸⁷⁰⁰+647)/9	December 5, 2010	Ray Chandler
93	18687	16639	16w39	(5·10¹⁸⁶⁸⁶-83)/3	December 5, 2010	Ray Chandler
94	18685		47w11	(43·10¹⁸⁶⁸⁴-601)/9	December 5, 2010	Ray Chandler
95	18681	30013	30w13	3·10¹⁸⁶⁸⁰+13	December 5, 2010	Ray Chandler
96	18680	52273	52w73	(47·10¹⁸⁶⁷⁹+457)/9	December 5, 2010	Ray Chandler
97	18673		661w7	(595·10¹⁸⁶⁷¹+53)/9	December 5, 2010	Ray Chandler
98	18672	50057	50w57	5·10¹⁸⁶⁷¹+57	December 5, 2010	Ray Chandler
99	18662	43361	43w61	(13·10¹⁸⁶⁶¹+83)/3	December 5, 2010	Ray Chandler
100	18660	87753	87w53	(79·10¹⁸⁶⁵⁹-223)/9	December 5, 2010	Ray Chandler

December 4, 2010

Markus Tervooren searched prime numbers of the form 99...997 to 407197-digit but no additional PRP was found.

Maksym Voznyy proved 3 quasi-repdigit primes and 2 near-repdigit-related primes by Primo 3.0.9.

Proven quasi-repdigit primes
	digits	flabel	wlabel	expression	when	who
219	2696	22201	2w01	(2·10²⁶⁹⁶-191)/9	December 4, 2010	Maksym Voznyy
234	2589	49949	49w49	5·10²⁵⁸⁸-51	December 4, 2010	Maksym Voznyy
267	2303	49949	49w49	5·10²³⁰²-51	December 4, 2010	Maksym Voznyy

Proven near-repdigit-related primes (except ru/nr/pd/qr)
	digits	flabel	wlabel	expression	when	who
262	2211	16649	16w49	(5·10²²¹⁰-53)/3	December 4, 2010	Maksym Voznyy
272	2076	12209	12w09	(11·10²⁰⁷⁵-119)/9	December 4, 2010	Maksym Voznyy

December 1, 2010

Maksym Voznyy proved 8 near-repdigit-related primes by Primo 3.0.9.

Proven near-repdigit-related primes (except ru/nr/pd/qr)
	digits	flabel	wlabel	expression	when	who
312	1614	68819	68w19	(62·10¹⁶¹³-629)/9	December 1, 2010	Maksym Voznyy
313	1600	46621	46w21	(14·10¹⁵⁹⁹-137)/3	December 1, 2010	Maksym Voznyy
314	1599	36631	36w31	(11·10¹⁵⁹⁸-107)/3	December 1, 2010	Maksym Voznyy
316	1597	34473	34w73	(31·10¹⁵⁹⁶+257)/9	December 1, 2010	Maksym Voznyy
324	1589	83327	83w27	(25·10¹⁵⁸⁸-19)/3	December 1, 2010	Maksym Voznyy
327	1583	68821	68w21	(62·10¹⁵⁸²-611)/9	December 1, 2010	Maksym Voznyy
331	1571	53329	53w29	(16·10¹⁵⁷⁰-13)/3	December 1, 2010	Maksym Voznyy
332	1569	35513	35w13	(32·10¹⁵⁶⁸-383)/9	December 1, 2010	Maksym Voznyy

November 2010

November 30, 2010

Primality certifications page is available.

Maksym Voznyy proved 1 quasi-repdigit prime and 26 near-repdigit-related primes by Primo 3.0.9.

Proven quasi-repdigit primes
	digits	flabel	wlabel	expression	when	who
570	1302	71101	71w01	(64·10¹³⁰¹-91)/9	November 30, 2010	Maksym Voznyy

Proven near-repdigit-related primes (except ru/nr/pd/qr)
	digits	flabel	wlabel	expression	when	who
331	1546	62271	62w71	(56·10¹⁵⁴⁵+439)/9	November 30, 2010	Maksym Voznyy
336	1526	75547	75w47	(68·10¹⁵²⁵-77)/9	November 30, 2010	Maksym Voznyy
344	1489	52263	52w63	(47·10¹⁴⁸⁸+367)/9	November 30, 2010	Maksym Voznyy
345	1485	31107	31w07	(28·10¹⁴⁸⁴-37)/9	November 30, 2010	Maksym Voznyy
347	1479	26641	26w41	(8·10¹⁴⁷⁸-77)/3	November 30, 2010	Maksym Voznyy
348	1463	53351	53w51	(16·10¹⁴⁶²+53)/3	November 30, 2010	Maksym Voznyy
350	1461		71w99	(64·10¹⁴⁶⁰+791)/9	November 30, 2010	Maksym Voznyy
361	1423	82287	82w87	(74·10¹⁴²²+583)/9	November 30, 2010	Maksym Voznyy
365	1416	23309	23w09	(7·10¹⁴¹⁵-73)/3	November 30, 2010	Maksym Voznyy
370	1395	35513	35w13	(32·10¹³⁹⁴-383)/9	November 30, 2010	Maksym Voznyy
371	1387	38851	38w51	(35·10¹³⁸⁶-341)/9	November 30, 2010	Maksym Voznyy
377	1361	35561	35w61	(32·10¹³⁶⁰+49)/9	November 30, 2010	Maksym Voznyy
380	1349	78809	78w09	(71·10¹³⁴⁸-719)/9	November 30, 2010	Maksym Voznyy
385	1336	15541	15w41	(14·10¹³³⁵-131)/9	November 30, 2010	Maksym Voznyy
393	1304	35501	35w01	(32·10¹³⁰³-491)/9	November 30, 2010	Maksym Voznyy
395	1300	26659	26w59	(8·10¹²⁹⁹-23)/3	November 30, 2010	Maksym Voznyy
408	1242		53w99	(16·10¹²⁴¹+197)/3	November 30, 2010	Maksym Voznyy
413	1224	24421	24w21	(22·10¹²²³-211)/9	November 30, 2010	Maksym Voznyy
417	1221	26641	26w41	(8·10¹²²⁰-77)/3	November 30, 2010	Maksym Voznyy
418	1220	97769	97w69	(88·10¹²¹⁹-79)/9	November 30, 2010	Maksym Voznyy
419	1218	94453	94w53	(85·10¹²¹⁷+77)/9	November 30, 2010	Maksym Voznyy
422	1214	35501	35w01	(32·10¹²¹³-491)/9	November 30, 2010	Maksym Voznyy
423	1210	37739	37w39	(34·10¹²⁰⁹-349)/9	November 30, 2010	Maksym Voznyy
424	1209		26w33	(8·10¹²⁰⁸-101)/3	November 30, 2010	Maksym Voznyy
427	1192	43369	43w69	(13·10¹¹⁹¹+107)/3	November 30, 2010	Maksym Voznyy
429	1190	27791	27w91	(25·10¹¹⁸⁹+119)/9	November 30, 2010	Maksym Voznyy

November 28, 2010

David Broadhurst proved the primality of 2 near-repdigit-related primes by chgcertd.gp. p2367 and p1692, the largest known prime factors of N-1/N+1, were certified by Primo.

Proven near-repdigit-related primes (except ru/nr/pd/qr)
	digits	flabel	wlabel	expression	when	who
79	11630	79921	79w21	8·10¹¹⁶²⁹-79	November 28, 2010	David Broadhurst
92	10030	23309	23w09	(7·10¹⁰⁰²⁹-73)/3	November 28, 2010	David Broadhurst

November 27, 2010

Serge Batalov proved the primality of N=(22·10⁴⁰⁹⁵-19)/3 by PFGW. An additional prime factor of N+1 is 51844513613. The largest known prime factor of N-1 is a 428-digit number.

Proven near-repdigit-related primes (except ru/nr/pd/qr)
	digits	flabel	wlabel	expression	when	who
181	4096	73327	73w27	(22·10⁴⁰⁹⁵-19)/3	November 27, 2010	Serge Batalov

Serge Batalov proved the primality of N=(8·10⁵⁵⁰³-77)/3 by KonPom.gp derivative. The largest known prime factor of N-1 is a 735-digit number.

Proven near-repdigit-related primes (except ru/nr/pd/qr)
	digits	flabel	wlabel	expression	when	who
159	5504	26641	26w41	(8·10⁵⁵⁰³-77)/3	November 27, 2010	Serge Batalov

https://groups.yahoo.com/neo/groups/primeform/files/KP/KonPom.gp

David Broadhurst proved the primality of N=(52·10¹¹⁵⁵⁰-61)/9 by kppm.gp. The largest known prime factor of N+1 is a 476-digit number.

Proven quasi-repdigit primes
	digits	flabel	wlabel	expression	when	who
58	11551	57771	57w1	(52·10¹¹⁵⁵⁰-61)/9	November 27, 2010	David Broadhurst

November 26, 2010

Maksym Voznyy proved primality of 2 near-repdigit-related primes by Primo 3.0.9.

Proven near-repdigit-related primes (except ru/nr/pd/qr)
	digits	flabel	wlabel	expression	when	who
401	1186	34473	34w73	(31·10¹¹⁸⁵+257)/9	November 26, 2010	Maksym Voznyy
404	1172	97789	97w89	(88·10¹¹⁷¹+101)/9	November 26, 2010	Maksym Voznyy

November 25, 2010

Maksym Voznyy proved primality of 5 quasi-repdigit primes and 11 near-repdigit-related primes by Primo 3.0.9.

Proven quasi-repdigit primes
	digits	flabel	wlabel	expression	when	who
322	2008	55549	5w49	(5·10²⁰⁰⁸-59)/9	November 25, 2010	Maksym Voznyy
690	1079	71101	71w01	(64·10¹⁰⁷⁸-91)/9	November 25, 2010	Maksym Voznyy
697	1074	91101	91w01	(82·10¹⁰⁷³-91)/9	November 25, 2010	Maksym Voznyy
709	1062	18777	187w	(169·10¹⁰⁶⁰-7)/9	November 25, 2010	Maksym Voznyy
710	1061	23323	23w23	(7·10¹⁰⁶⁰-31)/3	November 25, 2010	Maksym Voznyy

Proven near-repdigit-related primes (except ru/nr/pd/qr)
	digits	flabel	wlabel	expression	when	who
410	1155	26657	26w57	(8·10¹¹⁵⁴-29)/3	November 25, 2010	Maksym Voznyy
411	1144	31137	31w37	(28·10¹¹⁴³+233)/9	November 25, 2010	Maksym Voznyy
415	1126	36631	36w31	(11·10¹¹²⁵-107)/3	November 25, 2010	Maksym Voznyy
416	1124	83329	83w29	(25·10¹¹²³-13)/3	November 25, 2010	Maksym Voznyy
432	1093	17793	17w93	(16·10¹⁰⁹²+137)/9	November 25, 2010	Maksym Voznyy
434	1081	72279	72w79	(65·10¹⁰⁸⁰+511)/9	November 25, 2010	Maksym Voznyy
442	1068	56609	56w09	(17·10¹⁰⁶⁷-173)/3	November 25, 2010	Maksym Voznyy
444	1066	21129	21w29	(19·10¹⁰⁶⁵+161)/9	November 25, 2010	Maksym Voznyy
450	1056	12209	12w09	(11·10¹⁰⁵⁵-119)/9	November 25, 2010	Maksym Voznyy
456	1045	24419	24w19	(22·10¹⁰⁴⁴-229)/9	November 25, 2010	Maksym Voznyy
458	1043		83w11	(25·10¹⁰⁴²-67)/3	November 25, 2010	Maksym Voznyy

November 24, 2010

Ray Chandler found 2 near-repdigit primes, 4 quasi-repdigit primes, 1 near-repdigit-related prime, 2 near-repdigit PRPs, 63 quasi-repdigit PRPs, 188 near-repdigit-related PRPs by srsieve and PFGW.

Proven near-repdigit primes
	digits	flabel	wlabel	expression	when	who
62	17872		9949w	995·10¹⁷⁸⁶⁹-1	November 24, 2010	Ray Chandler
64	17297		9949w	995·10¹⁷²⁹⁴-1	November 24, 2010	Ray Chandler

Proven quasi-repdigit primes
	digits	flabel	wlabel	expression	when	who
17	17757	34999	349w	35·10¹⁷⁷⁵⁵-1	November 24, 2010	Ray Chandler
18	17454	52999	529w	53·10¹⁷⁴⁵²-1	November 24, 2010	Ray Chandler
19	17161	47999	479w	48·10¹⁷¹⁵⁹-1	November 24, 2010	Ray Chandler
20	17098	14999	149w	15·10¹⁷⁰⁹⁶-1	November 24, 2010	Ray Chandler

Proven near-repdigit-related primes (except ru/nr/pd/qr)
	digits	flabel	wlabel	expression	when	who
39	17523		550w1	55·10¹⁷⁵²¹+1	November 24, 2010	Ray Chandler

Unprovable near-repdigit PRPs
	digits	flabel	wlabel	expression	when	who
74	17834	99929	9w29	10¹⁷⁸³⁴-71	November 24, 2010	Ray Chandler
75	17719	77717	7w17	(7·10¹⁷⁷¹⁹-547)/9	November 24, 2010	Ray Chandler

Maksym Voznyy proved primality of 2 near-repdigit-related primes by Primo 3.0.9.

Proven near-repdigit-related primes (except ru/nr/pd/qr)
	digits	flabel	wlabel	expression	when	who
451	1011	86681	86w81	(26·10¹⁰¹⁰+43)/3	November 24, 2010	Maksym Voznyy
454	1002	94453	94w53	(85·10¹⁰⁰¹+77)/9	November 24, 2010	Maksym Voznyy

Darren Bedwell found the largest known near-repdigit palindrome prime by OpenPFGW.

Proven near-repdigit-related primes (except ru/nr/pd/qr)
	digits	flabel	wlabel	expression	when	who
1	134809	99899	9w89w	10¹³⁴⁸⁰⁹-10⁶⁷⁴⁰⁴-1	November 24, 2010	Darren Bedwell

November 23, 2010

Factorizations of 811...119 have been extended up to n=250. Composite numbers that appeared newly got through ECM 118 times at level 35. Most unknown factors are supposed to be greater than 10³⁰.

November 19, 2010

David Broadhurst found the largest known near-repdigit prime number. Congratulations!

Proven near-repdigit primes
	digits	flabel	wlabel	expression	when	who
1	319890	59999	59w	6·10³¹⁹⁸⁸⁹-1	November 19, 2010	David Broadhurst
2	293135	59999	59w	6·10²⁹³¹³⁴-1	November 19, 2010	David Broadhurst
3	270659	59999	59w	6·10²⁷⁰⁶⁵⁸-1	November 19, 2010	David Broadhurst

November 17, 2010

Factorizations of 900...001 have been extended up to n=250. Composite numbers that appeared newly got through ECM 118 times at level 35. Most unknown factors are supposed to be greater than 10³⁰.

Ray Chandler found a plateau and depression PRP by srsieve and PFGW.

Unprovable plateau and depression PRPs
	digits	flabel	wlabel	expression	when	who
4	74435	75557	75w7	(68·10⁷⁴⁴³⁴+13)/9	November 17, 2010	Ray Chandler

November 15, 2010

David Broadhurst found the largest known near-repdigit prime. Congratulations!

Proven near-repdigit primes
	digits	flabel	wlabel	expression	when	who
1	267599	59999	59w	6·10²⁶⁷⁵⁹⁸-1	November 15, 2010	David Broadhurst

Ray Chandler found 6 near-repdigit primes, 4 quasi-repdigit primes, 1 near-repdigit-related prime, 6 near-repdigit PRPs, 82 quasi-repdigit PRPs and 208 near-repdigit-related PRPs. See also primesize.txt.

Proven near-repdigit primes
	digits	wlabel	expression	when	who
60	17005	9999959w	999996·10¹⁶⁹⁹⁹-1	November 15, 2010	Ray Chandler
61	16914	999979w	99998·10¹⁶⁹⁰⁹-1	November 15, 2010	Ray Chandler
62	16478	999979w	99998·10¹⁶⁴⁷³-1	November 15, 2010	Ray Chandler
63	16427	999999959w	99999996·10¹⁶⁴¹⁹-1	November 15, 2010	Ray Chandler
64	16391	99999949w	9999995·10¹⁶³⁸⁴-1	November 15, 2010	Ray Chandler
66	16109	999999989w	99999999·10¹⁶¹⁰¹-1	November 15, 2010	Ray Chandler

Proven quasi-repdigit primes
	digits	flabel	wlabel	expression	when	who
17	16976	10999	109w	11·10¹⁶⁹⁷⁴-1	November 15, 2010	Ray Chandler
18	16830	14999	149w	15·10¹⁶⁸²⁸-1	November 15, 2010	Ray Chandler
19	16715	85999	859w	86·10¹⁶⁷¹³-1	November 15, 2010	Ray Chandler
20	16082	20999	209w	21·10¹⁶⁰⁸⁰-1	November 15, 2010	Ray Chandler

Proven near-repdigit-related primes (except ru/nr/pd/qr)
	digits	flabel	wlabel	expression	when	who
47	16538		330w1	33·10¹⁶⁵³⁶+1	November 15, 2010	Ray Chandler

November 14, 2010

Factorizations of 700...001 have been extended up to n=250. Composite numbers that appeared newly got through ECM 118 times at level 35. Most unknown factors are supposed to be greater than 10³⁰.

Max Dettweiler reported a near-repdigit prime number at Prime posting thread, part 2. (With a catch.) - Page 2 - mersenneforum.org.

Proven near-repdigit primes
	digits	flabel	wlabel	expression	when	who
22	81906		99959w	9996·10⁸¹⁹⁰²-1	November 14, 2010	Max Dettweiler

November 12, 2010

Factorizations of 233...33 have been extended up to n=250. Composite numbers that appeared newly got through ECM 118 times at level 35. Most unknown factors are supposed to be greater than 10³⁰.

Ray Chandler found a unprovable plateau and depression PRP by srsieve and PFGW.

Unprovable plateau and depression PRPs
	digits	flabel	wlabel	expression	when	who
4	72773	74447	74w7	(67·10⁷²⁷⁷²+23)/9	November 12, 2010	Ray Chandler

November 9, 2010

Factorizations of 877...779 have been extended up to n=200. Composite numbers that appeared newly got through ECM 118 times at level 35. Most unknown factors are supposed to be greater than 10³⁰.

David Broadhurst found the third largest known near-repdigit prime.

Proven near-repdigit primes
	digits	flabel	wlabel	expression	when	who
3	223872	89999	89w	9·10²²³⁸⁷¹-1	November 9, 2010	David Broadhurst

November 8, 2010

Ray Chandler found 3 near-repdigit primes and 6 quasi-repdigit primes by srsieve and PFGW.

Proven near-repdigit primes
	digits	wlabel	expression	when	who
58	15987	99999949w	9999995·10¹⁵⁹⁸⁰-1	November 8, 2010	Ray Chandler
59	15872	99959w	9996·10¹⁵⁸⁶⁸-1	November 8, 2010	Ray Chandler
62	15705	999929w	99993·10¹⁵⁷⁰⁰-1	November 8, 2010	Ray Chandler

Proven quasi-repdigit primes
	digits	flabel	wlabel	expression	when	who
17	15851	16999	169w	17·10¹⁵⁸⁴⁹-1	November 8, 2010	Ray Chandler
18	15842	25999	259w	26·10¹⁵⁸⁴⁰-1	November 8, 2010	Ray Chandler
19	15411	34999	349w	35·10¹⁵⁴⁰⁹-1	November 8, 2010	Ray Chandler
20	15196	26999	269w	27·10¹⁵¹⁹⁴-1	November 8, 2010	Ray Chandler
21	15183	80999	809w	81·10¹⁵¹⁸¹-1	November 8, 2010	Ray Chandler
22	15090	20999	209w	21·10¹⁵⁰⁸⁸-1	November 8, 2010	Ray Chandler

Ray Chandler found 8 near-repdigit PRPs, 75 quasi-repdigit PRPs and 207 near-repdigit-related PRPs (except ru/nr/pd/qr) by srsieve and PFGW. See primesize.txt.

