News <2012>

December 2012

December 31, 2012

Factorizations of 744...441 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 10³⁰.

December 29, 2012

Maksym Voznyy certificated the primality of the quasi-repdigit prime number 4·10³¹³¹+3 by Primo. Certification is available.

Proven quasi-repdigit primes (except pd)
	digits	flabel	wlabel	expression	when	who
290	3132	40003	40w3	4·10³¹³¹+3	December 29, 2012	Maksym Voznyy

December 27, 2012

Factorizations of 733...339 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 10³⁰.

December 26, 2012

Maksym Voznyy certificated the primality of the quasi-repdigit prime number 6·10³⁰¹⁶+7 by Primo. Certification is available.

Proven quasi-repdigit primes (except pd)
	digits	flabel	wlabel	expression	when	who
297	3017	60007	60w7	6·10³⁰¹⁶+7	December 26, 2012	Maksym Voznyy

December 24, 2012

Ray Chandler certificated 4 near-repdigit prime numbers, 40 quasi-repdigit prime numbers and 122 near-repdigit-related prime numbers by Primo. Certifications are available.

Proven near-repdigit primes
	digits	flabel	wlabel	expression	when	who
495	2676	77787	7w87	(7·10²⁶⁷⁶+83)/9	December 24, 2012	Ray Chandler
496	2671	77787	7w87	(7·10²⁶⁷¹+83)/9	December 24, 2012	Ray Chandler
499	2622	33313	3w13	(10²⁶²²-61)/3	December 24, 2012	Ray Chandler
501	2610	33343	3w43	(10²⁶¹⁰+29)/3	December 24, 2012	Ray Chandler

Proven quasi-repdigit primes (except pd)
	digits	flabel	wlabel	expression	when	who
334	2687	19997	19w7	2·10²⁶⁸⁶-3	December 24, 2012	Ray Chandler
335	2685	97111	971w	(874·10²⁶⁸³-1)/9	December 24, 2012	Ray Chandler
337	2684	88823	8w23	(8·10²⁶⁸⁴-593)/9	December 24, 2012	Ray Chandler
338	2681		8w11	(8·10²⁶⁸¹-701)/9	December 24, 2012	Ray Chandler
340	2679	40111	401w	(361·10²⁶⁷⁷-1)/9	December 24, 2012	Ray Chandler
341	2678	88831	8w31	(8·10²⁶⁷⁸-521)/9	December 24, 2012	Ray Chandler
342	2678	43441	434w1	(391·10²⁶⁷⁶-31)/9	December 24, 2012	Ray Chandler
343	2677	99901	9w01	10²⁶⁷⁷-99	December 24, 2012	Ray Chandler
344	2677	57797	57w97	(52·10²⁶⁷⁶+173)/9	December 24, 2012	Ray Chandler