November 7, 2010

Factorizations of 877...773 have been extended up to n=200. Composite numbers that appeared newly got through ECM 118 times at level 35. Most unknown factors are supposed to be greater than 10³⁰.

November 6, 2010

Factorizations of 877...771 have been extended up to n=200. Composite numbers that appeared newly got through ECM 118 times at level 35. Most unknown factors are supposed to be greater than 10³⁰.

David Broadhurst found the largest known near-repdigit prime. Congratulations!

Proven near-repdigit primes
	digits	flabel	wlabel	expression	when	who
1	260254	89999	89w	9·10²⁶⁰²⁵³-1	November 6, 2010	David Broadhurst
2	236892	79999	79w	8·10²³⁶⁸⁹¹-1	November 6, 2010	David Broadhurst

November 4, 2010

David Broadhurst found the largest known near-repdigit prime. Congratulations!

Proven near-repdigit primes
	digits	flabel	wlabel	expression	when	who
1	212904	89999	89w	9·10²¹²⁹⁰³-1	November 4, 2010	David Broadhurst
2	211030	49999	49w	5·10²¹¹⁰²⁹-1	November 4, 2010	David Broadhurst

November 3, 2010

Factorizations of 866...669 have been extended up to n=200. Composite numbers that appeared newly got through ECM 118 times at level 35. Most unknown factors are supposed to be greater than 10³⁰.

November 2, 2010

Factorizations of 855...559 have been extended up to n=200. Composite numbers that appeared newly got through ECM 118 times at level 35. Most unknown factors are supposed to be greater than 10³⁰.

November 1, 2010

Ray Chandler found 8 near-repdigit primes, 8 quasi-repdigit primes and 1 near-repdigit-related prime (except ru/nr/pd/qr) by srsieve and PFGW.

Proven near-repdigit primes
	digits	wlabel	expression	when	who
56	14958	99989w	9999·10¹⁴⁹⁵⁴-1	November 1, 2010	Ray Chandler
57	14918	9999989w	999999·10¹⁴⁹¹²-1	November 1, 2010	Ray Chandler
58	14788	9949w	995·10¹⁴⁷⁸⁵-1	November 1, 2010	Ray Chandler
59	14715	9999929w	999993·10¹⁴⁷⁰⁹-1	November 1, 2010	Ray Chandler
60	14703	9999989w	999999·10¹⁴⁶⁹⁷-1	November 1, 2010	Ray Chandler
61	14682	99999959w	9999996·10¹⁴⁶⁷⁵-1	November 1, 2010	Ray Chandler
62	14356	999919w	99992·10¹⁴³⁵¹-1	November 1, 2010	Ray Chandler
63	14095	9979w	998·10¹⁴⁰⁹²-1	November 1, 2010	Ray Chandler

Proven quasi-repdigit primes
	digits	flabel	wlabel	expression	when	who
17	14916	82999	829w	83·10¹⁴⁹¹⁴-1	November 1, 2010	Ray Chandler
18	14817	65999	659w	66·10¹⁴⁸¹⁵-1	November 1, 2010	Ray Chandler
19	14767	32999	329w	33·10¹⁴⁷⁶⁵-1	November 1, 2010	Ray Chandler
20	14753	38999	389w	39·10¹⁴⁷⁵¹-1	November 1, 2010	Ray Chandler
21	14719		119w	12·10¹⁴⁷¹⁷-1	November 1, 2010	Ray Chandler
22	14368	34999	349w	35·10¹⁴³⁶⁶-1	November 1, 2010	Ray Chandler
23	14334	83999	839w	84·10¹⁴³³²-1	November 1, 2010	Ray Chandler
24	14333	17999	179w	18·10¹⁴³³¹-1	November 1, 2010	Ray Chandler

Proven near-repdigit-related primes (except ru/nr/pd/qr)
	digits	flabel	wlabel	expression	when	who
53	14871		330w1	33·10¹⁴⁸⁶⁹+1	November 1, 2010	Ray Chandler

Ray Chandler found 10 near-repdigit PRPs, 83 quasi-repdigit PRPs and 232 near-repdigit-related PRPs (except ru/nr/pd/qr) by srsieve and PFGW. See primesize.txt.

October 2010

October 31, 2010

Ray Chandler proved 8 near-repdigit-related (except ru/nr/pd/qr) primes by PFGW.

Proven near-repdigit-related primes (except ru/nr/pd/qr)
	digits	flabel	wlabel	expression	when	who
112	7855	31109	31w09	(28·10⁷⁸⁵⁴-19)/9	October 31, 2010	Ray Chandler
117	7424	67709	67w09	(61·10⁷⁴²³-619)/9	October 31, 2010	Ray Chandler
135	6224	15539	15w39	(14·10⁶²²³-149)/9	October 31, 2010	Ray Chandler
156	5285	18869	18w69	(17·10⁵²⁸⁴-179)/9	October 31, 2010	Ray Chandler
164	4722	38849	38w49	(35·10⁴⁷²¹-359)/9	October 31, 2010	Ray Chandler
175	4212	90089	90w89	9·10⁴²¹¹+89	October 31, 2010	Ray Chandler
188	3619	86659	86w59	(26·10³⁶¹⁸-23)/3	October 31, 2010	Ray Chandler
189	3608	30029	30w29	3·10³⁶⁰⁷+29	October 31, 2010	Ray Chandler

October 30, 2010

Factorizations of 855...557 have been extended up to n=200. Composite numbers that appeared newly got through ECM 118 times at level 35. Most unknown factors are supposed to be greater than 10³⁰.

Ray Chandler found 1 plateau-and-depression PRP by srsieve and PFGW.

Unprovable plateau and depression PRPs
	digits	flabel	wlabel	expression	when	who
4	68505	75557	75w7	(68·10⁶⁸⁵⁰⁴+13)/9	October 30, 2010	Ray Chandler

October 28, 2010

Factorizations of 855...553 have been extended up to n=200. Composite numbers that appeared newly got through ECM 118 times at level 35. Most unknown factors are supposed to be greater than 10³⁰.

Ray Chandler found 6 near-repdigit primes and 8 quasi-repdigit primes by srsieve and PFGW.

Proven near-repdigit primes
	digits	flabel	wlabel	expression	when	who
56	13782		9999979w	999998·10¹³⁷⁷⁶-1	October 28, 2010	Ray Chandler
57	13570		9999919w	999992·10¹³⁵⁶⁴-1	October 28, 2010	Ray Chandler
58	13478		99999929w	9999993·10¹³⁴⁷¹-1	October 28, 2010	Ray Chandler
59	13409	92999	929w	93·10¹³⁴⁰⁷-1	October 28, 2010	Ray Chandler
60	13400		9949w	995·10¹³³⁹⁷-1	October 28, 2010	Ray Chandler
61	13360		9999919w	999992·10¹³³⁵⁴-1	October 28, 2010	Ray Chandler

Proven quasi-repdigit primes
	digits	flabel	wlabel	expression	when	who
17	13789	52999	529w	53·10¹³⁷⁸⁷-1	October 28, 2010	Ray Chandler
18	13721	41999	419w	42·10¹³⁷¹⁹-1	October 28, 2010	Ray Chandler
19	13598	34999	349w	35·10¹³⁵⁹⁶-1	October 28, 2010	Ray Chandler
20	13563	52999	529w	53·10¹³⁵⁶¹-1	October 28, 2010	Ray Chandler
22	13364	50999	509w	51·10¹³³⁶²-1	October 28, 2010	Ray Chandler
23	13227	13999	139w	14·10¹³²²⁵-1	October 28, 2010	Ray Chandler
24	13128	74999	749w	75·10¹³¹²⁶-1	October 28, 2010	Ray Chandler
25	13047	83999	839w	84·10¹³⁰⁴⁵-1	October 28, 2010	Ray Chandler

Ray Chandler found 13 near-repdigit PRPs, 77 quasi-repdigit PRPs and 242 near-repdigit-related PRPs (except ru/nr/pd/qr) by srsieve and PFGW. See primesize.txt for PRPs.

Ray Chandler proved 3 near-repdigit primes and 10 near-repdigit-related (except ru/nr/pd/qr) primes by PFGW.

Proven quasi-repdigit primes
	digits	flabel	wlabel	expression	when	who
121	4681	11109	1w09	(10⁴⁶⁸¹-19)/9	October 28, 2010	Ray Chandler
131	4082	66601	6w01	(2·10⁴⁰⁸²-197)/3	October 28, 2010	Ray Chandler
140	3781	77769	7w69	(7·10³⁷⁸¹-79)/9	October 28, 2010	Ray Chandler

Proven near-repdigit-related primes (except ru/nr/pd/qr)
	digits	flabel	wlabel	expression	when	who
119	7022	18871	18w71	(17·10⁷⁰²¹-161)/9	October 28, 2010	Ray Chandler
137	5941	95547	95w47	(86·10⁵⁹⁴⁰-77)/9	October 28, 2010	Ray Chandler
153	5233	95547	95w47	(86·10⁵²³²-77)/9	October 28, 2010	Ray Chandler
168	4242	19981	19w81	2·10⁴²⁴¹-19	October 28, 2010	Ray Chandler
169	4214	26641	26w41	(8·10⁴²¹³-77)/3	October 28, 2010	Ray Chandler
175	3889	97769	97w69	(88·10³⁸⁸⁸-79)/9	October 28, 2010	Ray Chandler
180	3673	51107	51w07	(46·10³⁶⁷²-37)/9	October 28, 2010	Ray Chandler
185	3530	48839	48w39	(44·10³⁵²⁹-449)/9	October 28, 2010	Ray Chandler
188	3451	42219	42w19	(38·10³⁴⁵⁰-29)/9	October 28, 2010	Ray Chandler
189	3438	12209	12w09	(11·10³⁴³⁷-119)/9	October 28, 2010	Ray Chandler

October 27, 2010

Ray Chandler proved 3 quasi-repdigit primes and 27 near-repdigit-related prime numbers (except ru/nr/pd/qr) by PFGW.

Proven quasi-repdigit primes
	digits	flabel	wlabel	expression	when	who
170	2929	22219	2w19	(2·10²⁹²⁹-29)/9	October 27, 2010	Ray Chandler
245	2198	49949	49w49	5·10²¹⁹⁷-51	October 27, 2010	Ray Chandler
257	2156	66601	6w01	(2·10²¹⁵⁶-197)/3	October 27, 2010	Ray Chandler

Proven near-repdigit-related primes (except ru/nr/pd/qr)
	digits	flabel	wlabel	expression	when	who
187	3267	62217	62w17	(56·10³²⁶⁶-47)/9	October 27, 2010	Ray Chandler
188	3230	56609	56w09	(17·10³²²⁹-173)/3	October 27, 2010	Ray Chandler
194	3122	49951	49w51	5·10³¹²¹-49	October 27, 2010	Ray Chandler
195	3110	26639	26w39	(8·10³¹⁰⁹-83)/3	October 27, 2010	Ray Chandler
196	3032	38849	38w49	(35·10³⁰³¹-359)/9	October 27, 2010	Ray Chandler
204	2732		23w11	(7·10²⁷³¹-67)/3	October 27, 2010	Ray Chandler
208	2584	95547	95w47	(86·10²⁵⁸³-77)/9	October 27, 2010	Ray Chandler
211	2567	14431	14w31	(13·10²⁵⁶⁶-121)/9	October 27, 2010	Ray Chandler
219	2442	56609	56w09	(17·10²⁴⁴¹-173)/3	October 27, 2010	Ray Chandler
225	2359	97769	97w69	(88·10²³⁵⁸-79)/9	October 27, 2010	Ray Chandler
226	2351	68821	68w21	(62·10²³⁵⁰-611)/9	October 27, 2010	Ray Chandler
236	2155	86659	86w59	(26·10²¹⁵⁴-23)/3	October 27, 2010	Ray Chandler
238	2150	49951	49w51	5·10²¹⁴⁹-49	October 27, 2010	Ray Chandler
240	2135	68821	68w21	(62·10²¹³⁴-611)/9	October 27, 2010	Ray Chandler
241	2135		45w11	(41·10²¹³⁴-401)/9	October 27, 2010	Ray Chandler
242	2126	15539	15w39	(14·10²¹²⁵-149)/9	October 27, 2010	Ray Chandler
256	1952	16649	16w49	(5·10¹⁹⁵¹-53)/3	October 27, 2010	Ray Chandler
257	1945	86659	86w59	(26·10¹⁹⁴⁴-23)/3	October 27, 2010	Ray Chandler
258	1938	26641	26w41	(8·10¹⁹³⁷-77)/3	October 27, 2010	Ray Chandler
259	1913	28859	28w59	(26·10¹⁹¹²-269)/9	October 27, 2010	Ray Chandler
265	1850	68821	68w21	(62·10¹⁸⁴⁹-611)/9	October 27, 2010	Ray Chandler
268	1802	57719	57w19	(52·10¹⁸⁰¹-529)/9	October 27, 2010	Ray Chandler
270	1787	47731	47w31	(43·10¹⁷⁸⁶-421)/9	October 27, 2010	Ray Chandler
272	1782		34w11	(31·10¹⁷⁸¹-301)/9	October 27, 2010	Ray Chandler
276	1762	64437	64w37	(58·10¹⁷⁶¹-67)/9	October 27, 2010	Ray Chandler
280	1682	47729	47w29	(43·10¹⁶⁸¹-439)/9	October 27, 2010	Ray Chandler
281	1670	57719	57w19	(52·10¹⁶⁶⁹-529)/9	October 27, 2010	Ray Chandler

October 26, 2010

Factorizations of 855...551 have been extended up to n=200. Composite numbers that appeared newly got through ECM 118 times at level 35. Most unknown factors are supposed to be greater than 10³⁰.

Ray Chandler proved 3 quasi-repdigit primes and 28 near-repdigit-related prime numbers (except ru/nr/pd/qr) by PFGW.

Proven quasi-repdigit primes
	digits	flabel	wlabel	expression	when	who
426	1499	93323	93w23	(28·10¹⁴⁹⁸-31)/3	October 26, 2010	Ray Chandler
427	1497	97767	97w67	(88·10¹⁴⁹⁶-97)/9	October 26, 2010	Ray Chandler
497	1366	97767	97w67	(88·10¹³⁶⁵-97)/9	October 26, 2010	Ray Chandler

Proven near-repdigit-related primes (except ru/nr/pd/qr)
	digits	flabel	wlabel	expression	when	who
282	1663	91103	91w03	(82·10¹⁶⁶²-73)/9	October 26, 2010	Ray Chandler
284	1649	14431	14w31	(13·10¹⁶⁴⁸-121)/9	October 26, 2010	Ray Chandler
285	1597	86657	86w57	(26·10¹⁵⁹⁶-29)/3	October 26, 2010	Ray Chandler
293	1586	67709	67w09	(61·10¹⁵⁸⁵-619)/9	October 26, 2010	Ray Chandler
294	1586	28861	28w61	(26·10¹⁵⁸⁵-251)/9	October 26, 2010	Ray Chandler
300	1562	16651	16w51	(5·10¹⁵⁶¹-47)/3	October 26, 2010	Ray Chandler
303	1550	58829	58w29	(53·10¹⁵⁴⁹-539)/9	October 26, 2010	Ray Chandler
312	1507	73327	73w27	(22·10¹⁵⁰⁶-19)/3	October 26, 2010	Ray Chandler
321	1452	23309	23w09	(7·10¹⁴⁵¹-73)/3	October 26, 2010	Ray Chandler
331	1400		12w11	(11·10¹³⁹⁹-101)/9	October 26, 2010	Ray Chandler
338	1361	86657	86w57	(26·10¹³⁶⁰-29)/3	October 26, 2010	Ray Chandler
339	1351	71103	71w03	(64·10¹³⁵⁰-73)/9	October 26, 2010	Ray Chandler
347	1331	68821	68w21	(62·10¹³³⁰-611)/9	October 26, 2010	Ray Chandler
348	1321	51107	51w07	(46·10¹³²⁰-37)/9	October 26, 2010	Ray Chandler
357	1277	64439	64w39	(58·10¹²⁷⁶-49)/9	October 26, 2010	Ray Chandler
360	1266	95547	95w47	(86·10¹²⁶⁵-77)/9	October 26, 2010	Ray Chandler
363	1262	18869	18w69	(17·10¹²⁶¹-179)/9	October 26, 2010	Ray Chandler
366	1231	73327	73w27	(22·10¹²³⁰-19)/3	October 26, 2010	Ray Chandler
371	1221	62217	62w17	(56·10¹²²⁰-47)/9	October 26, 2010	Ray Chandler
376	1190	46619	46w19	(14·10¹¹⁸⁹-143)/3	October 26, 2010	Ray Chandler
391	1120	31109	31w09	(28·10¹¹¹⁹-19)/9	October 26, 2010	Ray Chandler
402	1093	62217	62w17	(56·10¹⁰⁹²-47)/9	October 26, 2010	Ray Chandler
408	1070	25531	25w31	(23·10¹⁰⁶⁹-221)/9	October 26, 2010	Ray Chandler
414	1058	34409	34w09	(31·10¹⁰⁵⁷-319)/9	October 26, 2010	Ray Chandler
418	1052	36631	36w31	(11·10¹⁰⁵¹-107)/3	October 26, 2010	Ray Chandler
424	1032	31107	31w07	(28·10¹⁰³¹-37)/9	October 26, 2010	Ray Chandler
425	1028	36629	36w29	(11·10¹⁰²⁷-113)/3	October 26, 2010	Ray Chandler
430	1006	68821	68w21	(62·10¹⁰⁰⁵-611)/9	October 26, 2010	Ray Chandler

October 25, 2010

Factorizations of 844...449 have been extended up to n=200. Composite numbers that appeared newly got through ECM 118 times at level 35. Most unknown factors are supposed to be greater than 10³⁰.

Ray Chandler found 5 near-repdigit primes, 6 quasi-repdigit primes, 3 near-repdigit-related primes (except ru/nr/pd/qr), 9 near-repdigit PRPs, 86 quasi-repdigit PRPs and 249 near-repdigit-related PRPs (except ru/nr/pd/qr). See primesize.txt for PRPs.

Proven near-repdigit primes
	digits	wlabel	expression	when	who
56	12929	99989w	9999·10¹²⁹²⁵-1	October 25, 2010	Ray Chandler
57	12892	999999989w	99999999·10¹²⁸⁸⁴-1	October 25, 2010	Ray Chandler
59	12383	9929w	993·10¹²³⁸⁰-1	October 25, 2010	Ray Chandler
61	12067	999999949w	99999995·10¹²⁰⁵⁹-1	October 25, 2010	Ray Chandler
62	12067	99929w	9993·10¹²⁰⁶³-1	October 25, 2010	Ray Chandler

Proven quasi-repdigit primes
	digits	flabel	wlabel	expression	when	who
18	12796	47999	479w	48·10¹²⁷⁹⁴-1	October 25, 2010	Ray Chandler
19	12572	17999	179w	18·10¹²⁵⁷⁰-1	October 25, 2010	Ray Chandler
20	12508	20999	209w	21·10¹²⁵⁰⁶-1	October 25, 2010	Ray Chandler
21	12490	74999	749w	75·10¹²⁴⁸⁸-1	October 25, 2010	Ray Chandler
22	12363	83999	839w	84·10¹²³⁶¹-1	October 25, 2010	Ray Chandler
23	12018	56999	569w	57·10¹²⁰¹⁶-1	October 25, 2010	Ray Chandler

Proven near-repdigit-related primes (except ru/nr/pd/qr)
	digits	wlabel	expression	when	who
67	12592	220w1	22·10¹²⁵⁹⁰+1	October 25, 2010	Ray Chandler
68	12518	330w1	33·10¹²⁵¹⁶+1	October 25, 2010	Ray Chandler
70	12111	660w1	66·10¹²¹⁰⁹+1	October 25, 2010	Ray Chandler

October 23, 2010

Factorizations of 988...887 have been extended up to n=200. Composite numbers that appeared newly got through ECM 118 times at level 35. Most unknown factors are supposed to be greater than 10³⁰.

Ray Chandler found 9 near-repdigit primes, 8 quasi-repdigit primes, 6 near-repdigit PRPs, 93 quasi-repdigit PRPs and 268 near-repdigit-related PRPs (except ru/nr/pd/qr). See primesize.txt for details.

Proven near-repdigit primes
	digits	flabel	wlabel	expression	when	who
58	11870		99989w	9999·10¹¹⁸⁶⁶-1	October 23, 2010	Ray Chandler
59	11345		9999919w	999992·10¹¹³³⁹-1	October 23, 2010	Ray Chandler
61	11304		999999979w	99999998·10¹¹²⁹⁶-1	October 23, 2010	Ray Chandler
62	11274		999999949w	99999995·10¹¹²⁶⁶-1	October 23, 2010	Ray Chandler
63	11271		999929w	99993·10¹¹²⁶⁶-1	October 23, 2010	Ray Chandler
64	11234		9999929w	999993·10¹¹²²⁸-1	October 23, 2010	Ray Chandler
65	11211		99929w	9993·10¹¹²⁰⁷-1	October 23, 2010	Ray Chandler
66	11181		99999989w	9999999·10¹¹¹⁷⁴-1	October 23, 2010	Ray Chandler
68	11112	97999	979w	98·10¹¹¹¹⁰-1	October 23, 2010	Ray Chandler

Proven quasi-repdigit primes
	digits	flabel	wlabel	expression	when	who
18	11998	50999	509w	51·10¹¹⁹⁹⁶-1	October 23, 2010	Ray Chandler
19	11992	14999	149w	15·10¹¹⁹⁹⁰-1	October 23, 2010	Ray Chandler
20	11961		449w	45·10¹¹⁹⁵⁹-1	October 23, 2010	Ray Chandler
21	11883	61999	619w	62·10¹¹⁸⁸¹-1	October 23, 2010	Ray Chandler
22	11346	61999	619w	62·10¹¹³⁴⁴-1	October 23, 2010	Ray Chandler
23	11302	86999	869w	87·10¹¹³⁰⁰-1	October 23, 2010	Ray Chandler
24	11145	35999	359w	36·10¹¹¹⁴³-1	October 23, 2010	Ray Chandler
25	11058	26999	269w	27·10¹¹⁰⁵⁶-1	October 23, 2010	Ray Chandler

October 22, 2010

5 quasi-repdigit prime numbers have been certified by N-1/N+1 test.

Proven quasi-repdigit primes
	digits	flabel	wlabel	expression	when	who
155	2941	33329	3w29	(10²⁹⁴¹-13)/3	October 22, 2010	Makoto Kamada
274	2004	33301	3w01	(10²⁰⁰⁴-97)/3	October 22, 2010	Makoto Kamada
293	1902	77701	7w01	(7·10¹⁹⁰²-691)/9	October 22, 2010	Makoto Kamada
305	1874	55501	5w01	(5·10¹⁸⁷⁴-491)/9	October 22, 2010	Makoto Kamada
323	1796	33301	3w01	(10¹⁷⁹⁶-97)/3	October 22, 2010	Makoto Kamada

October 21, 2010

Factorizations of 988...883 have been extended up to n=200. Composite numbers that appeared newly got through ECM 118 times at level 35. Most unknown factors are supposed to be greater than 10³⁰.

The ratio of factored part of repunit-related PRPs is available on primesize.txt. Execute `grep "%" primesize.txt`.

The algebraic factorization type of PRPs is also available on primesize.txt. Execute `grep ":" primesize.txt`.

October 20, 2010

Erik Branger proved primality of near-repdigit number (2·10³⁶⁴⁹-17)/3 by N-1 test.

Proven near-repdigit primes
	digits	flabel	wlabel	expression	when	who
162	3649	66661	6w1	(2·10³⁶⁴⁹-17)/3	October 20, 2010	Erik Branger

October 19, 2010

Factorizations of 988...881 have been extended up to n=200. Composite numbers that appeared newly got through ECM 118 times at level 35. Most unknown factors are supposed to be greater than 10³⁰.

Ray Chandler's research found some inconsistencies between Henri & Renaud Lifchitz's PRP Top records, Plateau and Depression Primes and primesize.txt. The following records were corrected.

Unprovable near-repdigit PRPs
	digits	flabel	wlabel	expression	when	who
82	14602	88881	8w1	(8·10¹⁴⁶⁰²-71)/9	May 2002	Daniel Heuer
99	12130	33331	3w1	(10¹²¹³⁰-7)/3	May 2002	Daniel Heuer
101	11960	33331	3w1	(10¹¹⁹⁶⁰-7)/3	May 2002	Daniel Heuer
105	11245	33331	3w1	(10¹¹²⁴⁵-7)/3	May 2002	Daniel Heuer
94	12456	66667	6w7	(2·10¹²⁴⁵⁶+1)/3	May 2002	Daniel Heuer

Unprovable plateau and depression PRPs
	digits	flabel	wlabel	expression	when	who
19	37785	92229	92w9	(83·10³⁷⁷⁸⁴+61)/9	June 26, 2005	Patrick De Geest

October 17, 2010

Factorizations of 977...773 have been extended up to n=200. Composite numbers that appeared newly got through ECM 118 times at level 35. Most unknown factors are supposed to be greater than 10³⁰.

Serge Batalov proved primality of near-repdigit number (5·10²⁷⁷⁴-23)/9 by N-1 test. (5·10²⁷⁷⁴-23)/9-1 = 32·(25·10⁹²³-1)/3·(625·10¹⁸⁴⁶+25·10⁹²³+1)/3. (25·10⁹²³-1)/3 = 4409·84653·43201253·2957799751·79596993237627302347·119042686224571112175325031·P853.

Proven near-repdigit primes
	digits	flabel	wlabel	expression	when	who
191	2774	55553	5w3	(5·10²⁷⁷⁴-23)/9	October 17, 2010	Serge Batalov

October 16, 2010

Markus Tervooren found the largest known unprovable near-repdigit PRP by using sr2sieve, mprime and PFGW. Congratulations!

Unprovable near-repdigit PRPs
	digits	flabel	wlabel	expression	when	who
1	232599	99997	9w7	10²³²⁵⁹⁹-3	October 16, 2010	Markus Tervooren

# pfgw -f0 -tc -u0 -q"10^232599-3"
PFGW Version 3.3.6.20100907.x86_Stable [GWNUM 25.14]

No factoring at all, not even trivial division
Primality testing 10^232599-3 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 2                                                  
Running N+1 test using discriminant 5, base 4+sqrt(5)
Calling N-1 BLS with factored part 0.01% and helper 0.00% (0.02% proof)
10^232599-3 is Fermat and Lucas PRP! (4500.3722s+0.0064s)

October 15, 2010

Ray Chandler found 9 near-repdigit primes by using srsieve and PFGW.

Proven near-repdigit primes
	digits	wlabel	expression	when	who
52	10817	999999929w	99999993·10¹⁰⁸⁰⁹-1	October 15, 2010	Ray Chandler
53	10720	9999919w	999992·10¹⁰⁷¹⁴-1	October 15, 2010	Ray Chandler
54	10649	9999929w	999993·10¹⁰⁶⁴³-1	October 15, 2010	Ray Chandler
55	10531	99989w	9999·10¹⁰⁵²⁷-1	October 15, 2010	Ray Chandler
56	10453	9919w	992·10¹⁰⁴⁵⁰-1	October 15, 2010	Ray Chandler
57	10412	999999929w	99999993·10¹⁰⁴⁰⁴-1	October 15, 2010	Ray Chandler
58	10206	999999949w	99999995·10¹⁰¹⁹⁸-1	October 15, 2010	Ray Chandler
59	10168	99949w	9995·10¹⁰¹⁶⁴-1	October 15, 2010	Ray Chandler
60	10106	999919w	99992·10¹⁰¹⁰¹-1	October 15, 2010	Ray Chandler

Ray Chandler found 6 quasi-repdigit primes by using srsieve and PFGW.

Proven quasi-repdigit primes
	digits	flabel	wlabel	expression	when	who
18	10990	86999	869w	87·10¹⁰⁹⁸⁸-1	October 15, 2010	Ray Chandler
19	10859	34999	349w	35·10¹⁰⁸⁵⁷-1	October 15, 2010	Ray Chandler
20	10762	40999	409w	41·10¹⁰⁷⁶⁰-1	October 15, 2010	Ray Chandler
22	10346	71999	719w	72·10¹⁰³⁴⁴-1	October 15, 2010	Ray Chandler
23	10195	70999	709w	71·10¹⁰¹⁹³-1	October 15, 2010	Ray Chandler
24	10026	10999	109w	11·10¹⁰⁰²⁴-1	October 15, 2010	Ray Chandler

Ray Chandler found 9 near-repdigit PRPs by using srsieve and PFGW.

Unprovable near-repdigit PRPs
	digits	flabel	wlabel	expression	when	who
108	10941	77727	7w27	(7·10¹⁰⁹⁴¹-457)/9	October 15, 2010	Ray Chandler
See primesize.txt
122	10214	33343	3w43	(10¹⁰²¹⁴+29)/3	October 15, 2010	Ray Chandler

Ray Chandler found 101 quasi-repdigit PRPs by using srsieve and PFGW.

Unprovable quasi-repdigit PRPs
	digits	flabel	wlabel	expression	when	who
425	10994	87797	87w97	(79·10¹⁰⁹⁹³+173)/9	October 15, 2010	Ray Chandler
See primesize.txt
556	10029	60667	606w7	(182·10¹⁰⁰²⁷+1)/3	October 15, 2010	Ray Chandler

Ray Chandler found 309 near-repdigit-related PRPs (except ru/nr/pd/qr) by using srsieve and PFGW.

Unprovable near-repdigit-related PRPs (except ru/nr/pd/qr)
	digits	flabel	wlabel	expression	when	who
84	11001		32w11	(29·10¹¹⁰⁰⁰-101)/9	October 15, 2010	Ray Chandler
See primesize.txt
398	10010	31193	31w93	(28·10¹⁰⁰⁰⁹+737)/9	October 15, 2010	Ray Chandler

Ray Chandler noticed that Patrick De Geest reported 2 quasi-repdigit PRPs at Henri & Renaud Lifchitz's PRP Top on December 2004.

Unprovable quasi-repdigit PRPs
	digits	flabel	wlabel	expression	when	who
405	11653	89989	89w89	9·10¹¹⁶⁵²-11	December 2004	Patrick De Geest
519	10450	89989	89w89	9·10¹⁰⁴⁴⁹-11	December 2004	Patrick De Geest

Serge Batalov proved primality of 12891-digit near-repdigit number (10¹²⁸⁹¹+11)/3 by using Primo 3.0.9.1 and PFGW.

Proven near-repdigit primes
	digits	flabel	wlabel	expression	when	who
49	12891	33337	3w7	(10¹²⁸⁹¹+11)/3	October 15, 2010	Serge Batalov

Serge Batalov proved primality of 2915-digit quasi-repdigit number 9·10²⁹¹⁴+7 by using Primo 3.0.9.

Proven quasi-repdigit primes
	digits	flabel	wlabel	expression	when	who
155	2915	90007	90w7	9·10²⁹¹⁴+7	October 15, 2010	Serge Batalov

October 14, 2010

Factorizations of 977...771 have been extended up to n=200. Composite numbers that appeared newly got through ECM 118 times at level 35. Most unknown factors are supposed to be greater than 10³⁰.

Serge Batalov found 3 quasi-repdigit PRPs.

Unprovable quasi-repdigit PRPs
	digits	flabel	wlabel	expression	when	who
56	43213	87773	87w3	(79·10⁴³²¹²-43)/9	October 14, 2010	Serge Batalov
62	40158	86669	86w9	(26·10⁴⁰¹⁵⁷+7)/3	October 14, 2010	Serge Batalov
63	39992	86669	86w9	(26·10³⁹⁹⁹¹+7)/3	October 14, 2010	Serge Batalov

Ray Chandler found 7 near-repdigit primes by using srsieve and PFGW.

Proven near-repdigit primes
	digits	flabel	wlabel	expression	when	who
61	9646		999999959w	99999996·10⁹⁶³⁸-1	October 14, 2010	Ray Chandler
63	9623	95999	959w	96·10⁹⁶²¹-1	October 14, 2010	Ray Chandler
64	9603		9959w	996·10⁹⁶⁰⁰-1	October 14, 2010	Ray Chandler
65	9480	95999	959w	96·10⁹⁴⁷⁸-1	October 14, 2010	Ray Chandler
67	9163		99919w	9992·10⁹¹⁵⁹-1	October 14, 2010	Ray Chandler
68	9136		9949w	995·10⁹¹³³-1	October 14, 2010	Ray Chandler
69	9045		9929w	993·10⁹⁰⁴²-1	October 14, 2010	Ray Chandler

Ray Chandler found 8 quasi-repdigit primes by using srsieve and PFGW.

Proven quasi-repdigit primes
	digits	flabel	wlabel	expression	when	who
25	9771	82999	829w	83·10⁹⁷⁶⁹-1	October 14, 2010	Ray Chandler
27	9538	23999	239w	24·10⁹⁵³⁶-1	October 14, 2010	Ray Chandler
28	9510	65999	659w	66·10⁹⁵⁰⁸-1	October 14, 2010	Ray Chandler
29	9350	31999	319w	32·10⁹³⁴⁸-1	October 14, 2010	Ray Chandler
30	9251	16999	169w	17·10⁹²⁴⁹-1	October 14, 2010	Ray Chandler
31	9187	68999	689w	69·10⁹¹⁸⁵-1	October 14, 2010	Ray Chandler
32	9144	82999	829w	83·10⁹¹⁴²-1	October 14, 2010	Ray Chandler
33	9021	61999	619w	62·10⁹⁰¹⁹-1	October 14, 2010	Ray Chandler

Ray Chandler found 1 near-repdigit-related prime (except ru/nr/pd/qr) by using srsieve and PFGW.

Proven near-repdigit-related primes (except ru/nr/pd/qr)
	digits	flabel	wlabel	expression	when	who
92	9135		330w1	33·10⁹¹³³+1	October 14, 2010	Ray Chandler

Ray Chandler found 5 near-repdigit PRPs by using srsieve and PFGW.

Unprovable near-repdigit PRPs
	digits	flabel	wlabel	expression	when	who
123	9955	17111	171w	(154·10⁹⁹⁵³-1)/9	October 14, 2010	Ray Chandler
See primesize.txt
136	9165	31333	313w	(94·10⁹¹⁶³-1)/3	October 14, 2010	Ray Chandler

Ray Chandler found 121 quasi-repdigit PRPs by using srsieve and PFGW.

Unprovable quasi-repdigit PRPs
	digits	flabel	wlabel	expression	when	who
559	9997	74111	741w	(667·10⁹⁹⁹⁵-1)/9	October 14, 2010	Ray Chandler
See primesize.txt
713	9016	80883	808w3	(728·10⁹⁰¹⁴-53)/9	October 14, 2010	Ray Chandler

Ray Chandler found 361 near-repdigit-related PRPs (except ru/nr/pd/qr) by using srsieve and PFGW.

Unprovable near-repdigit-related PRPs (except ru/nr/pd/qr)
	digits	flabel	wlabel	expression	when	who
399	9998	69931	69w31	7·10⁹⁹⁹⁷-69	October 14, 2010	Ray Chandler
See primesize.txt
764	9004	82219	82w19	(74·10⁹⁰⁰³-29)/9	October 14, 2010	Ray Chandler

October 13, 2010

Serge Batalov found 2 near-repdigit PRPs.

Unprovable near-repdigit PRPs
	digits	flabel	wlabel	expression	when	who
17	41034	27777	27w	(25·10⁴¹⁰³³-7)/9	October 13, 2010	Serge Batalov
23	37923	31111	31w	(28·10³⁷⁹²²-1)/9	October 13, 2010	Serge Batalov

October 12, 2010

Serge Batalov found 2 quasi-repdigit PRPs.

Unprovable quasi-repdigit PRPs
	digits	flabel	wlabel	expression	when	who
40	57507	39997	39w7	4·10⁵⁷⁵⁰⁶-3	October 12, 2010	Serge Batalov
80	34889	98887	98w7	(89·10³⁴⁸⁸⁸-17)/9	October 12, 2010	Serge Batalov

October 9, 2010

Factorizations of 966...667 have been extended up to n=200. Composite numbers that appeared newly got through ECM 118 times at level 35. Most unknown factors are supposed to be greater than 10³⁰.

Ray Chandler found 10 near-repdigit primes and 6 quasi-repdigit primes by using srsieve and PFGW.

Proven near-repdigit primes
	digits	flabel	wlabel	expression	when	who
54	8968		9979w	998·10⁸⁹⁶⁵-1	October 9, 2010	Ray Chandler
55	8866	95999	959w	96·10⁸⁸⁶⁴-1	October 9, 2010	Ray Chandler
56	8845		9999929w	999993·10⁸⁸³⁹-1	October 9, 2010	Ray Chandler
57	8823		9999989w	999999·10⁸⁸¹⁷-1	October 9, 2010	Ray Chandler
59	8670		99959w	9996·10⁸⁶⁶⁶-1	October 9, 2010	Ray Chandler
60	8637	92999	929w	93·10⁸⁶³⁵-1	October 9, 2010	Ray Chandler
61	8619		9929w	993·10⁸⁶¹⁶-1	October 9, 2010	Ray Chandler
62	8526	98999	989w	99·10⁸⁵²⁴-1	October 9, 2010	Ray Chandler
64	8366		99999979w	9999998·10⁸³⁵⁹-1	October 9, 2010	Ray Chandler
65	8264		999919w	99992·10⁸²⁵⁹-1	October 9, 2010	Ray Chandler

Proven quasi-repdigit primes
	digits	flabel	wlabel	expression	when	who
21	8988	46999	469w	47·10⁸⁹⁸⁶-1	October 9, 2010	Ray Chandler
23	8786	47999	479w	48·10⁸⁷⁸⁴-1	October 9, 2010	Ray Chandler
24	8342	47999	479w	48·10⁸³⁴⁰-1	October 9, 2010	Ray Chandler
25	8331	43999	439w	44·10⁸³²⁹-1	October 9, 2010	Ray Chandler
26	8301	13999	139w	14·10⁸²⁹⁹-1	October 9, 2010	Ray Chandler
27	8064	83999	839w	84·10⁸⁰⁶²-1	October 9, 2010	Ray Chandler

Ray Chandler found 14 near-repdigit PRPs, 118 quasi-repdigit PRPs and 355 near-repdigit-related PRPs (except ru/nr/pd/qr) by using srsieve and PFGW.