345	2676	30007	30w7	3·10²⁶⁷⁵+7	December 24, 2012	Ray Chandler
346	2675	96667	96w7	(29·10²⁶⁷⁴+1)/3	December 24, 2012	Ray Chandler
347	2669	45449	454w9	(409·10²⁶⁶⁷+41)/9	December 24, 2012	Ray Chandler
349	2669	22207	2w07	(2·10²⁶⁶⁹-137)/9	December 24, 2012	Ray Chandler
351	2662	61669	616w9	(185·10²⁶⁶⁰+7)/3	December 24, 2012	Ray Chandler
352	2661		4w99	(4·10²⁶⁶¹+491)/9	December 24, 2012	Ray Chandler
353	2660	61669	616w9	(185·10²⁶⁵⁸+7)/3	December 24, 2012	Ray Chandler
354	2660	56557	565w7	(509·10²⁶⁵⁸+13)/9	December 24, 2012	Ray Chandler
355	2659	82333	823w	(247·10²⁶⁵⁷-1)/3	December 24, 2012	Ray Chandler
356	2654	54449	54w9	(49·10²⁶⁵³+41)/9	December 24, 2012	Ray Chandler
357	2650	76661	76w1	(23·10²⁶⁴⁹-17)/3	December 24, 2012	Ray Chandler
358	2650	42447	424w7	(382·10²⁶⁴⁸+23)/9	December 24, 2012	Ray Chandler
359	2642	44419	4w19	(4·10²⁶⁴²-229)/9	December 24, 2012	Ray Chandler
361	2638	71151	71w51	(64·10²⁶³⁷+359)/9	December 24, 2012	Ray Chandler
362	2637	57557	575w7	(518·10²⁶³⁵+13)/9	December 24, 2012	Ray Chandler
363	2633	71101	71w01	(64·10²⁶³²-91)/9	December 24, 2012	Ray Chandler
365	2631		6w77	(2·10²⁶³¹+31)/3	December 24, 2012	Ray Chandler
366	2631	25221	252w1	(227·10²⁶²⁹-11)/9	December 24, 2012	Ray Chandler
367	2631	23223	232w3	(209·10²⁶²⁹+7)/9	December 24, 2012	Ray Chandler
370	2629	73393	73w93	(22·10²⁶²⁸+179)/3	December 24, 2012	Ray Chandler
372	2625	59559	595w9	(536·10²⁶²³+31)/9	December 24, 2012	Ray Chandler
375	2622	79979	79w79	8·10²⁶²¹-21	December 24, 2012	Ray Chandler
378	2620	86333	863w	(259·10²⁶¹⁸-1)/3	December 24, 2012	Ray Chandler
379	2619	89929	89w29	9·10²⁶¹⁸-71	December 24, 2012	Ray Chandler
380	2619	11127	1w27	(10²⁶¹⁹+143)/9	December 24, 2012	Ray Chandler
381	2616	58551	585w1	(527·10²⁶¹⁴-41)/9	December 24, 2012	Ray Chandler
382	2616	28111	281w	(253·10²⁶¹⁴-1)/9	December 24, 2012	Ray Chandler
383	2613	40111	401w	(361·10²⁶¹¹-1)/9	December 24, 2012	Ray Chandler
384	2611	56333	563w	(169·10²⁶⁰⁹-1)/3	December 24, 2012	Ray Chandler
385	2611		113w	(34·10²⁶⁰⁹-1)/3	December 24, 2012	Ray Chandler
386	2608	50553	505w3	(455·10²⁶⁰⁶-23)/9	December 24, 2012	Ray Chandler

Proven near-repdigit-related primes (except ru/nr/pd/qr)
	digits	flabel	wlabel	expression	when	who
2238	2684	52273	52w73	(47·10²⁶⁸³+457)/9	December 24, 2012	Ray Chandler
2239	2683	58801	58w01	(53·10²⁶⁸²-791)/9	December 24, 2012	Ray Chandler
2240	2683		448w9	(404·10²⁶⁸¹+1)/9	December 24, 2012	Ray Chandler
2241	2683	10019	10w19	10²⁶⁸²+19	December 24, 2012	Ray Chandler
2244	2682	76637	76w37	(23·10²⁶⁸¹-89)/3	December 24, 2012	Ray Chandler
2246	2681	97739	97w39	(88·10²⁶⁸⁰-349)/9	December 24, 2012	Ray Chandler
2247	2681		85w77	(77·10²⁶⁸⁰+193)/9	December 24, 2012	Ray Chandler
2248	2681	57703	57w03	(52·10²⁶⁸⁰-673)/9	December 24, 2012	Ray Chandler
2250	2680	98859	98w59	(89·10²⁶⁷⁹-269)/9	December 24, 2012	Ray Chandler
2253	2679	68813	68w13	(62·10²⁶⁷⁸-683)/9	December 24, 2012	Ray Chandler
2254	2679	45587	45w87	(41·10²⁶⁷⁸+283)/9	December 24, 2012	Ray Chandler
2255	2678	56639	56w39	(17·10²⁶⁷⁷-83)/3	December 24, 2012	Ray Chandler
2256	2678		228w9	(206·10²⁶⁷⁶+1)/9	December 24, 2012	Ray Chandler
2257	2677	67703	67w03	(61·10²⁶⁷⁶-673)/9	December 24, 2012	Ray Chandler
2259	2675	90023	90w23	9·10²⁶⁷⁴+23	December 24, 2012	Ray Chandler
2260	2674	98869	98w69	(89·10²⁶⁷³-179)/9	December 24, 2012	Ray Chandler
2261	2674		445w3	(401·10²⁶⁷²-23)/9	December 24, 2012	Ray Chandler
2262	2674	40057	40w57	4·10²⁶⁷³+57	December 24, 2012	Ray Chandler
2264	2673	86609	86w09	(26·10²⁶⁷²-173)/3	December 24, 2012	Ray Chandler
2265	2673		776w3	(233·10²⁶⁷¹-11)/3	December 24, 2012	Ray Chandler
2268	2670	18861	18w61	(17·10²⁶⁶⁹-251)/9	December 24, 2012	Ray Chandler
2270	2668		883w1	(265·10²⁶⁶⁶-7)/3	December 24, 2012	Ray Chandler
2271	2668		442w3	(398·10²⁶⁶⁶+7)/9	December 24, 2012	Ray Chandler
2272	2668		336w1	(101·10²⁶⁶⁶-17)/3	December 24, 2012	Ray Chandler
2274	2667		998w7	(899·10²⁶⁶⁵-17)/9	December 24, 2012	Ray Chandler
2276	2667	39913	39w13	4·10²⁶⁶⁶-87	December 24, 2012	Ray Chandler
2278	2666		559w7	56·10²⁶⁶⁴-3	December 24, 2012	Ray Chandler
2280	2665	67713	67w13	(61·10²⁶⁶⁴-583)/9	December 24, 2012	Ray Chandler
2281	2664	52259	52w59	(47·10²⁶⁶³+331)/9	December 24, 2012	Ray Chandler
2282	2664	26621	26w21	(8·10²⁶⁶³-137)/3	December 24, 2012	Ray Chandler
2283	2664		228w7	(206·10²⁶⁶²-17)/9	December 24, 2012	Ray Chandler
2285	2662	52287	52w87	(47·10²⁶⁶¹+583)/9	December 24, 2012	Ray Chandler
2286	2661	83329	83w29	(25·10²⁶⁶⁰-13)/3	December 24, 2012	Ray Chandler
2287	2659	78871	78w71	(71·10²⁶⁵⁸-161)/9	December 24, 2012	Ray Chandler
2288	2659		663w1	(199·10²⁶⁵⁷-7)/3	December 24, 2012	Ray Chandler
2289	2659		30w77	3·10²⁶⁵⁸+77	December 24, 2012	Ray Chandler
2291	2657	78823	78w23	(71·10²⁶⁵⁶-593)/9	December 24, 2012	Ray Chandler
2292	2656	92271	92w71	(83·10²⁶⁵⁵+439)/9	December 24, 2012	Ray Chandler
2293	2655	94497	94w97	(85·10²⁶⁵⁴+473)/9	December 24, 2012	Ray Chandler