Unprovable near-repdigit PRPs
	digits	flabel	wlabel	expression	when	who
122	8984	77767	7w67	(7·10⁸⁹⁸⁴-97)/9	October 9, 2010	Ray Chandler
123	8933	17111	171w	(154·10⁸⁹³¹-1)/9	October 9, 2010	Ray Chandler
See primesize.txt
143	8105	33323	3w23	(10⁸¹⁰⁵-31)/3	October 9, 2010	Ray Chandler
144	8088	77797	7w97	(7·10⁸⁰⁸⁸+173)/9	October 9, 2010	Ray Chandler

Unprovable quasi-repdigit PRPs
	digits	flabel	wlabel	expression	when	who
486	8994	47767	47w67	(43·10⁸⁹⁹³-97)/9	October 9, 2010	Ray Chandler
487	8986	97767	97w67	(88·10⁸⁹⁸⁵-97)/9	October 9, 2010	Ray Chandler
See primesize.txt
632	8006	28223	282w3	(254·10⁸⁰⁰⁴+7)/9	October 9, 2010	Ray Chandler
633	8005	59553	595w3	(536·10⁸⁰⁰³-23)/9	October 9, 2010	Ray Chandler

Unprovable near-repdigit-related PRPs (except ru/nr/pd/qr)
	digits	flabel	wlabel	expression	when	who
95	8998	36623	36w23	(11·10⁸⁹⁹⁷-131)/3	October 9, 2010	Ray Chandler
97	8995	71163	71w63	(64·10⁸⁹⁹⁴+467)/9	October 9, 2010	Ray Chandler
See primesize.txt
452	8002	57741	57w41	(52·10⁸⁰⁰¹-331)/9	October 9, 2010	Ray Chandler
453	8002		26w77	(8·10⁸⁰⁰¹+31)/3	October 9, 2010	Ray Chandler

October 6, 2010

Factorizations of 966...661 have been extended up to n=200. Composite numbers that appeared newly got through ECM 118 times at level 35. Most unknown factors are supposed to be greater than 10³⁰.

Ray Chandler found 9 near-repdigit primes by using srsieve and PFGW.

Proven near-repdigit primes
	digits	flabel	wlabel	expression	when	who
57	7951	92999	929w	93·10⁷⁹⁴⁹-1	October 6, 2010	Ray Chandler
58	7890	95999	959w	96·10⁷⁸⁸⁸-1	October 6, 2010	Ray Chandler
See primesize.txt

Ray Chandler found 10 quasi-repdigit primes by using srsieve and PFGW.

Proven quasi-repdigit primes
	digits	flabel	wlabel	expression	when	who
22	7805	38999	389w	39·10⁷⁸⁰³-1	October 6, 2010	Ray Chandler
23	7759	73999	739w	74·10⁷⁷⁵⁷-1	October 6, 2010	Ray Chandler
See primesize.txt

Ray Chandler found 1 near-repdigit-related prime by using srsieve and PFGW.

Proven near-repdigit-related primes (except ru/nr/pd/qr)
	digits	flabel	wlabel	expression	when	who
104	7962		550w1	55·10⁷⁹⁶⁰+1	October 6, 2010	Ray Chandler

Ray Chandler found 1 near-repdigit PRP by using srsieve and PFGW.

Unprovable near-repdigit PRPs
	digits	flabel	wlabel	expression	when	who
148	7128	77797	7w97	(7·10⁷¹²⁸+173)/9	October 6, 2010	Ray Chandler

Ray Chandler found 136 quasi-repdigit PRPs by using srsieve and PFGW.

Unprovable quasi-repdigit PRPs
	digits	flabel	wlabel	expression	when	who
516	7995	60777	607w	(547·10⁷⁹⁹³-7)/9	October 6, 2010	Ray Chandler
517	7993	22261	2w61	(2·10⁷⁹⁹³+349)/9	October 6, 2010	Ray Chandler
See primesize.txt

Ray Chandler found 454 near-repdigit-related PRPs by using srsieve and PFGW.

Unprovable near-repdigit-related PRPs (except ru/nr/pd/qr)
	digits	flabel	wlabel	expression	when	who
99	7994		21w33	(19·10⁷⁹⁹³+197)/9	October 6, 2010	Ray Chandler
100	7993	14493	14w93	(13·10⁷⁹⁹²+437)/9	October 6, 2010	Ray Chandler
See primesize.txt

October 4, 2010

Factorizations of 77...771 have been extended up to n=300 by Erik Branger. Composite numbers that appeared newly got through ECM 500 times at level 40. Most unknown factors are supposed to be greater than 10³⁵.

Ray Chandler found 12 near-repdigit primes by using srsieve and PFGW.

Proven near-repdigit primes
	digits	wlabel	expression	when	who
59	6978	99989w	9999·10⁶⁹⁷⁴-1	October 4, 2010	Ray Chandler
60	6905	999999929w	99999993·10⁶⁸⁹⁷-1	October 4, 2010	Ray Chandler
See primesize.txt

Ray Chandler found 19 quasi-repdigit primes by using srsieve and PFGW.

Proven quasi-repdigit primes
	digits	flabel	wlabel	expression	when	who
23	6984	10999	109w	11·10⁶⁹⁸²-1	October 4, 2010	Ray Chandler
24	6977	85999	859w	86·10⁶⁹⁷⁵-1	October 4, 2010	Ray Chandler
See primesize.txt

Ray Chandler found 162 quasi-repdigit PRPs by using srsieve and PFGW.

Unprovable quasi-repdigit PRPs
	digits	flabel	wlabel	expression	when	who
541	7000	11187	1w87	(10⁷⁰⁰⁰+683)/9	October 4, 2010	Ray Chandler
542	6998	78779	787w9	(709·10⁶⁹⁹⁶+11)/9	October 4, 2010	Ray Chandler
See primesize.txt

Ray Chandler found 1 near-repdigit-related prime by using srsieve and PFGW.

Proven near-repdigit-related primes (except ru/nr/pd/qr)
	digits	flabel	wlabel	expression	when	who
121	6456		550w1	55·10⁶⁴⁵⁴+1	October 4, 2010	Ray Chandler

Ray Chandler found 485 near-repdigit-related PRPs by using srsieve and PFGW.

Unprovable near-repdigit-related PRPs (except ru/nr/pd/qr)
	digits	flabel	wlabel	expression	when	who
11	29204	96697	96w97	(29·10²⁹²⁰³+91)/3	October 4, 2010	Ray Chandler
13	28602		226w9	(68·10²⁸⁶⁰⁰+7)/3	October 4, 2010	Ray Chandler
103	6997		880w7	88·10⁶⁹⁹⁵+7	October 4, 2010	Ray Chandler
104	6992	92243	92w43	(83·10⁶⁹⁹¹+187)/9	October 4, 2010	Ray Chandler
See primesize.txt

October 3, 2010

Factorizations of 955...557 have been extended up to n=200. Composite numbers that appeared newly got through ECM 118 times at level 35. Most unknown factors are supposed to be greater than 10³⁰.

October 1, 2010

Ray Chandler found 20 near-repdigit primes by using srsieve and PFGW.

Proven near-repdigit primes
	digits	wlabel	expression	when	who
49	12371	9999999989w	999999999·10¹²³⁶²-1	October 1, 2010	Ray Chandler
54	8735	9999999989w	999999999·10⁸⁷²⁶-1	October 1, 2010	Ray Chandler
See primesize.txt
387	744	9999999989w	999999999·10⁷³⁵-1	October 1, 2010	Ray Chandler
677	231	9999999989w	999999999·10²²²-1	October 1, 2010	Ray Chandler

Ray Chandler found 19 quasi-repdigit primes by using srsieve and PFGW.

Proven quasi-repdigit primes
	digits	flabel	wlabel	expression	when	who
24	5982	28999	289w	29·10⁵⁹⁸⁰-1	October 1, 2010	Ray Chandler
25	5980	32999	329w	33·10⁵⁹⁷⁸-1	October 1, 2010	Ray Chandler
See primesize.txt
41	5064	32999	329w	33·10⁵⁰⁶²-1	October 1, 2010	Ray Chandler
42	5015	25999	259w	26·10⁵⁰¹³-1	October 1, 2010	Ray Chandler

Ray Chandler found 213 quasi-repdigit PRPs by using srsieve and PFGW.

Unprovable quasi-repdigit PRPs
	digits	flabel	wlabel	expression	when	who
591	6001	87767	87w67	(79·10⁶⁰⁰⁰-97)/9	October 1, 2010	Ray Chandler
592	5996	77741	7w41	(7·10⁵⁹⁹⁶-331)/9	October 1, 2010	Ray Chandler
See primesize.txt
862	5009	44419	4w19	(4·10⁵⁰⁰⁹-229)/9	October 1, 2010	Ray Chandler
863	5008	40449	404w9	(364·10⁵⁰⁰⁶+41)/9	October 1, 2010	Ray Chandler

Ray Chandler found 3 near-repdigit-related primes by using srsieve and PFGW.

Proven near-repdigit-related primes (except ru/nr/pd/qr)
	digits	wlabel	expression	when	who
128	5963	550w1	55·10⁵⁹⁶¹+1	October 1, 2010	Ray Chandler
138	5681	330w1	33·10⁵⁶⁷⁹+1	October 1, 2010	Ray Chandler
141	5526	880w1	88·10⁵⁵²⁴+1	October 1, 2010	Ray Chandler

Ray Chandler found 610 near-repdigit-related PRPs by using srsieve and PFGW.

Unprovable near-repdigit-related PRPs (except ru/nr/pd/qr)
	digits	flabel	wlabel	expression	when	who
24	22357	96697	96w97	(29·10²²³⁵⁶+91)/3	October 1, 2010	Ray Chandler
107	6001	60047	60w47	6·10⁶⁰⁰⁰+47	October 1, 2010	Ray Chandler
See primesize.txt
720	5005	95569	95w69	(86·10⁵⁰⁰⁴+121)/9	October 1, 2010	Ray Chandler
721	5002	80081	80w81	8·10⁵⁰⁰¹+81	October 1, 2010	Ray Chandler

September 2010

September 30, 2010

Factorizations of 955...553 have been extended up to n=200. Composite numbers that appeared newly got through ECM 118 times at level 35. Most unknown factors are supposed to be greater than 10³⁰.

Ray Chandler proved 2 quasi-repdigit primes by using Primo 3.0.9.

Proven quasi-repdigit primes
	digits	flabel	wlabel	expression	when	who
60	2478	13337	13w7	(4·10²⁴⁷⁷+11)/3	September 30, 2010	Ray Chandler
63	2460	28887	28w7	(26·10²⁴⁵⁹-17)/9	September 30, 2010	Ray Chandler

Ray Chandler found 1 near-repdigit-related PRP by using srsieve and PFGW.

Unprovable near-repdigit-related PRPs
	digits	flabel	wlabel	expression	when	who
373	19060	76697	76w97	(23·10¹⁹⁰⁵⁹+91)/3	September 30, 2010	Ray Chandler

September 29, 2010

Ray Chandler found 1 plateau and depression PRP by using srsieve and PFGW.

Unprovable plateau and depression PRPs
	digits	flabel	wlabel	expression	when	who
7	56043	75557	75w7	(68·10⁵⁶⁰⁴²+13)/9	September 29, 2010	Ray Chandler

Ray Chandler found 29 near-repdigit-related primes by using srsieve and PFGW.

Proven near-repdigit-related primes
	digits	flabel	wlabel	expression	when	who
56	29091	96001	960w1	96·10²⁹⁰⁸⁹+1	September 29, 2010	Ray Chandler
See primesize.txt for 28 other primes in the range of 4007-4982 digits.

Ray Chandler found 982 near-repdigit-related PRPs by using srsieve and PFGW.

Unprovable near-repdigit-related PRPs
	digits	flabel	wlabel	expression	when	who
168	29139	70087	70w87	7·10²⁹¹³⁸+87	September 29, 2010	Ray Chandler
391	18469	71183	71w83	(64·10¹⁸⁴⁶⁸+647)/9	September 29, 2010	Ray Chandler
427	17215	76697	76w97	(23·10¹⁷²¹⁴+91)/3	September 29, 2010	Ray Chandler
447	16588	35503	35w03	(32·10¹⁶⁵⁸⁷-473)/9	September 29, 2010	Ray Chandler
448	16553		226w9	(68·10¹⁶⁵⁵¹+7)/3	September 29, 2010	Ray Chandler
468	16017	53327	53w27	(16·10¹⁶⁰¹⁶-19)/3	September 29, 2010	Ray Chandler
469	15995	96697	96w97	(29·10¹⁵⁹⁹⁴+91)/3	September 29, 2010	Ray Chandler
539	13937	76697	76w97	(23·10¹³⁹³⁶+91)/3	September 29, 2010	Ray Chandler
549	13683	96697	96w97	(29·10¹³⁶⁸²+91)/3	September 29, 2010	Ray Chandler
589	12560		226w9	(68·10¹²⁵⁵⁸+7)/3	September 29, 2010	Ray Chandler
See primesize.txt for 972 other PRPs in the range of 4002-4999 digits.

September 28, 2010

Factorizations of 955...551 have been extended up to n=200. Composite numbers that appeared newly got through ECM 118 times at level 35. Most unknown factors are supposed to be greater than 10³⁰.

Ray Chandler found 49 near-repdigit-related primes by using srsieve and PFGW.

Proven near-repdigit-related primes
	digits	flabel	wlabel	expression	when	who
56	28307	48001	480w1	48·10²⁸³⁰⁵+1	September 28, 2010	Ray Chandler
57	28211	81001	810w1	81·10²⁸²⁰⁹+1	September 28, 2010	Ray Chandler
58	27935	61001	610w1	61·10²⁷⁹³³+1	September 28, 2010	Ray Chandler
60	27712	91001	910w1	91·10²⁷⁷¹⁰+1	September 28, 2010	Ray Chandler
61	27638	63001	630w1	63·10²⁷⁶³⁶+1	September 28, 2010	Ray Chandler
62	27305	75001	750w1	75·10²⁷³⁰³+1	September 28, 2010	Ray Chandler
63	26242	37001	370w1	37·10²⁶²⁴⁰+1	September 28, 2010	Ray Chandler
66	25933	76001	760w1	76·10²⁵⁹³¹+1	September 28, 2010	Ray Chandler
See primesize.txt for 41 other primes in the range of 3046-3928 digits.

Ray Chandler found 1131 near-repdigit-related PRP by using srsieve and PFGW. See primesize.txt for 1131 PRPs in the range of 3002-4001 digits.

September 27, 2010

Ray Chandler found 2 near-repdigit-related primes by using srsieve and PFGW.

Proven near-repdigit-related primes
	digits	flabel	wlabel	expression	when	who
60	25600	12001	120w1	12·10²⁵⁵⁹⁸+1	September 27, 2010	Ray Chandler
61	24831	73001	730w1	73·10²⁴⁸²⁹+1	September 27, 2010	Ray Chandler

Ray Chandler found 1 near-repdigit-related PRP by using srsieve and PFGW.

Unprovable near-repdigit-related PRPs
	digits	flabel	wlabel	expression	when	who
241	24801	60091	60w91	6·10²⁴⁸⁰⁰+91	September 27, 2010	Ray Chandler

September 26, 2010

Factorizations of 944...447 have been extended up to n=200. Composite numbers that appeared newly got through ECM 118 times at level 35. Most unknown factors are supposed to be greater than 10³⁰.

Ray Chandler found 52 near-repdigit-related primes by using srsieve and PFGW.

Proven near-repdigit-related primes
	digits	flabel	wlabel	expression	when	who
63	22707	63001	630w1	63·10²²⁷⁰⁵+1	September 26, 2010	Ray Chandler
64	21904	85001	850w1	85·10²¹⁹⁰²+1	September 26, 2010	Ray Chandler
65	21847	24001	240w1	24·10²¹⁸⁴⁵+1	September 26, 2010	Ray Chandler
See primesize.txt for 49 other primes in the range of 2012-2997 digits.

Ray Chandler found 1652 near-repdigit-related PRPs by using srsieve and PFGW.

Unprovable near-repdigit-related PRPs
	digits	flabel	wlabel	expression	when	who
267	23347	70087	70w87	7·10²³³⁴⁶+87	September 26, 2010	Ray Chandler
269	23260		69w77	7·10²³²⁵⁹-23	September 26, 2010	Ray Chandler
290	22352		229w3	23·10²²³⁵⁰-7	September 26, 2010	Ray Chandler
298	21844	60091	60w91	6·10²¹⁸⁴³+91	September 26, 2010	Ray Chandler
299	21829		69w77	7·10²¹⁸²⁸-23	September 26, 2010	Ray Chandler
See primesize.txt for 1647 other PRPs in the range of 2002-3001 digits.

September 25, 2010

Ray Chandler proved 2 quasi-repdigit primes by using Primo 3.0.9.

Proven quasi-repdigit primes
	digits	flabel	wlabel	expression	when	who
63	2444	72223	72w3	(65·10²⁴⁴³+7)/9	September 25, 2010	Ray Chandler
64	2436	52227	52w7	(47·10²⁴³⁵+43)/9	September 25, 2010	Ray Chandler

Erik Branger proved 2 near-repdigit-related primes by the N+1 or N-1 test with PFGW.

Proven near-repdigit-related primes
	digits	flabel	wlabel	expression	when	who
283	3161	50051	50w51	5·10³¹⁶⁰+51	September 25, 2010	Erik Branger
396	2222	59939	59w39	6·10²²²¹-61	September 25, 2010	Erik Branger

Ray Chandler found 91 near-repdigit-related primes by using srsieve and PFGW.

Proven near-repdigit-related primes
	digits	flabel	wlabel	expression	when	who
61	21628	72001	720w1	72·10²¹⁶²⁶+1	September 25, 2010	Ray Chandler
62	21583	43001	430w1	43·10²¹⁵⁸¹+1	September 25, 2010	Ray Chandler
63	21501	73001	730w1	73·10²¹⁴⁹⁹+1	September 25, 2010	Ray Chandler
65	21450	46001	460w1	46·10²¹⁴⁴⁸+1	September 25, 2010	Ray Chandler
67	21237	94001	940w1	94·10²¹²³⁵+1	September 25, 2010	Ray Chandler
68	21184	72001	720w1	72·10²¹¹⁸²+1	September 25, 2010	Ray Chandler
70	20609	96001	960w1	96·10²⁰⁶⁰⁷+1	September 25, 2010	Ray Chandler
74	19935	84001	840w1	84·10¹⁹⁹³³+1	September 25, 2010	Ray Chandler
75	19606	25001	250w1	25·10¹⁹⁶⁰⁴+1	September 25, 2010	Ray Chandler
77	18741	82001	820w1	82·10¹⁸⁷³⁹+1	September 25, 2010	Ray Chandler
78	18734	49001	490w1	49·10¹⁸⁷³²+1	September 25, 2010	Ray Chandler
80	18211	28001	280w1	28·10¹⁸²⁰⁹+1	September 25, 2010	Ray Chandler
81	17964	13001	130w1	13·10¹⁷⁹⁶²+1	September 25, 2010	Ray Chandler
82	17871	21001	210w1	21·10¹⁷⁸⁶⁹+1	September 25, 2010	Ray Chandler
See primesize.txt for 77 other primes in the range of 1010-1985 digits.

Ray Chandler found 1 near-repdigit PRP by using srsieve and PFGW.

Unprovable near-repdigit PRPs
	digits	flabel	wlabel	expression	when	who
43	23939	61111	61w	(55·10²³⁹³⁸-1)/9	September 25, 2010	Ray Chandler

Ray Chandler found 2207 near-repdigit-related PRPs by using srsieve and PFGW.

Unprovable near-repdigit-related PRPs
	digits	flabel	wlabel	expression	when	who
331	20031	60091	60w91	6·10²⁰⁰³⁰+91	September 25, 2010	Ray Chandler
360	19171		69w77	7·10¹⁹¹⁷⁰-23	September 25, 2010	Ray Chandler
382	18331	69983	69w83	7·10¹⁸³³⁰-17	September 25, 2010	Ray Chandler
390	17972	70087	70w87	7·10¹⁷⁹⁷¹+87	September 25, 2010	Ray Chandler
See primesize.txt for 2204 other PRPs in the range of 1002-2001 digits.

September 24, 2010

Ray Chandler proved 2 quasi-repdigit primes by using Primo 3.0.9.

Proven quasi-repdigit primes
	digits	flabel	wlabel	expression	when	who
63	2432	25559	25w9	(23·10²⁴³¹+31)/9	September 24, 2010	Ray Chandler
64	2428	72223	72w3	(65·10²⁴²⁷+7)/9	September 24, 2010	Ray Chandler

September 23, 2010

Factorizations of 299...99 have been extended up to n=250. Composite numbers that appeared newly got through ECM 118 times at level 35. Most unknown factors are supposed to be greater than 10³⁰.