2294	2655	56609	56w09	(17·10²⁶⁵⁴-173)/3	December 24, 2012	Ray Chandler
2295	2655	32279	32w79	(29·10²⁶⁵⁴+511)/9	December 24, 2012	Ray Chandler
2296	2655	24429	24w29	(22·10²⁶⁵⁴-139)/9	December 24, 2012	Ray Chandler
2297	2654	37781	37w81	(34·10²⁶⁵³+29)/9	December 24, 2012	Ray Chandler
2298	2654	30079	30w79	3·10²⁶⁵³+79	December 24, 2012	Ray Chandler
2299	2654		10w33	10²⁶⁵³+33	December 24, 2012	Ray Chandler
2300	2653		880w3	88·10²⁶⁵¹+3	December 24, 2012	Ray Chandler
2301	2653	68821	68w21	(62·10²⁶⁵²-611)/9	December 24, 2012	Ray Chandler
2302	2653	50089	50w89	5·10²⁶⁵²+89	December 24, 2012	Ray Chandler
2303	2652	98837	98w37	(89·10²⁶⁵¹-467)/9	December 24, 2012	Ray Chandler
2304	2652		884w1	(796·10²⁶⁵⁰-31)/9	December 24, 2012	Ray Chandler
2307	2650	58827	58w27	(53·10²⁶⁴⁹-557)/9	December 24, 2012	Ray Chandler
2309	2649	14473	14w73	(13·10²⁶⁴⁸+257)/9	December 24, 2012	Ray Chandler
2310	2648	61129	61w29	(55·10²⁶⁴⁷+161)/9	December 24, 2012	Ray Chandler
2311	2648	34463	34w63	(31·10²⁶⁴⁷+167)/9	December 24, 2012	Ray Chandler
2312	2647	57743	57w43	(52·10²⁶⁴⁶-313)/9	December 24, 2012	Ray Chandler
2313	2646		87w11	(79·10²⁶⁴⁵-601)/9	December 24, 2012	Ray Chandler
2314	2645	86657	86w57	(26·10²⁶⁴⁴-29)/3	December 24, 2012	Ray Chandler
2315	2644	97739	97w39	(88·10²⁶⁴³-349)/9	December 24, 2012	Ray Chandler
2316	2644		56w33	(17·10²⁶⁴³-101)/3	December 24, 2012	Ray Chandler
2317	2643		889w7	89·10²⁶⁴¹-3	December 24, 2012	Ray Chandler
2318	2643		883w7	(265·10²⁶⁴¹+11)/3	December 24, 2012	Ray Chandler
2319	2643	34461	34w61	(31·10²⁶⁴²+149)/9	December 24, 2012	Ray Chandler
2320	2643	21163	21w63	(19·10²⁶⁴²+467)/9	December 24, 2012	Ray Chandler
2321	2642	76637	76w37	(23·10²⁶⁴¹-89)/3	December 24, 2012	Ray Chandler
2323	2640	69961	69w61	7·10²⁶³⁹-39	December 24, 2012	Ray Chandler
2324	2640	43319	43w19	(13·10²⁶³⁹-43)/3	December 24, 2012	Ray Chandler
2325	2639	19973	19w73	2·10²⁶³⁸-27	December 24, 2012	Ray Chandler
2326	2638	14457	14w57	(13·10²⁶³⁷+113)/9	December 24, 2012	Ray Chandler
2328	2636	91129	91w29	(82·10²⁶³⁵+161)/9	December 24, 2012	Ray Chandler
2329	2636		56w33	(17·10²⁶³⁵-101)/3	December 24, 2012	Ray Chandler
2331	2635	60037	60w37	6·10²⁶³⁴+37	December 24, 2012	Ray Chandler
2333	2634		559w1	56·10²⁶³²-9	December 24, 2012	Ray Chandler
2334	2634	31147	31w47	(28·10²⁶³³+323)/9	December 24, 2012	Ray Chandler
2335	2634	25581	25w81	(23·10²⁶³³+229)/9	December 24, 2012	Ray Chandler
2336	2634	24487	24w87	(22·10²⁶³³+383)/9	December 24, 2012	Ray Chandler
2338	2633		74w11	(67·10²⁶³²-301)/9	December 24, 2012	Ray Chandler
2339	2633	35579	35w79	(32·10²⁶³²+211)/9	December 24, 2012	Ray Chandler
2340	2633	29903	29w03	3·10²⁶³²-97	December 24, 2012	Ray Chandler
2342	2631	65519	65w19	(59·10²⁶³⁰-329)/9	December 24, 2012	Ray Chandler