Ray Chandler proved 2 quasi-repdigit primes by using Primo 3.0.9.

Proven quasi-repdigit primes
	digits	flabel	wlabel	expression	when	who
63	2425	72223	72w3	(65·10²⁴²⁴+7)/9	September 23, 2010	Ray Chandler
65	2419	54441	54w1	(49·10²⁴¹⁸-31)/9	September 23, 2010	Ray Chandler

Ray Chandler found 1 unprovable near-repdigit PRP by using srsieve and PFGW.

Unprovable near-repdigit PRPs
	digits	flabel	wlabel	expression	when	who
71	16705	21111	21w	(19·10¹⁶⁷⁰⁴-1)/9	September 23, 2010	Ray Chandler

Ray Chandler found 44 near-repdigit-related primes by using srsieve and PFGW.

Proven near-repdigit-related primes
	digits	flabel	wlabel	expression	when	who
70	17507	16001	160w1	16·10¹⁷⁵⁰⁵+1	September 23, 2010	Ray Chandler
71	17503	19001	190w1	19·10¹⁷⁵⁰¹+1	September 23, 2010	Ray Chandler
72	17426	85001	850w1	85·10¹⁷⁴²⁴+1	September 23, 2010	Ray Chandler
73	17401	37001	370w1	37·10¹⁷³⁹⁹+1	September 23, 2010	Ray Chandler
74	17350	97001	970w1	97·10¹⁷³⁴⁸+1	September 23, 2010	Ray Chandler
75	17314	46001	460w1	46·10¹⁷³¹²+1	September 23, 2010	Ray Chandler
76	17109	64001	640w1	64·10¹⁷¹⁰⁷+1	September 23, 2010	Ray Chandler
77	16590	18001	180w1	18·10¹⁶⁵⁸⁸+1	September 23, 2010	Ray Chandler
78	16414	61001	610w1	61·10¹⁶⁴¹²+1	September 23, 2010	Ray Chandler
79	16159	52001	520w1	52·10¹⁶¹⁵⁷+1	September 23, 2010	Ray Chandler
81	16123	19001	190w1	19·10¹⁶¹²¹+1	September 23, 2010	Ray Chandler
82	15874	46001	460w1	46·10¹⁵⁸⁷²+1	September 23, 2010	Ray Chandler
86	15572	16001	160w1	16·10¹⁵⁵⁷⁰+1	September 23, 2010	Ray Chandler
87	15476	93001	930w1	93·10¹⁵⁴⁷⁴+1	September 23, 2010	Ray Chandler
88	14972	91001	910w1	91·10¹⁴⁹⁷⁰+1	September 23, 2010	Ray Chandler
89	14472	28001	280w1	28·10¹⁴⁴⁷⁰+1	September 23, 2010	Ray Chandler
90	14433	46001	460w1	46·10¹⁴⁴³¹+1	September 23, 2010	Ray Chandler
91	14360	85001	850w1	85·10¹⁴³⁵⁸+1	September 23, 2010	Ray Chandler
92	14333	58001	580w1	58·10¹⁴³³¹+1	September 23, 2010	Ray Chandler
93	14031	19001	190w1	19·10¹⁴⁰²⁹+1	September 23, 2010	Ray Chandler
94	13962	63001	630w1	63·10¹³⁹⁶⁰+1	September 23, 2010	Ray Chandler
95	13959	13001	130w1	13·10¹³⁹⁵⁷+1	September 23, 2010	Ray Chandler
96	13930	84001	840w1	84·10¹³⁹²⁸+1	September 23, 2010	Ray Chandler
97	13589	31001	310w1	31·10¹³⁵⁸⁷+1	September 23, 2010	Ray Chandler
100	13161		990w1	99·10¹³¹⁵⁹+1	September 23, 2010	Ray Chandler
101	12878	91001	910w1	91·10¹²⁸⁷⁶+1	September 23, 2010	Ray Chandler
102	12811	28001	280w1	28·10¹²⁸⁰⁹+1	September 23, 2010	Ray Chandler
103	12803	61001	610w1	61·10¹²⁸⁰¹+1	September 23, 2010	Ray Chandler
104	12137	18001	180w1	18·10¹²¹³⁵+1	September 23, 2010	Ray Chandler
105	11883	91001	910w1	91·10¹¹⁸⁸¹+1	September 23, 2010	Ray Chandler
106	11868	51001	510w1	51·10¹¹⁸⁶⁶+1	September 23, 2010	Ray Chandler
108	11597	75001	750w1	75·10¹¹⁵⁹⁵+1	September 23, 2010	Ray Chandler
109	11548	72001	720w1	72·10¹¹⁵⁴⁶+1	September 23, 2010	Ray Chandler
111	11215	24001	240w1	24·10¹¹²¹³+1	September 23, 2010	Ray Chandler
113	10969	21001	210w1	21·10¹⁰⁹⁶⁷+1	September 23, 2010	Ray Chandler
114	10864	39001	390w1	39·10¹⁰⁸⁶²+1	September 23, 2010	Ray Chandler
115	10838	49001	490w1	49·10¹⁰⁸³⁶+1	September 23, 2010	Ray Chandler
116	10823	84001	840w1	84·10¹⁰⁸²¹+1	September 23, 2010	Ray Chandler
117	10584	81001	810w1	81·10¹⁰⁵⁸²+1	September 23, 2010	Ray Chandler
119	10451	21001	210w1	21·10¹⁰⁴⁴⁹+1	September 23, 2010	Ray Chandler
120	10372	67001	670w1	67·10¹⁰³⁷⁰+1	September 23, 2010	Ray Chandler
121	10327	93001	930w1	93·10¹⁰³²⁵+1	September 23, 2010	Ray Chandler
122	10149	19001	190w1	19·10¹⁰¹⁴⁷+1	September 23, 2010	Ray Chandler
123	10015	31001	310w1	31·10¹⁰⁰¹³+1	September 23, 2010	Ray Chandler

Ray Chandler found 6 unprovable near-repdigit-related PRPs by using srsieve and PFGW.

Unprovable near-repdigit-related PRPs
	digits	flabel	wlabel	expression	when	who
414	17142	70087	70w87	7·10¹⁷¹⁴¹+87	September 23, 2010	Ray Chandler
512	14122		229w3	23·10¹⁴¹²⁰-7	September 23, 2010	Ray Chandler
552	13027	70087	70w87	7·10¹³⁰²⁶+87	September 23, 2010	Ray Chandler
562	12775		69w77	7·10¹²⁷⁷⁴-23	September 23, 2010	Ray Chandler
647	10675		229w3	23·10¹⁰⁶⁷³-7	September 23, 2010	Ray Chandler
668	10350		229w3	23·10¹⁰³⁴⁸-7	September 23, 2010	Ray Chandler

September 22, 2010

Ray Chandler proved (73·10²⁴¹⁰+71)/9 is prime by using Primo 3.0.9.

September 21, 2010

Factorizations of 944...443 have been extended up to n=200. Composite numbers that appeared newly got through ECM 118 times at level 35. Most unknown factors are supposed to be greater than 10³⁰.

Ray Chandler found an unprovable plateau and depression PRP.

Unprovable plateau and depression PRPs
	digits	flabel	wlabel	expression	when	who
7	51779	72227	72w7	(65·10⁵¹⁷⁷⁸+43)/9	September 21, 2010	Ray Chandler

Ray Chandler proved (31·10²³⁷⁸+41)/9, (31·10²⁴⁰⁶+41)/9 and (19·10²³⁹⁸-7)/3 are prime by using Primo 3.0.9.

Ray Chandler found a near-repdigit PRP.

Unprovable near-repdigit PRPs
	digits	flabel	wlabel	expression	when	who
106	10297	21111	21w	(19·10¹⁰²⁹⁶-1)/9	September 21, 2010	Ray Chandler

September 20, 2010

Ray Chandler proved (83·10²³⁴⁹-11)/9 and (17·10²³⁷⁴-53)/9 are prime by using Primo 3.0.9.

Ray Chandler found two unprovable quasi-repdigit PRPs.

Unprovable quasi-repdigit PRPs
	digits	flabel	wlabel	expression	when	who
104	28645	43331	43w1	(13·10²⁸⁶⁴⁴-7)/3	September 20, 2010	Ray Chandler
145	25714	43331	43w1	(13·10²⁵⁷¹³-7)/3	September 20, 2010	Ray Chandler

Ray Chandler found an unprovable plateau and depression PRP.

Unprovable plateau and depression PRPs
	digits	flabel	wlabel	expression	when	who
7	51009	37773	37w3	(34·10⁵¹⁰⁰⁸-43)/9	September 20, 2010	Ray Chandler

September 19, 2010

Ray Chandler proved (61·10²³¹⁶+11)/9, 4·10²³²³+7 and (43·10²³⁴⁰-61)/9 are prime by using Primo 3.0.9.

September 18, 2010

Ray Chandler found two unprovable quasi-repdigit PRPs.

Unprovable quasi-repdigit PRPs
	digits	flabel	wlabel	expression	when	who
94	29455	81113	81w3	(73·10²⁹⁴⁵⁴+17)/9	September 18, 2010	Ray Chandler
97	29337	65553	65w3	(59·10²⁹³³⁶-23)/9	September 18, 2010	Ray Chandler

Ray Chandler proved (52·10²¹⁹⁹+11)/9, (41·10²²¹⁴-23)/9 and (58·10²²⁹⁵-13)/9 are prime by using Primo 3.0.9.

September 17, 2010

Ray Chandler found two unprovable quasi-repdigit PRPs.

Unprovable quasi-repdigit PRPs
	digits	flabel	wlabel	expression	when	who
107	28099	58881	58w1	(53·10²⁸⁰⁹⁸-71)/9	September 17, 2010	Ray Chandler
111	27752	57779	57w9	(52·10²⁷⁷⁵¹+11)/9	September 17, 2010	Ray Chandler

Ray Chandler proved (74·10²¹⁹⁸+43)/9 is prime by using Primo 3.0.9.

Ray Chandler successfully proved (89·10⁴⁸⁸⁵-17)/9, a 4886-digit number, is prime by using Primo 3.0.9. It started on August 24, 2010 and took 425 hours. Congratulations!

September 16, 2010

Ray Chandler found 2 unprovable quasi-repdigit PRPs.

Unprovable quasi-repdigit PRPs
	digits	flabel	wlabel	expression	when	who
121	26839	67773	67w3	(61·10²⁶⁸³⁸-43)/9	September 16, 2010	Ray Chandler
185	21689	64447	64w7	(58·10²¹⁶⁸⁸+23)/9	September 16, 2010	Ray Chandler

Ray Chandler proved 8·10²¹⁹⁴-7 is prime by using Primo 3.0.9.

September 15, 2010

Ray Chandler found 5 unprovable quasi-repdigit PRPs.

Unprovable quasi-repdigit PRPs
	digits	flabel	wlabel	expression	when	who
126	26430	81117	81w7	(73·10²⁶⁴²⁹+53)/9	September 15, 2010	Ray Chandler
127	26420	65551	65w1	(59·10²⁶⁴¹⁹-41)/9	September 15, 2010	Ray Chandler
131	26120	81113	81w3	(73·10²⁶¹¹⁹+17)/9	September 15, 2010	Ray Chandler
132	26104	51113	51w3	(46·10²⁶¹⁰³+17)/9	September 15, 2010	Ray Chandler
316	14888	68887	68w7	(62·10¹⁴⁸⁸⁷-17)/9	September 15, 2010	Ray Chandler

September 14, 2010

Ray Chandler found 7 unprovable quasi-repdigit PRPs.

Unprovable quasi-repdigit PRPs
	digits	flabel	wlabel	expression	when	who
95	29370	72221	72w1	(65·10²⁹³⁶⁹-11)/9	September 14, 2010	Ray Chandler
98	29239	75553	75w3	(68·10²⁹²³⁸-23)/9	September 14, 2010	Ray Chandler
139	25150	87773	87w3	(79·10²⁵¹⁴⁹-43)/9	September 14, 2010	Ray Chandler
144	24949	81113	81w3	(73·10²⁴⁹⁴⁸+17)/9	September 14, 2010	Ray Chandler
149	24398	82229	82w9	(74·10²⁴³⁹⁷+61)/9	September 14, 2010	Ray Chandler
152	23729	65551	65w1	(59·10²³⁷²⁸-41)/9	September 14, 2010	Ray Chandler
153	23649	61119	61w9	(55·10²³⁶⁴⁸+71)/9	September 14, 2010	Ray Chandler

Ray Chandler proved (23·10²¹⁹²-17)/3 is prime by using Primo 3.0.9.

September 13, 2010

Ray Chandler found 5 unprovable quasi-repdigit PRPs.

Unprovable quasi-repdigit PRPs
	digits	flabel	wlabel	expression	when	who
126	26011	75553	75w3	(68·10²⁶⁰¹⁰-23)/9	September 13, 2010	Ray Chandler
147	23772	85553	85w3	(77·10²³⁷⁷¹-23)/9	September 13, 2010	Ray Chandler
160	22939	54447	54w7	(49·10²²⁹³⁸+23)/9	September 13, 2010	Ray Chandler
162	22802	52223	52w3	(47·10²²⁸⁰¹+7)/9	September 13, 2010	Ray Chandler
165	22683	68883	68w3	(62·10²²⁶⁸²-53)/9	September 13, 2010	Ray Chandler

Ray Chandler proved (16·10²¹⁷⁹+17)/3 is prime by using Primo 3.0.9.

September 12, 2010

Ray Chandler found 5 unprovable quasi-repdigit PRPs.

Unprovable quasi-repdigit PRPs
	digits	flabel	wlabel	expression	when	who
173	21428	82223	82w3	(74·10²¹⁴²⁷+7)/9	September 12, 2010	Ray Chandler
174	21320	81113	81w3	(73·10²¹³¹⁹+17)/9	September 12, 2010	Ray Chandler
180	20843	65551	65w1	(59·10²⁰⁸⁴²-41)/9	September 12, 2010	Ray Chandler
187	20103	58887	58w7	(53·10²⁰¹⁰²-17)/9	September 12, 2010	Ray Chandler
195	19747	54441	54w1	(49·10¹⁹⁷⁴⁶-31)/9	September 12, 2010	Ray Chandler

September 11, 2010

Ray Chandler found 6 unprovable quasi-repdigit PRPs.

Unprovable quasi-repdigit PRPs
	digits	flabel	wlabel	expression	when	who
94	29419	76669	76w9	(23·10²⁹⁴¹⁸+7)/3	September 11, 2010	Ray Chandler
169	21631	74441	74w1	(67·10²¹⁶³⁰-31)/9	September 11, 2010	Ray Chandler
198	19626	61113	61w3	(55·10¹⁹⁶²⁵+17)/9	September 11, 2010	Ray Chandler
199	19561	67773	67w3	(61·10¹⁹⁵⁶⁰-43)/9	September 11, 2010	Ray Chandler
210	18734	65551	65w1	(59·10¹⁸⁷³³-41)/9	September 11, 2010	Ray Chandler
211	18694	58881	58w1	(53·10¹⁸⁶⁹³-71)/9	September 11, 2010	Ray Chandler

September 10, 2010

Ray Chandler found 25 unprovable quasi-repdigit PRPs.

Unprovable quasi-repdigit PRPs
	digits	flabel	wlabel	expression	when	who
101	28612	76669	76w9	(23·10²⁸⁶¹¹+7)/3	September 10, 2010	Ray Chandler
184	20075	74449	74w9	(67·10²⁰⁰⁷⁴+41)/9	September 10, 2010	Ray Chandler
193	19703	63331	63w1	(19·10¹⁹⁷⁰²-7)/3	September 10, 2010	Ray Chandler
200	19496	75553	75w3	(68·10¹⁹⁴⁹⁵-23)/9	September 10, 2010	Ray Chandler
212	18611	74441	74w1	(67·10¹⁸⁶¹⁰-31)/9	September 10, 2010	Ray Chandler
214	18268	84443	84w3	(76·10¹⁸²⁶⁷-13)/9	September 10, 2010	Ray Chandler
218	17939	81113	81w3	(73·10¹⁷⁹³⁸+17)/9	September 10, 2010	Ray Chandler
220	17803	84441	84w1	(76·10¹⁷⁸⁰²-31)/9	September 10, 2010	Ray Chandler
230	17500	64443	64w3	(58·10¹⁷⁴⁹⁹-13)/9	September 10, 2010	Ray Chandler
236	17263	84441	84w1	(76·10¹⁷²⁶²-31)/9	September 10, 2010	Ray Chandler
239	17165	52223	52w3	(47·10¹⁷¹⁶⁴+7)/9	September 10, 2010	Ray Chandler
244	16854	52227	52w7	(47·10¹⁶⁸⁵³+43)/9	September 10, 2010	Ray Chandler
249	16677	65553	65w3	(59·10¹⁶⁶⁷⁶-23)/9	September 10, 2010	Ray Chandler
260	16175	81119	81w9	(73·10¹⁶¹⁷⁴+71)/9	September 10, 2010	Ray Chandler
261	16163	57773	57w3	(52·10¹⁶¹⁶²-43)/9	September 10, 2010	Ray Chandler
264	16049	81119	81w9	(73·10¹⁶⁰⁴⁸+71)/9	September 10, 2010	Ray Chandler
278	15633	56663	56w3	(17·10¹⁵⁶³²-11)/3	September 10, 2010	Ray Chandler
279	15606	54447	54w7	(49·10¹⁵⁶⁰⁵+23)/9	September 10, 2010	Ray Chandler
281	15531	54447	54w7	(49·10¹⁵⁵³⁰+23)/9	September 10, 2010	Ray Chandler
286	15115	52227	52w7	(47·10¹⁵¹¹⁴+43)/9	September 10, 2010	Ray Chandler
287	15098	62221	62w1	(56·10¹⁵⁰⁹⁷-11)/9	September 10, 2010	Ray Chandler
309	13976	56663	56w3	(17·10¹³⁹⁷⁵-11)/3	September 10, 2010	Ray Chandler
347	12392	63331	63w1	(19·10¹²³⁹¹-7)/3	September 10, 2010	Ray Chandler
348	12389	63331	63w1	(19·10¹²³⁸⁸-7)/3	September 10, 2010	Ray Chandler
404	10542	53339	53w9	(16·10¹⁰⁵⁴¹+17)/3	September 10, 2010	Ray Chandler

September 9, 2010

Ray Chandler found 35 unprovable quasi-repdigit PRPs.

Unprovable quasi-repdigit PRPs
	digits	flabel	wlabel	expression	when	who
168	21594	86669	86w9	(26·10²¹⁵⁹³+7)/3	September 9, 2010	Ray Chandler
227	17101	78883	78w3	(71·10¹⁷¹⁰⁰-53)/9	September 9, 2010	Ray Chandler
238	16525	75553	75w3	(68·10¹⁶⁵²⁴-23)/9	September 9, 2010	Ray Chandler
244	16213	72223	72w3	(65·10¹⁶²¹²+7)/9	September 9, 2010	Ray Chandler
255	15926	72223	72w3	(65·10¹⁵⁹²⁵+7)/9	September 9, 2010	Ray Chandler
270	15138	74449	74w9	(67·10¹⁵¹³⁷+41)/9	September 9, 2010	Ray Chandler
274	15085	87779	87w9	(79·10¹⁵⁰⁸⁴+11)/9	September 9, 2010	Ray Chandler
279	14708	73339	73w9	(22·10¹⁴⁷⁰⁷+17)/3	September 9, 2010	Ray Chandler
291	14164	65551	65w1	(59·10¹⁴¹⁶³-41)/9	September 9, 2010	Ray Chandler
295	13948	68887	68w7	(62·10¹³⁹⁴⁷-17)/9	September 9, 2010	Ray Chandler
296	13945	78883	78w3	(71·10¹³⁹⁴⁴-53)/9	September 9, 2010	Ray Chandler
298	13894	78883	78w3	(71·10¹³⁸⁹³-53)/9	September 9, 2010	Ray Chandler
301	13742	75551	75w1	(68·10¹³⁷⁴¹-41)/9	September 9, 2010	Ray Chandler
302	13712	82229	82w9	(74·10¹³⁷¹¹+61)/9	September 9, 2010	Ray Chandler
308	13395	54441	54w1	(49·10¹³³⁹⁴-31)/9	September 9, 2010	Ray Chandler
313	13111	54449	54w9	(49·10¹³¹¹⁰+41)/9	September 9, 2010	Ray Chandler
314	13097	82223	82w3	(74·10¹³⁰⁹⁶+7)/9	September 9, 2010	Ray Chandler
334	12253	74441	74w1	(67·10¹²²⁵²-31)/9	September 9, 2010	Ray Chandler
338	12129	75551	75w1	(68·10¹²¹²⁸-41)/9	September 9, 2010	Ray Chandler
339	12010	58881	58w1	(53·10¹²⁰⁰⁹-71)/9	September 9, 2010	Ray Chandler
342	11841	85559	85w9	(77·10¹¹⁸⁴⁰+31)/9	September 9, 2010	Ray Chandler
343	11778	61119	61w9	(55·10¹¹⁷⁷⁷+71)/9	September 9, 2010	Ray Chandler
344	11701	61113	61w3	(55·10¹¹⁷⁰⁰+17)/9	September 9, 2010	Ray Chandler
347	11658	64443	64w3	(58·10¹¹⁶⁵⁷-13)/9	September 9, 2010	Ray Chandler
348	11656	76661	76w1	(23·10¹¹⁶⁵⁵-17)/3	September 9, 2010	Ray Chandler
351	11551	57771	57w1	(52·10¹¹⁵⁵⁰-61)/9	September 9, 2010	Ray Chandler
354	11399	71119	71w9	(64·10¹¹³⁹⁸+71)/9	September 9, 2010	Ray Chandler
362	11117	52229	52w9	(47·10¹¹¹¹⁶+61)/9	September 9, 2010	Ray Chandler
366	11023	64443	64w3	(58·10¹¹⁰²²-13)/9	September 9, 2010	Ray Chandler
371	10837	62221	62w1	(56·10¹⁰⁸³⁶-11)/9	September 9, 2010	Ray Chandler
377	10735	57771	57w1	(52·10¹⁰⁷³⁴-61)/9	September 9, 2010	Ray Chandler
380	10705	67779	67w9	(61·10¹⁰⁷⁰⁴+11)/9	September 9, 2010	Ray Chandler
384	10610	72221	72w1	(65·10¹⁰⁶⁰⁹-11)/9	September 9, 2010	Ray Chandler
388	10544	75551	75w1	(68·10¹⁰⁵⁴³-41)/9	September 9, 2010	Ray Chandler
394	10284	75551	75w1	(68·10¹⁰²⁸³-41)/9	September 9, 2010	Ray Chandler

September 8, 2010

Ray Chandler proved (76·10²¹⁷⁰-13)/9 is prime by using Primo 3.0.9.

Ray Chandler found 10 unprovable quasi-repdigit PRPs.

Unprovable quasi-repdigit PRPs
	digits	flabel	wlabel	expression	when	who
161	22096	92227	92w7	(83·10²²⁰⁹⁵+43)/9	September 8, 2010	Ray Chandler
194	19271	92227	92w7	(83·10¹⁹²⁷⁰+43)/9	September 8, 2010	Ray Chandler
213	17555	92221	92w1	(83·10¹⁷⁵⁵⁴-11)/9	September 8, 2010	Ray Chandler
219	17318	86663	86w3	(26·10¹⁷³¹⁷-11)/3	September 8, 2010	Ray Chandler
237	16295	86663	86w3	(26·10¹⁶²⁹⁴-11)/3	September 8, 2010	Ray Chandler
240	16037	92221	92w1	(83·10¹⁶⁰³⁶-11)/9	September 8, 2010	Ray Chandler
250	15727	92223	92w3	(83·10¹⁵⁷²⁶+7)/9	September 8, 2010	Ray Chandler
260	14876	92227	92w7	(83·10¹⁴⁸⁷⁵+43)/9	September 8, 2010	Ray Chandler
318	11693	92221	92w1	(83·10¹¹⁶⁹²-11)/9	September 8, 2010	Ray Chandler
335	11116	87773	87w3	(79·10¹¹¹¹⁵-43)/9	September 8, 2010	Ray Chandler

September 7, 2010

Ray Chandler proved (83·10²¹⁵⁷+43)/9, 5·10²¹⁵⁷-7 and (68·10²¹⁶²-41)/9 are prime by using Primo 3.0.9.

Ray Chandler found four unprovable quasi-repdigit PRPs.

Unprovable quasi-repdigit PRPs
	digits	flabel	wlabel	expression	when	who
98	28768	93337	93w7	(28·10²⁸⁷⁶⁷+11)/3	September 7, 2010	Ray Chandler
106	27736	93337	93w7	(28·10²⁷⁷³⁵+11)/3	September 7, 2010	Ray Chandler
112	27110	93337	93w7	(28·10²⁷¹⁰⁹+11)/3	September 7, 2010	Ray Chandler
162	21923	94441	94w1	(85·10²¹⁹²²-31)/9	September 7, 2010	Ray Chandler

Erik Branger found 32 unprovable quasi-repdigit PRPs.

Unprovable quasi-repdigit PRPs
	digits	flabel	wlabel	expression	when	who
94	29307	45557	45w7	(41·10²⁹³⁰⁶+13)/9	September 7, 2010	Erik Branger
99	28628	46663	46w3	(14·10²⁸⁶²⁷-11)/3	September 7, 2010	Erik Branger
100	28576	45553	45w3	(41·10²⁸⁵⁷⁵-23)/9	September 7, 2010	Erik Branger
105	27744	43339	43w9	(13·10²⁷⁷⁴³+17)/3	September 7, 2010	Erik Branger
108	27307	48883	48w3	(44·10²⁷³⁰⁶-53)/9	September 7, 2010	Erik Branger
113	27061	46661	46w1	(14·10²⁷⁰⁶⁰-17)/3	September 7, 2010	Erik Branger
114	26981	45559	45w9	(41·10²⁶⁹⁸⁰+31)/9	September 7, 2010	Erik Branger
128	25849	43337	43w7	(13·10²⁵⁸⁴⁸+11)/3	September 7, 2010	Erik Branger
144	23415	46663	46w3	(14·10²³⁴¹⁴-11)/3	September 7, 2010	Erik Branger
150	22961	41113	41w3	(37·10²²⁹⁶⁰+17)/9	September 7, 2010	Erik Branger
165	21650	42227	42w7	(38·10²¹⁶⁴⁹+43)/9	September 7, 2010	Erik Branger
177	20235	41119	41w9	(37·10²⁰²³⁴+71)/9	September 7, 2010	Erik Branger
179	20066	41117	41w7	(37·10²⁰⁰⁶⁵+53)/9	September 7, 2010	Erik Branger
189	19673	41117	41w7	(37·10¹⁹⁶⁷²+53)/9	September 7, 2010	Erik Branger
195	18866	43337	43w7	(13·10¹⁸⁸⁶⁵+11)/3	September 7, 2010	Erik Branger
217	17222	41117	41w7	(37·10¹⁷²²¹+53)/9	September 7, 2010	Erik Branger
220	16895	45553	45w3	(41·10¹⁶⁸⁹⁴-23)/9	September 7, 2010	Erik Branger
223	16769	46661	46w1	(14·10¹⁶⁷⁶⁸-17)/3	September 7, 2010	Erik Branger
227	16629	48887	48w7	(44·10¹⁶⁶²⁸-17)/9	September 7, 2010	Erik Branger
230	16441	45553	45w3	(41·10¹⁶⁴⁴⁰-23)/9	September 7, 2010	Erik Branger
233	16097	42227	42w7	(38·10¹⁶⁰⁹⁶+43)/9	September 7, 2010	Erik Branger
238	15891	43339	43w9	(13·10¹⁵⁸⁹⁰+17)/3	September 7, 2010	Erik Branger
258	14462	46667	46w7	(14·10¹⁴⁴⁶¹+1)/3	September 7, 2010	Erik Branger
278	13052	41113	41w3	(37·10¹³⁰⁵¹+17)/9	September 7, 2010	Erik Branger
289	12725	42223	42w3	(38·10¹²⁷²⁴+7)/9	September 7, 2010	Erik Branger
298	11912	42227	42w7	(38·10¹¹⁹¹¹+43)/9	September 7, 2010	Erik Branger
301	11583	41119	41w9	(37·10¹¹⁵⁸²+71)/9	September 7, 2010	Erik Branger
302	11527	45559	45w9	(41·10¹¹⁵²⁶+31)/9	September 7, 2010	Erik Branger
317	10833	43337	43w7	(13·10¹⁰⁸³²+11)/3	September 7, 2010	Erik Branger
325	10657	42223	42w3	(38·10¹⁰⁶⁵⁶+7)/9	September 7, 2010	Erik Branger
326	10640	46667	46w7	(14·10¹⁰⁶³⁹+1)/3	September 7, 2010	Erik Branger
328	10580	41117	41w7	(37·10¹⁰⁵⁷⁹+53)/9	September 7, 2010	Erik Branger

September 6, 2010

Ray Chandler proved (49·10²¹⁴⁷-31)/9 is prime by using Primo 3.0.9.

Ray Chandler found four unprovable quasi-repdigit PRPs.

Unprovable quasi-repdigit PRPs
	digits	flabel	wlabel	expression	when	who
92	29932	98887	98w7	(89·10²⁹⁹³¹-17)/9	September 6, 2010	Ray Chandler
183	17960	96667	96w7	(29·10¹⁷⁹⁵⁹+1)/3	September 6, 2010	Ray Chandler
218	15533	96667	96w7	(29·10¹⁵⁵³²+1)/3	September 6, 2010	Ray Chandler
293	10559	96667	96w7	(29·10¹⁰⁵⁵⁸+1)/3	September 6, 2010	Ray Chandler

September 5, 2010

Ray Chandler proved (41·10²¹³⁹-23)/9 and 8·10²¹⁴⁶-7 are prime by using Primo 3.0.9.

Ray Chandler found an unprovable quasi-repdigit PRP.

Unprovable quasi-repdigit PRPs
	digits	flabel	wlabel	expression	when	who
59	40169	49991	49w1	5·10⁴⁰¹⁶⁸-9	September 5, 2010	Ray Chandler

September 4, 2010

Ray Chandler proved (23·10²¹³²+7)/3 and (55·10²¹³⁸+71)/9 are prime by using Primo 3.0.9.

Erik Branger proved 257 prime numbers, listed in the List of near-repdigit-related prime numbers, up to 1600-digit by using Primo 3.0.9.

September 3, 2010

Ray Chandler proved (47·10²¹⁰³-11)/9 and (22·10²¹⁰⁵+17)/3 are prime by using Primo 3.0.9.

Ray Chandler found two unprovable quasi-repdigit PRPs.

Unprovable quasi-repdigit PRPs
	digits	flabel	wlabel	expression	when	who
98	27770	49991	49w1	5·10²⁷⁷⁶⁹-9	September 3, 2010	Ray Chandler
119	25055	49991	49w1	5·10²⁵⁰⁵⁴-9	September 3, 2010	Ray Chandler

September 2, 2010

Ray Chandler proved (64·10²⁰⁸⁴+71)/9 is prime by using Primo 3.0.9.

Ray Chandler found an unprovable quasi-repdigit PRP.

Unprovable quasi-repdigit PRPs
	digits	flabel	wlabel	expression	when	who
62	39267	40009	40w9	4·10³⁹²⁶⁶+9	September 2, 2010	Ray Chandler

September 1, 2010

Ray Chandler proved (74·10²⁰⁵³+7)/9, (58·10²⁰⁶³+23)/9 and (67·10²⁰⁶⁴-31)/9 are prime by using Primo 3.0.9.

August 2010

August 31, 2010

Ray Chandler found an unprovable quasi-repdigit PRP.

Unprovable quasi-repdigit PRPs
	digits	flabel	wlabel	expression	when	who
79	34415	40009	40w9	4·10³⁴⁴¹⁴+9	August 31, 2010	Ray Chandler

August 30, 2010

Ray Chandler found that 4·10³²⁸³⁵+1 is prime.

Erik Branger proved 972 prime numbers, listed in the List of near-repdigit-related prime numbers, up to 1000-digit by using Primo 3.0.9.

August 29, 2010

Ray Chandler found two unprovable quasi-repdigit PRPs.

Unprovable quasi-repdigit PRPs
	digits	flabel	wlabel	expression	when	who
147	21062	40003	40w3	4·10²¹⁰⁶¹+3	August 29, 2010	Ray Chandler
268	11294	40003	40w3	4·10¹¹²⁹³+3	August 29, 2010	Ray Chandler

August 27, 2010

Maksym Voznyy's web page have been moved. The new page is: http://individual.utoronto.ca/mvoznyy/

Serge Batalov found six unprovable quasi-repdigit PRPs.

Unprovable quasi-repdigit PRPs
	digits	flabel	wlabel	expression	when	who
57	41657	96661	96w1	(29·10⁴¹⁶⁵⁶-17)/3	August 27, 2010	Serge Batalov
68	37915	96661	96w1	(29·10³⁷⁹¹⁴-17)/3	August 27, 2010	Serge Batalov
168	19037	97771	97w1	(88·10¹⁹⁰³⁶-61)/9	August 27, 2010	Serge Batalov
189	17239	97773	97w3	(88·10¹⁷²³⁸-43)/9	August 27, 2010	Serge Batalov
232	13648	97773	97w3	(88·10¹³⁶⁴⁷-43)/9	August 27, 2010	Serge Batalov
254	12539	97771	97w1	(88·10¹²⁵³⁸-61)/9	August 27, 2010	Serge Batalov

August 25, 2010

Ray Chandler found two unprovable quasi-repdigit PRPs.

Unprovable quasi-repdigit PRPs
	digits	flabel	wlabel	expression	when	who
233	13189	98887	98w7	(89·10¹³¹⁸⁸-17)/9	August 25, 2010	Ray Chandler
240	12952	98887	98w7	(89·10¹²⁹⁵¹-17)/9	August 25, 2010	Ray Chandler

August 24, 2010

Sean A. Irvine found (79·10¹⁶⁸²⁴-61)/9 was PRP on September 2009. He reported it to OEIS at that time. I'm sorry that I neglected to collect it.

Unprovable quasi-repdigit PRPs
	digits	flabel	wlabel	expression	when	who
188	16825	87771	87w1	(79·10¹⁶⁸²⁴-61)/9	September 10, 2009	Sean A. Irvine

August 22, 2010

Erik Branger proved that 9·10²⁸¹⁷-91, 6·10¹³²¹-61 and 5·10⁹⁸⁵-51 are prime by N+1 test. primesize.txt was updated.

August 21, 2010

Lionel Debroux proved that 10²⁰⁰²-99 is prime by using Primo. primesize.txt was updated. NOTE: N-1 test can be used for this number.

Erik Branger proved that 2·10³⁶¹²-3 is prime by N+1 test.

August 18, 2010

Serge Batalov found three unprovable quasi-repdigit PRPs.

Unprovable quasi-repdigit PRPs
	digits	flabel	wlabel	expression	when	who
125	23347	95551	95w1	(86·10²³³⁴⁶-41)/9	August 18, 2010	Serge Batalov
170	18610	95551	95w1	(86·10¹⁸⁶⁰⁹-41)/9	August 18, 2010	Serge Batalov
229	13480	95551	95w1	(86·10¹³⁴⁷⁹-41)/9	August 18, 2010	Serge Batalov

August 17, 2010

Serge Batalov found two unprovable quasi-repdigit PRPs.

Unprovable quasi-repdigit PRPs
	digits	flabel	wlabel	expression	when	who
118	24862	98881	98w1	(89·10²⁴⁸⁶¹-71)/9	August 17, 2010	Serge Batalov
192	16351	98883	98w3	(89·10¹⁶³⁵⁰-53)/9	August 17, 2010	Serge Batalov

August 16, 2010

Serge Batalov found two unprovable quasi-repdigit PRPs.

Unprovable quasi-repdigit PRPs
	digits	flabel	wlabel	expression	when	who
117	24888	95553	95w3	(86·10²⁴⁸⁸⁷-23)/9	August 16, 2010	Serge Batalov
142	21559	94443	94w3	(85·10²¹⁵⁵⁸-13)/9	August 16, 2010	Serge Batalov

August 15, 2010

Serge Batalov found two unprovable quasi-repdigit PRPs.

Unprovable quasi-repdigit PRPs
	digits	flabel	wlabel	expression	when	who
183	16785	94447	94w7	(85·10¹⁶⁷⁸⁴+23)/9	August 15, 2010	Serge Batalov
248	11391	94443	94w3	(85·10¹¹³⁹⁰-13)/9	August 15, 2010	Serge Batalov

August 13, 2010

Serge Batalov found an unprovable quasi-repdigit PRP.

Unprovable quasi-repdigit PRPs
	digits	flabel	wlabel	expression	when	who
168	17865	94441	94w1	(85·10¹⁷⁸⁶⁴-31)/9	August 13, 2010	Serge Batalov

August 12, 2010

Factorizations of 944...441 have been extended up to n=200. Composite numbers that appeared newly have passed 118 times ECM runs at level 35. Unknown factors have probably 30 digits or more.

July 2010

July 28, 2010

Markus Tervooren found an unprovable near-repdigit PRP.

Unprovable near-repdigit PRPs
	digits	flabel	wlabel	expression	when	who
5	87720	99997	9w7	10⁸⁷⁷²⁰-3	July 28, 2010	Markus Tervooren

July 25, 2010

Factorizations of 933...337 have been extended up to n=200. Composite numbers that appeared newly have passed 118 times ECM runs at level 35. Unknown factors have probably 30 digits or more.

Serge Batalov broke his own largest known unprovable quasi-repdigit PRP record again. Congratulations!

Unprovable quasi-repdigit PRPs
	digits	flabel	wlabel	expression	when	who
1	198530	58889	58w9	(53·10¹⁹⁸⁵²⁹+1)/9	July 25, 2010	Serge Batalov

July 24, 2010

Serge Batalov found the largest known unprovable quasi-repdigit PRP in our tables again. Congratulations! It was ranked second, behind Maksym Voznyy's largest known repunit PRP, in near-repdigit-related (probable) prime numbers.

Unprovable quasi-repdigit PRPs
	digits	flabel	wlabel	expression	when	who
1	196685	48889	48w9	(44·10¹⁹⁶⁶⁸⁴+1)/9	July 24, 2010	Serge Batalov

July 19, 2010

NOTE: 3·10²⁸²+1 = P8 · P14 · P32 · P37 · P44 · P45 · P107. P32 and P44: Serge Batalov, ECM, B1=2000000. P37: Ignacio Santos, ECM, B1=11000000. P45: Wataru Sakai, ECM, B1=11000000.

July 17, 2010

Serge Batalov found the largest known unprovable quasi-repdigit PRP in our tables. Congratulations! It's greater than the largest known unprovable near-repdigit PRP in our tables and greater than the largest known near-repdigit prime too. It was ranked second, behind Maksym Voznyy's largest known repunit PRP, in near-repdigit-related (probable) prime numbers.

Unprovable quasi-repdigit PRPs
	digits	flabel	wlabel	expression	when	who
1	191074	38889	38w9	(35·10¹⁹¹⁰⁷³+1)/9	July 17, 2010	Serge Batalov

July 11, 2010

Erik Branger proved 1199 prime numbers, listed in the List of near-repdigit-related prime numbers, up to 800-digit by using Primo 3.0.9.

June 2010

June 18, 2010

The threshold of composite numbers which are longer than 95 percent of the corresponding SNFS polynomial has been lowered from 96 percent at the suggestion of Serge Batalov.

June 14, 2010

Serge Batalov found 2 PRPs.

Unprovable quasi-repdigit PRPs
	digits	flabel	wlabel	expression	when	who
8	106650	38889	38w9	(35·10¹⁰⁶⁶⁴⁹+1)/9	June 14, 2010	Serge Batalov
10	98447	78889	78w9	(71·10⁹⁸⁴⁴⁶+1)/9	June 14, 2010	Serge Batalov

June 10, 2010

Erik Branger found 25 PRPs.

Unprovable quasi-repdigit PRPs
	digits	flabel	wlabel	expression	when	who
94	26905	30007	30w7	3·10²⁶⁹⁰⁴+7	June 10, 2010	Erik Branger
95	26745	39997	39w7	4·10²⁶⁷⁴⁴-3	June 10, 2010	Erik Branger
102	26001	36661	36w1	(11·10²⁶⁰⁰⁰-17)/3	June 10, 2010	Erik Branger
113	24841	35557	35w7	(32·10²⁴⁸⁴⁰+13)/9	June 10, 2010	Erik Branger
121	23006	38881	38w1	(35·10²³⁰⁰⁵-71)/9	June 10, 2010	Erik Branger
122	22926	37771	37w1	(34·10²²⁹²⁵-61)/9	June 10, 2010	Erik Branger
124	22741	36667	36w7	(11·10²²⁷⁴⁰+1)/3	June 10, 2010	Erik Branger
127	22612	32221	32w1	(29·10²²⁶¹¹-11)/9	June 10, 2010	Erik Branger
128	22519	32221	32w1	(29·10²²⁵¹⁸-11)/9	June 10, 2010	Erik Branger
133	21727	37779	37w9	(34·10²¹⁷²⁶+11)/9	June 10, 2010	Erik Branger
140	20791	35557	35w7	(32·10²⁰⁷⁹⁰+13)/9	June 10, 2010	Erik Branger
149	19780	32221	32w1	(29·10¹⁹⁷⁷⁹-11)/9	June 10, 2010	Erik Branger
154	19651	32229	32w9	(29·10¹⁹⁶⁵⁰+61)/9	June 10, 2010	Erik Branger
170	17514	36661	36w1	(11·10¹⁷⁵¹³-17)/3	June 10, 2010	Erik Branger
173	17355	35559	35w9	(32·10¹⁷³⁵⁴+31)/9	June 10, 2010	Erik Branger
184	16021	38881	38w1	(35·10¹⁶⁰²⁰-71)/9	June 10, 2010	Erik Branger
204	14500	35551	35w1	(32·10¹⁴⁴⁹⁹-41)/9	June 10, 2010	Erik Branger
210	14080	38881	38w1	(35·10¹⁴⁰⁷⁹-71)/9	June 10, 2010	Erik Branger
226	12820	38881	38w1	(35·10¹²⁸¹⁹-71)/9	June 10, 2010	Erik Branger
230	12591	36661	36w1	(11·10¹²⁵⁹⁰-17)/3	June 10, 2010	Erik Branger
245	11104	35557	35w7	(32·10¹¹¹⁰³+13)/9	June 10, 2010	Erik Branger
254	10740	36661	36w1	(11·10¹⁰⁷³⁹-17)/3	June 10, 2010	Erik Branger
255	10734	37779	37w9	(34·10¹⁰⁷³³+11)/9	June 10, 2010	Erik Branger
259	10525	32229	32w9	(29·10¹⁰⁵²⁴+61)/9	June 10, 2010	Erik Branger
260	10500	37771	37w1	(34·10¹⁰⁴⁹⁹-61)/9	June 10, 2010	Erik Branger

Serge Batalov found a PRP.

Unprovable quasi-repdigit PRPs
	digits	flabel	wlabel	expression	when	who
5	118217	58889	58w9	(53·10¹¹⁸²¹⁶+1)/9	June 10, 2010	Serge Batalov

June 5, 2010

Serge Batalov found two PRPs.

Unprovable quasi-repdigit PRPs
	digits	flabel	wlabel	expression	when	who
6	109674	68889	68w9	(62·10¹⁰⁹⁶⁷³+1)/9	June 5, 2010	Serge Batalov
7	100543	38889	38w9	(35·10¹⁰⁰⁵⁴²+1)/9	June 5, 2010	Serge Batalov

June 2, 2010

Factorizations of 844...447 have been extended up to n=200. Composite numbers that appeared newly have passed 118 times ECM runs at level 35. Unknown factors have probably 30 digits or more.

May 2010

May 31, 2010

Factorizations of 922...227 have been extended up to n=200. Composite numbers that appeared newly have passed 118 times ECM runs at level 35. Unknown factors have probably 30 digits or more.

May 29, 2010

Factorizations of 300...001 have been extended up to n=300. Composite numbers that appeared newly have passed 118 times ECM runs at level 35. Unknown factors have probably 30 digits or more.

May 22, 2010

Serge Batalov found the largest known near-repdigit PRP so far in our tables again. Congratulations!

[38889] (35·10⁶⁸⁷¹⁸+1)/9 is PRP.
[88889] (8·10¹⁴⁸³²⁸+1)/9 is PRP.

May 21, 2010

Serge Batalov found the largest known near-repdigit PRP so far in our tables again. Congratulations!

[68889] (62·10⁶⁵³³¹+1)/9 is PRP.
[88889] (8·10¹⁴⁴⁶⁸³+1)/9 is PRP.

May 20, 2010

Factorizations of 922...221 have been extended up to n=200. Composite numbers that appeared newly have passed 118 times ECM runs at level 35. Unknown factors have probably 30 digits or more.

May 18, 2010

Serge Batalov broke his own record again. Congratulations!

[58889] (53·10⁵⁹³⁸⁹+1)/9 is PRP.
[48889] (44·10⁵⁹⁴⁵⁴+1)/9 is PRP.
[28889] (26·10¹³⁹²⁸⁹+1)/9 is PRP.

May 17, 2010

Serge Batalov found the largest known quasi-repdigit PRP so far in our tables. Congratulations!

[78889] (71·10¹³⁷²⁵⁰+1)/9 is PRP.

Factorizations of 844...443 have been extended up to n=200. Composite numbers that appeared newly have passed 118 times ECM runs at level 35. Unknown factors have probably 30 digits or more.

May 16, 2010

Factorizations of 911...117 have been extended up to n=200. Composite numbers that appeared newly have passed 118 times ECM runs at level 35. Unknown factors have probably 30 digits or more.

May 15, 2010

Serge Batalov found four PRPs. (89·10¹³³⁵⁸⁰+1)/9 is the largest known Plateau and Depression PRP. Congratulations!

[38889] (35·10⁴⁶⁷⁹⁹+1)/9 is PRP.
[38889] (35·10⁴⁹⁶⁸²+1)/9 is PRP.
[68889] (62·10⁵³¹¹¹+1)/9 is PRP.
[98889] (89·10¹³³⁵⁸⁰+1)/9 is PRP.

May 13, 2010

Serge Batalov found a PRP.

[28889] (26·10³⁴⁴²³+1)/9 is PRP.

Factorizations of 911...113 have been extended up to n=200. Composite numbers that appeared newly have passed 118 times ECM runs at level 35. Unknown factors have probably 30 digits or more.

May 12, 2010

Serge Batalov found six PRPs.

[78889] (71·10¹⁰⁷⁸²+1)/9 is PRP.
[48889] (44·10¹¹³⁷⁰+1)/9 is PRP.
[38889] (35·10¹⁹⁸⁵⁴+1)/9 is PRP.
[78889] (71·10²⁵³⁶⁶+1)/9 is PRP.
[38889] (35·10²⁷⁸⁴²+1)/9 is PRP.
[28889] (26·10³⁰²⁵⁴+1)/9 is PRP.

May 10, 2010

Serge Batalov found four PRPs by using srsieve, sr1sieve, Prime95 and PFGW 3.3.3. One of them is the largest known quasi-repdigit PRP so far in our tables. Congratulations!

[18889] (17·10³⁷⁹⁹²+1)/9 is PRP.
[18889] (17·10⁵⁴¹¹⁷+1)/9 is PRP.
[18889] (17·10¹²¹²⁴²+1)/9 is PRP.
[18889] (17·10¹²¹⁶²¹+1)/9 is PRP.

May 8, 2010

RSALS and Jeff Gilchrist factored c248 = P46 · P52 · P71 · P81 from 10²⁵⁰+3. It's the largest number factored by snfs in our tables so far. Congratulations!

NOTE: This number should have been factored by ECM up to 55-digit at least. To save time and energy, let's not rely on NFS against huge numbers from the beginning!

May 7, 2010

Factorizations of 844...441 have been extended up to n=200. Composite numbers that appeared newly have passed 118 times ECM runs at level 35. Unknown factors have probably 30 digits or more.

April 2010

April 29, 2010

Erik Branger reported 41 PRPs.

[21113] (19·10¹⁴¹⁶¹+17)/9 is PRP.
[21119] (19·10¹¹³⁸³+71)/9 is PRP.
[21119] (19·10¹⁵⁴¹⁵+71)/9 is PRP.
[21119] (19·10²⁶³⁸²+71)/9 is PRP.
[23339] (7·10²³⁰⁵⁵+17)/3 is PRP.
[24441] (22·10²⁴⁹⁸⁹-31)/9 is PRP.
[24447] (22·10²³⁴⁸¹+23)/9 is PRP.
[24447] (22·10²⁷⁸⁵⁵+23)/9 is PRP.
[24449] (22·10¹²¹⁴²+41)/9 is PRP.
[24449] (22·10¹³⁰⁴⁸+41)/9 is PRP.
[25551] (23·10¹⁸⁷⁹⁸-41)/9 is PRP.
[25557] (23·10¹²⁷⁷³+13)/9 is PRP.
[25557] (23·10¹⁷⁷⁰²+13)/9 is PRP.
[25557] (23·10¹⁹¹²⁸+13)/9 is PRP.
[25557] (23·10²²²⁰⁶+13)/9 is PRP.
[25557] (23·10²²³⁸⁶+13)/9 is PRP.
[25557] (23·10²⁵⁰⁵³+13)/9 is PRP.
[25559] (23·10¹⁵⁸⁸⁶+31)/9 is PRP.
[25559] (23·10¹⁹⁹¹²+31)/9 is PRP.
[26669] (8·10¹²⁸²⁸+7)/3 is PRP.
[26669] (8·10¹⁴⁹⁵⁹+7)/3 is PRP.
[26669] (8·10¹⁷⁹⁹⁵+7)/3 is PRP.
[26669] (8·10¹⁹⁷³⁰+7)/3 is PRP.
[26669] (8·10²⁶⁴⁸⁰+7)/3 is PRP.
[27771] (25·10²⁰⁷⁸⁶-61)/9 is PRP.
[27773] (25·10¹⁰⁰⁶⁹-43)/9 is PRP.
[27773] (25·10¹⁷³⁵⁶-43)/9 is PRP.
[27773] (25·10²⁵⁸⁰⁴-43)/9 is PRP.
[27773] (25·10²⁹⁰⁵²-43)/9 is PRP.
[27773] (25·10²⁹⁰⁸²-43)/9 is PRP.
[27779] (25·10¹⁴⁶⁴⁶+11)/9 is PRP.
[27779] (25·10²²⁷⁹⁴+11)/9 is PRP.
[27779] (25·10²⁵⁶⁴⁸+11)/9 is PRP.
[28881] (26·10¹⁰⁸⁹⁵-71)/9 is PRP.
[28881] (26·10¹⁷¹⁰⁵-71)/9 is PRP.
[28883] (26·10¹⁵⁸⁶⁵-53)/9 is PRP.
[28887] (26·10¹⁴²⁴⁹-17)/9 is PRP.
[29993] 3·10¹³¹²²-7 is PRP.
[29993] 3·10¹³⁸³²-7 is PRP.
[29993] 3·10²²⁶⁷⁶-7 is PRP.
[29993] 3·10²⁵⁰²⁰-7 is PRP.

April 28, 2010

Short wanted list of Phi_n(10) is available. However, no exclusive reservation system for Phi_n(10) will be provided because many people are collecting repunit factors.

April 23, 2010

RSALS + Zeta-Flux factored c241 from 17777_248: (16·10²⁴⁸-7)/9 by snfs/Msieve. The 250-digit polynomial is the largest in our tables so far. Congratulations!

Juno Fukos factored 150-digit composite factor of Phi_840(10) by gnfs/Msieve. Congratulations!

Number: c150
N = 191413141591299314411353617644492718709042398621746359743575335167576218516274501587918765785208170431266534615378694736680781077885837943706833300081 (150 digits)
Divisors found:
r1=1146780383632163283649175272843774050715065531735480891145232027761 (pp67)
r2=166913512232431273140362987966641859731500109846278942036790211593884632236221381121 (pp84)
Version: Msieve v. 1.44
Total time: 1321.70 hours.
Factorization parameters were as follows:
n: 191413141591299314411353617644492718709042398621746359743575335167576218516274501587918765785208170431266534615378694736680781077885837943706833300081 
skew: 581056.87 
# norm 3.49e+020 
c5: 417300 
c4: 6293707890075 
c3: 661926573905922818 
c2: -1142910230692705225820950 
c1: -305033470566634835042268478702 
c0: 13979210859054806935193981807485035 
# alpha -5.68 
Y1: 22746208757392231 
Y0: -53988855542895713658925943846 
# Murphy_E 4.74e-012 
# M 42516010405424856805684090534471339985472838519578990692918969250315963958564685692805011963349843096316919602745856301635282723806748487864856881786 
type: gnfs 
rlim: 20800000 
alim: 20800000 
lpbr: 29 
lpba: 29 
mfbr: 58 
mfba: 58 
rlambda: 2.6 
alambda: 2.6 
qintsize: 100000
Factor base limits: 20800000/20800000
Large primes per side: 3
Large prime bits: 29/29
Sieved algebraic special-q in [10400000, 33200000)
Total raw relations: 45598432
Relations: 6859564 relations
Pruned matrix : 4250955 x 4251180
Polynomial selection time: 0.00 hours.
Total sieving time: 1224.80 hours.
Total relation processing time: 0.71 hours.
Matrix solve time: 88.93 hours.
time per square root: 7.25 hours.
Prototype def-par.txt line would be: gnfs,149,5,65,2000,1e-05,0.28,250,20,50000,3600,20800000,20800000,29,29,58,58,2.6,2.6,100000
total time: 1321.70 hours.
 --------- CPU info (if available) ----------

April 21, 2010

The following sections were divided from this page.

Reserved numbers and submitted numbers page links to not the table body but the Contribution and Reservation page.

April 11, 2010

List of near-repdigit-related prime numbers was updated.

Ignacio Santos added 162 prime numbers of the form k·10ⁿ+1 and the following 16 PRPs.

[69w77] 7·10²⁰³⁷-23 is PRP.
[69w77] 7·10⁴⁵⁵⁷-23 is PRP.
[69w77] 7·10⁸⁹⁹⁵-23 is PRP.
[229w3] 23·10²³⁷⁹-7 is PRP.
[229w3] 23·10²⁶¹⁵-7 is PRP.
[229w3] 23·10⁴⁰⁰⁸-7 is PRP.
[229w3] 23·10⁴²⁹⁵-7 is PRP.
[229w3] 23·10⁴⁴⁹⁵-7 is PRP.
[229w3] 23·10⁴⁵²⁶-7 is PRP.
[229w3] 23·10⁹⁹⁹⁶-7 is PRP.
[69983] 7·10²¹⁷⁸-17 is PRP.
[69983] 7·10⁸⁹¹⁶-17 is PRP.
[69983] 7·10⁹⁴⁷¹-17 is PRP.
[76697] (23·10²⁰⁵³+91)/3 is PRP.
[76697] (23·10²⁹⁹⁷+91)/3 is PRP.
[76697] (23·10⁴⁰⁶⁵+91)/3 is PRP.

Lionel Debroux proved the following two prime numbers by using Primo.

[40079] 4·10⁹⁹⁹+79 is prime.
[77719] (7·10¹⁵⁰³-529)/9 is prime.

==== NOTE ====

In primedifficulty.txt, difficulty = 0.00% means that the sequence consists of composite numbers except finite exceptions. For example, [38111] (343·10ⁿ-1)/9 is generally a composite number because

(343·10^3·k+1-1)/9 = 3·(126910·(10^3·(k-1)+...+10^3·0)+127) for k≥1,
(343·10^3·k+2-1)/9 = 37·(102900·(10^3·(k-1)+...+10^3·0)+103) for k≥1 and
(343·10^3·k-1)/9 = (21·(10^k-1+...+10⁰)+2)·(1617·(10^2·(k-1)+...+10^2·0)+21·(10^k-1+...+10⁰)+19) for k≥1.

April 10, 2010

Erik Branger proved 4424 prime numbers, listed in the List of near-repdigit-related prime numbers, up to 600-digit by using Primo 3.0.9.

April 9, 2010

List of near-repdigit-related prime numbers was updated with new prime numbers of the form k·10ⁿ+1 searched by Ignacio Santos.

April 6, 2010

Serge Batalov found a PRP.

(77·10³⁶⁴⁶⁴+13)/9 = 8(5)₃₆₄₆₃7_<36465> is PRP.

April 2, 2010

Serge Batalov found 2 PRPs.

(77·10¹⁹⁸³⁵+13)/9 = 8(5)₁₉₈₃₄7_<19836> is PRP.
(77·10²⁰⁰¹⁸+13)/9 = 8(5)₂₀₀₁₇7_<20019> is PRP.

Prime numbers of the form k·10ⁿ-1 (k:small) are easy to prove by n+1 test. 10metreh tested prime numbers of the form that had not been marked as 'proven' in primesize.txt.

April 1, 2010

The ratio of current factored part of each repunit number is available at Factorizations of 11...11 (Repunit). For example, current factored part of R4416 = (10⁴⁴¹⁶-1)/9 is 35.87%. Then, you can prove the primality of 4417-digit near-repdigit number 88...881 : (8·10⁴⁴¹⁷-71)/9 = 80·R4416+1 by using n-1 test. See also (8*10^4417-71)/9 is prime (4417 digits).

27811-digit near-repdigit number 88...881 : (8·10²⁷⁸¹¹-71)/9 is PRP that was found by Erik Branger on January 31, 2010. And then, current factored part of (10²⁷⁸¹⁰-1)/9 is 32.99%. Additional prime factors of Phi_515(10), Phi_1030(10), Phi_1545(10), Phi_1854(10), Phi_2781(10), Phi_3090(10), Phi_4635(10), Phi_5562(10), Phi_9270(10), Phi_27810(10) and 7334-digit gigantic ECPP for Phi_13905(10)/83431/333721 will make 27811-digit near-repdigit prime number proven. Contributions are welcome.

$ ./pfgw -tc -h"88881_27811.h" -q"(8*10^27811-71)/9"
PFGW Version 3.3.3.20100325.Win_Stable [GWNUM 25.14]

Primality testing (8*10^27811-71)/9 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Reading factors from helper file 88881_27811.h
Running N-1 test using base 17
Running N-1 test using base 23
Running N-1 test using base 43
Running N+1 test using discriminant 53, base 6+sqrt(53)
Calling N-1 BLS with factored part 33.00% and helper 0.03% (99.02% proof)
(8*10^27811-71)/9 is Fermat and Lucas PRP! (698.8483s+0.0032s)

March 2010

March 30, 2010

Factorizations of 822...227, Factorizations of 822...229 and Factorizations of 833...339 have been extended up to n=200. Composite numbers that appeared newly have passed 118 times ECM runs at level 35. Unknown factors have probably 30 digits or more.

March 24, 2010

RSALS and Zeta-Flux factored 2·10²⁴¹+9: c165 = P54 · P112. It's the largest GNFS factorization in our tables so far. Congratulations!

March 23, 2010

Erik Branger found 20 PRPs by using PFGW.

(11·10¹⁷⁷¹⁵+7)/9 = 1(2)₁₇₇₁₄3_<17716> is PRP.
(11·10¹¹⁹²⁴+43)/9 = 1(2)₁₁₉₂₃7_<11925> is PRP.
(4·10¹⁴⁶³⁰+11)/3 = 1(3)₁₄₆₂₉7_<14631> is PRP.
(4·10²⁰⁹³²+11)/3 = 1(3)₂₀₉₃₁7_<20933> is PRP.
(13·10¹⁷²⁹³+41)/9 = 1(4)₁₇₂₉₂9_<17294> is PRP.
(13·10²³²⁷⁰+41)/9 = 1(4)₂₃₂₆₉9_<23271> is PRP.
(13·10²⁷¹⁹⁷+41)/9 = 1(4)₂₇₁₉₆9_<27198> is PRP.
(14·10¹⁰⁶⁷⁴+31)/9 = 1(5)₁₀₆₇₃9_<10675> is PRP.
(14·10¹¹⁶¹⁷+31)/9 = 1(5)₁₁₆₁₆9_<11618> is PRP.
(14·10¹³²⁵⁷+31)/9 = 1(5)₁₃₂₅₆9_<13258> is PRP.
(14·10¹⁴³⁷¹+31)/9 = 1(5)₁₄₃₇₀9_<14372> is PRP.
(14·10²⁰¹⁷⁶+31)/9 = 1(5)₂₀₁₇₅9_<20177> is PRP.
(5·10¹²⁵⁴⁶-11)/3 = 1(6)₁₂₅₄₅3_<12547> is PRP.
(5·10²²⁴⁴³-11)/3 = 1(6)₂₂₄₄₂3_<22444> is PRP.
(5·10¹⁷⁷⁶⁵+1)/3 = 1(6)₁₇₇₆₄7_<17766> is PRP.
(5·10¹⁹³⁰⁵+7)/3 = 1(6)₁₉₃₀₄9_<19306> is PRP.
(16·10²⁶⁰⁰⁰+11)/9 = 1(7)₂₅₉₉₉9_<26001> is PRP.
(17·10²²⁶⁶⁶-53)/9 = 1(8)₂₂₆₆₅3_<22667> is PRP.
(17·10²⁹²⁹²-53)/9 = 1(8)₂₉₂₉₁3_<29293> is PRP.
(17·10²⁹⁵⁰⁸-53)/9 = 1(8)₂₉₅₀₇3_<29509> is PRP.

March 20, 2010

Factorizations of 811...119, Factorizations of 822...221 and Factorizations of 822...223 have been extended up to n=200. Composite numbers that appeared newly have passed 118 times ECM runs at level 35. Unknown factors have probably 30 digits or more.

March 18, 2010

RSALS and Jeff Gilchrist factored (16·10²⁴⁶-7)/9: c243 = P112 · P132. It's the largest SNFS factorization and P112 is the largest prime factor in our tables so far. Congratulations!

March 15, 2010

Factorizations of 599...99 have been extended up to n=300. Composite numbers that appeared newly have passed 118 times ECM runs at level 35. Unknown factors have probably 30 digits or more.

March 10, 2010

Information of ECM efforts is available in the Contributions page.

March 8, 2010

Dmitry Domanov found 4 primes and 68 PRPs by using Prime95 v25.11 and pfgw. 2·10¹¹³⁹⁴¹+9 is the largest unprovable quasi-repdigit PRP in our tables so far. Congratulations!

6·10⁸⁶²⁸⁷+1 = 6(0)₈₆₂₈₆1_<86288> is prime.
7·10²⁰³¹⁰+1 = 7(0)₂₀₃₀₉1_<20311> is prime.
7·10²⁰³⁶⁰+1 = 7(0)₂₀₃₅₉1_<20361> is prime.
9·10⁹¹⁸³⁶+1 = 9(0)₉₁₈₃₅1_<91837> is prime.
2·10⁴²⁷⁶²-7 = 1(9)₄₂₇₆₁3_<42763> is PRP.
2·10⁹⁰⁵⁹⁷-7 = 1(9)₉₀₅₉₆3_<90598> is PRP.
2·10¹⁰⁸⁵⁶-3 = 1(9)₁₀₈₅₅7_<10857> is PRP.
2·10²⁵⁹⁵⁹-3 = 1(9)₂₅₉₅₈7_<25960> is PRP.
2·10⁶⁴⁸⁸²-3 = 1(9)₆₄₈₈₁7_<64883> is PRP.
2·10²⁷²¹⁷+3 = 2(0)₂₇₂₁₆3_<27218> is PRP.
2·10²⁷⁶⁹³+3 = 2(0)₂₇₆₉₂3_<27694> is PRP.
2·10²⁶⁶⁶⁹+9 = 2(0)₂₆₆₆₈9_<26670> is PRP.
2·10¹¹³⁹⁴¹+9 = 2(0)₁₁₃₉₄₀9_<113942> is PRP.
5·10²⁰⁷¹⁸-7 = 4(9)₂₀₇₁₇3_<20719> is PRP.
5·10⁵¹¹⁶³-7 = 4(9)₅₁₁₆₂3_<51164> is PRP.
5·10³⁵³²⁶-3 = 4(9)₃₅₃₂₅7_<35327> is PRP.
5·10³⁶⁹⁹¹-3 = 4(9)₃₆₉₉₀7_<36992> is PRP.
5·10⁵⁹⁵⁸⁶-3 = 4(9)₅₉₅₈₅7_<59587> is PRP.
5·10⁸⁸²⁶¹-3 = 4(9)₈₈₂₆₀7_<88262> is PRP.
5·10¹⁹⁷³⁷+3 = 5(0)₁₉₇₃₆3_<19738> is PRP.
5·10³²¹⁹⁷+3 = 5(0)₃₂₁₉₆3_<32198> is PRP.
5·10⁵¹⁵⁰⁸+3 = 5(0)₅₁₅₀₇3_<51509> is PRP.
5·10⁵⁸²⁷⁵+3 = 5(0)₅₈₂₇₄3_<58276> is PRP.
5·10⁶²²³³+3 = 5(0)₆₂₂₃₂3_<62234> is PRP.
5·10⁹⁰⁰³³+3 = 5(0)₉₀₀₃₂3_<90034> is PRP.
5·10²⁴⁸⁵³+9 = 5(0)₂₄₈₅₂9_<24854> is PRP.
5·10³⁹⁶²⁹+9 = 5(0)₃₉₆₂₈9_<39630> is PRP.
5·10⁵³⁴⁹²+9 = 5(0)₅₃₄₉₁9_<53493> is PRP.
5·10⁷¹²³⁷+9 = 5(0)₇₁₂₃₆9_<71238> is PRP.
5·10⁷²³⁰²+9 = 5(0)₇₂₃₀₁9_<72303> is PRP.
5·10⁸¹⁶⁵³+9 = 5(0)₈₁₆₅₂9_<81654> is PRP.
6·10¹³⁹³⁶-7 = 5(9)₁₃₉₃₅3_<13937> is PRP.
6·10¹⁶⁴⁸⁶-7 = 5(9)₁₆₄₈₅3_<16487> is PRP.
6·10⁸⁵⁹¹⁰-7 = 5(9)₈₅₉₀₉3_<85911> is PRP.
6·10¹⁴⁹²⁷+7 = 6(0)₁₄₉₂₆7_<14928> is PRP.
6·10³⁴⁵⁶²+7 = 6(0)₃₄₅₆₁7_<34563> is PRP.
6·10⁶⁴³⁸⁷+7 = 6(0)₆₄₃₈₆7_<64388> is PRP.
6·10⁷¹²⁹⁹+7 = 6(0)₇₁₂₉₈7_<71300> is PRP.
6·10⁷¹⁹⁵¹+7 = 6(0)₇₁₉₅₀7_<71952> is PRP.
7·10³⁴⁹⁴³-9 = 6(9)₃₄₉₄₂1_<34944> is PRP.
7·10³⁷⁶⁵²-9 = 6(9)₃₇₆₅₁1_<37653> is PRP.
7·10³⁸¹⁰⁸-9 = 6(9)₃₈₁₀₇1_<38109> is PRP.
7·10³⁸⁶⁸⁶-9 = 6(9)₃₈₆₈₅1_<38687> is PRP.
7·10³⁹³⁸⁴-9 = 6(9)₃₉₃₈₃1_<39385> is PRP.
7·10⁴³³⁹³-9 = 6(9)₄₃₃₉₂1_<43394> is PRP.
7·10⁴⁷²⁸⁰-9 = 6(9)₄₇₂₇₉1_<47281> is PRP.
7·10⁵⁵⁰³⁰-9 = 6(9)₅₅₀₂₉1_<55031> is PRP.
7·10¹⁰⁴⁹¹-3 = 6(9)₁₀₄₉₀7_<10492> is PRP.
7·10¹¹¹⁹⁹-3 = 6(9)₁₁₁₉₈7_<11200> is PRP.
7·10¹²¹⁹⁰-3 = 6(9)₁₂₁₈₉7_<12191> is PRP.
7·10³³⁵⁹⁴-3 = 6(9)₃₃₅₉₃7_<33595> is PRP.
7·10³⁸²⁵⁶-3 = 6(9)₃₈₂₅₅7_<38257> is PRP.
7·10⁸⁹¹⁶⁹-3 = 6(9)₈₉₁₆₈7_<89170> is PRP.
7·10⁶³³⁵¹+9 = 7(0)₆₃₃₅₀9_<63352> is PRP.
8·10⁴⁸⁰⁸¹-9 = 7(9)₄₈₀₈₀1_<48082> is PRP.
8·10¹⁵⁷⁸⁹-7 = 7(9)₁₅₇₈₈3_<15790> is PRP.
8·10²³⁰⁷⁴-7 = 7(9)₂₃₀₇₃3_<23075> is PRP.
8·10³⁸⁴⁶⁶-7 = 7(9)₃₈₄₆₅3_<38467> is PRP.
8·10⁶⁸⁴⁰⁰-7 = 7(9)₆₈₃₉₉3_<68401> is PRP.
8·10²⁰⁹¹¹+9 = 8(0)₂₀₉₁₀9_<20912> is PRP.
8·10²⁴³⁴⁵+9 = 8(0)₂₄₃₄₄9_<24346> is PRP.
8·10³¹⁹⁶⁴+9 = 8(0)₃₁₉₆₃9_<31965> is PRP.
8·10⁶⁷⁷⁴²+9 = 8(0)₆₇₇₄₁9_<67743> is PRP.
9·10²³⁶⁴⁰-7 = 8(9)₂₃₆₃₉3_<23641> is PRP.
9·10³¹⁴⁴⁰-7 = 8(9)₃₁₄₃₉3_<31441> is PRP.
9·10³¹⁸³⁹-7 = 8(9)₃₁₈₃₈3_<31840> is PRP.
9·10³²²⁸⁷-7 = 8(9)₃₂₂₈₆3_<32288> is PRP.
9·10²¹⁶⁰⁴+7 = 9(0)₂₁₆₀₃7_<21605> is PRP.
9·10²⁵⁸⁹¹+7 = 9(0)₂₅₈₉₀7_<25892> is PRP.
9·10²⁶⁷²⁵+7 = 9(0)₂₆₇₂₄7_<26726> is PRP.
9·10³⁴⁸³⁸+7 = 9(0)₃₄₈₃₇7_<34839> is PRP.
9·10⁶⁷⁴⁶⁸+7 = 9(0)₆₇₄₆₇7_<67469> is PRP.

March 5, 2010

Robert Backstrom factored (71·10¹⁸⁹+1)/9: c186 = P93 · P93. It's the second largest nice split so far in our tables. Congratulations!

March 4, 2010

Factorizations of 811...113 and Factorizations of 811...117 have been extended up to n=200. Composite numbers that appeared newly have passed 118 times ECM runs at level 35. Unknown factors have probably 30 digits or more.

February 2010

February 25, 2010

Erik Branger found the following 22 PRPs.

(7·10¹⁸⁸⁹⁵-1)/3 = 2(3)₁₈₈₉₅_<18896> is PRP.
(25·10¹⁵⁷⁹⁵-7)/9 = 2(7)₁₅₇₉₅_<15796> is PRP.
(25·10²²⁵³⁵-7)/9 = 2(7)₂₂₅₃₅_<22536> is PRP.
(25·10²⁷⁷⁵²-7)/9 = 2(7)₂₇₇₅₂_<27753> is PRP.
(28·10¹⁵⁸⁹²-1)/9 = 3(1)₁₅₈₉₂_<15893> is PRP.
(28·10²⁴⁰²²-1)/9 = 3(1)₂₄₀₂₂_<24023> is PRP.
(28·10²⁷⁰⁴¹-1)/9 = 3(1)₂₇₀₄₁_<27042> is PRP.
(13·10¹⁵²⁰⁶-1)/3 = 4(3)₁₅₂₀₆_<15207> is PRP.
(13·10²⁴⁰⁴¹-1)/3 = 4(3)₂₄₀₄₁_<24042> is PRP.
(13·10²⁵³²¹-1)/3 = 4(3)₂₅₃₂₁_<25322> is PRP.
(43·10²¹⁸²³-7)/9 = 4(7)₂₁₈₂₃_<21824> is PRP.
(46·10¹²³⁹⁰-1)/9 = 5(1)₁₂₃₉₀_<12391> is PRP.
(46·10²⁸⁶⁰⁸-1)/9 = 5(1)₂₈₆₀₈_<28609> is PRP.
(52·10¹³³⁴⁴-7)/9 = 5(7)₁₃₃₄₄_<13345> is PRP.
(22·10¹¹⁰³⁹-1)/3 = 7(3)₁₁₀₃₉_<11040> is PRP.
(22·10¹¹²⁴⁷-1)/3 = 7(3)₁₁₂₄₇_<11248> is PRP.
(22·10¹³²⁷⁵-1)/3 = 7(3)₁₃₂₇₅_<13276> is PRP.
(22·10¹⁶⁷⁸¹-1)/3 = 7(3)₁₆₇₈₁_<16782> is PRP.
(22·10²⁰¹³⁸-1)/3 = 7(3)₂₀₁₃₈_<20139> is PRP.
(79·10¹⁵²¹⁰-7)/9 = 8(7)₁₅₂₁₀_<15211> is PRP.
(82·10¹⁸⁵⁹²-1)/9 = 9(1)₁₈₅₉₂_<18593> is PRP.
(88·10¹¹³⁹⁵-7)/9 = 9(7)₁₁₃₉₅_<11396> is PRP.

February 24, 2010

Factorizations of 166...667 have been extended up to n=300. Composite numbers that appeared newly have passed 118 times ECM runs at level 35. Unknown factors have probably 30 digits or more.

February 22, 2010

The Factorizations of Phi_n(10) had been updated. Click numbers followed by three dots to view all digits of Φ_n(10) (n≤100000) and those factors. This function uses JavaScript and Java applet.

February 21, 2010

Factorizations of 866...669, Factorizations of 877...771, Factorizations of 877...773 and Factorizations of 877...779 have been extended up to n=150. Composite numbers that appeared newly have passed 118 times ECM runs at level 35. Unknown factors have probably 30 digits or more.

February 15, 2010

Factorizations of 499...99 have been extended up to n=300. Composite numbers that appeared newly have passed 118 times ECM runs at level 35. Unknown factors have probably 30 digits or more.

Factorizations of 855...551, Factorizations of 855...553, Factorizations of 855...557 and Factorizations of 855...559 have been extended up to n=150. Composite numbers that appeared newly have passed 118 times ECM runs at level 35. Unknown factors have probably 30 digits or more.

February 8, 2010

Markus Tervooren factored 8·10²⁴⁴-1 : c164 = P60 · P104 by gnfs. It's the largest number factored by gnfs in our table so far. Congratulations!

February 5, 2010

Factorizations of 788...883 and Factorizations of 788...889 have been extended up to n=200. Composite numbers that appeared newly have passed 118 times ECM runs at level 35. Unknown factors have probably 30 digits or more.

February 4, 2010

JPascoa factored (73·10²¹⁸-1)/9 : c156 = P58 · P99 by gnfs. It's the largest number factored by gnfs in our table so far. Congratulations!

February 1, 2010

Erik Branger reported 20 PRPs. (2·10¹⁵⁶¹⁷+7)/9 = (2)₁₅₆₁₆3_<15617>, (2·10²⁶⁴⁵⁹+7)/9 = (2)₂₆₄₅₈3_<26459>, (2·10¹⁰³⁹¹+61)/9 = (2)₁₀₃₉₀9_<10391>, (2·10¹²¹⁰⁵+61)/9 = (2)₁₂₁₀₄9_<12105>, (2·10¹⁹⁶¹⁶+61)/9 = (2)₁₉₆₁₅9_<19616>, (4·10¹²³³⁸-31)/9 = (4)₁₂₃₃₇1_<12338>, (4·10²⁰¹⁹⁴-31)/9 = (4)₂₀₁₉₃1_<20194>, (4·10²⁸⁹³⁴+23)/9 = (4)₂₈₉₃₃7_<28934>, (4·10²⁰²⁰⁸+41)/9 = (4)₂₀₂₀₇9_<20208>, (5·10¹⁸⁵²²+13)/9 = (5)₁₈₅₂₁7_<18522>, (2·10¹⁰³⁹²-17)/3 = (6)₁₀₃₉₁1_<10392>, (2·10¹²⁴⁵⁸-17)/3 = (6)₁₂₄₅₇1_<12458>, (2·10²¹⁰⁵⁷-17)/3 = (6)₂₁₀₅₆1_<21057>, (2·10²⁶²²³-17)/3 = (6)₂₆₂₂₂1_<26223>, (7·10²¹¹⁶⁷-43)/9 = (7)₂₁₁₆₆3_<21167>, (8·10²⁷⁸¹¹-71)/9 = (8)₂₇₈₁₀1_<27811>, (8·10²⁹¹⁸⁸-71)/9 = (8)₂₉₁₈₇1_<29188>, (8·10¹⁸¹⁷³-53)/9 = (8)₁₈₁₇₂3_<18173>, (8·10¹⁸⁹⁷¹-53)/9 = (8)₁₈₉₇₀3_<18971>, (8·10²¹⁹⁰⁶-17)/9 = (8)₂₁₉₀₅7_<21906>.

January 2010

January 27, 2010

Factorizations of 766...661, Factorizations of 766...663 and Factorizations of 766...669 have been extended up to n=200. Composite numbers that appeared newly have passed 118 times ECM runs at level 35. Unknown factors have probably 30 digits or more.

January 25, 2010

Records were changed. Top 100 big SNFS factorizations are not sorted by the composite number but sorted by the value of the polynomial.

January 22, 2010

RSALS + Jeff Gilchrist factored 2·10²²⁹+9 = c230 = P109 · P121. c230 is the third largest number factored by snfs in our tables so far. And also, P109 is the second largest prime factor found by snfs in our tables so far. Congratulations! P109 is almost the number one. Markus Tervooren's P110 has been submitted only 28 hours ago.

January 20, 2010

Markus Tervooren factored 6·10²⁴²+1 = c243 = P110 · P134. c243 is the largest number factored by snfs in our tables so far. And also, P110 is the largest prime factor found by snfs in our tables so far. Congratulations!

January 14, 2010

Factorizations of 844...441, Factorizations of 844...443, Factorizations of 844...447 and Factorizations of 844...449 have been extended up to n=150. Composite numbers that appeared newly have passed 118 times ECM runs at level 35. Unknown factors have probably 30 digits or more.

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