2343	2631	12273	12w73	(11·10²⁶³⁰+457)/9	December 24, 2012	Ray Chandler
2344	2630	85597	85w97	(77·10²⁶²⁹+373)/9	December 24, 2012	Ray Chandler
2345	2630	58871	58w71	(53·10²⁶²⁹-161)/9	December 24, 2012	Ray Chandler
2347	2630		12w99	(11·10²⁶²⁹+691)/9	December 24, 2012	Ray Chandler
2349	2629		86w99	(26·10²⁶²⁸+97)/3	December 24, 2012	Ray Chandler
2350	2629	57731	57w31	(52·10²⁶²⁸-421)/9	December 24, 2012	Ray Chandler
2351	2629		448w1	(404·10²⁶²⁷-71)/9	December 24, 2012	Ray Chandler
2352	2627	14423	14w23	(13·10²⁶²⁶-193)/9	December 24, 2012	Ray Chandler
2353	2627	12239	12w39	(11·10²⁶²⁶+151)/9	December 24, 2012	Ray Chandler
2355	2626	68863	68w63	(62·10²⁶²⁵-233)/9	December 24, 2012	Ray Chandler
2356	2624	17789	17w89	(16·10²⁶²³+101)/9	December 24, 2012	Ray Chandler
2357	2623	89971	89w71	9·10²⁶²²-29	December 24, 2012	Ray Chandler
2358	2623	59953	59w53	6·10²⁶²²-47	December 24, 2012	Ray Chandler
2360	2623	20027	20w27	2·10²⁶²²+27	December 24, 2012	Ray Chandler
2361	2622	73367	73w67	(22·10²⁶²¹+101)/3	December 24, 2012	Ray Chandler
2363	2621	93391	93w91	(28·10²⁶²⁰+173)/3	December 24, 2012	Ray Chandler
2364	2620	91103	91w03	(82·10²⁶¹⁹-73)/9	December 24, 2012	Ray Chandler
2365	2620	85549	85w49	(77·10²⁶¹⁹-59)/9	December 24, 2012	Ray Chandler
2369	2619		224w7	(202·10²⁶¹⁷+23)/9	December 24, 2012	Ray Chandler
2370	2618	85531	85w31	(77·10²⁶¹⁷-221)/9	December 24, 2012	Ray Chandler
2371	2618		331w9	(298·10²⁶¹⁶+71)/9	December 24, 2012	Ray Chandler
2372	2618	26693	26w93	(8·10²⁶¹⁷+79)/3	December 24, 2012	Ray Chandler
2373	2617		229w3	23·10²⁶¹⁵-7	December 24, 2012	Ray Chandler
2374	2616	78863	78w63	(71·10²⁶¹⁵-233)/9	December 24, 2012	Ray Chandler
2375	2616		56w33	(17·10²⁶¹⁵-101)/3	December 24, 2012	Ray Chandler
2376	2615	40093	40w93	4·10²⁶¹⁴+93	December 24, 2012	Ray Chandler
2378	2614		59w33	6·10²⁶¹³-67	December 24, 2012	Ray Chandler
2379	2614	58821	58w21	(53·10²⁶¹³-611)/9	December 24, 2012	Ray Chandler
2380	2613	50041	50w41	5·10²⁶¹²+41	December 24, 2012	Ray Chandler
2381	2613	12213	12w13	(11·10²⁶¹²-83)/9	December 24, 2012	Ray Chandler
2382	2612	74471	74w71	(67·10²⁶¹¹+239)/9	December 24, 2012	Ray Chandler
2383	2612	64453	64w53	(58·10²⁶¹¹+77)/9	December 24, 2012	Ray Chandler
2384	2612	51103	51w03	(46·10²⁶¹¹-73)/9	December 24, 2012	Ray Chandler
2385	2612	26687	26w87	(8·10²⁶¹¹+61)/3	December 24, 2012	Ray Chandler
2386	2610	72213	72w13	(65·10²⁶⁰⁹-83)/9	December 24, 2012	Ray Chandler
2388	2607	10037	10w37	10²⁶⁰⁶+37	December 24, 2012	Ray Chandler
2389	2606	15523	15w23	(14·10²⁶⁰⁵-293)/9	December 24, 2012	Ray Chandler
2391	2604	98849	98w49	(89·10²⁶⁰³-359)/9	December 24, 2012	Ray Chandler
2392	2604	95571	95w71	(86·10²⁶⁰³+139)/9	December 24, 2012	Ray Chandler
2395	2603		28w77	(26·10²⁶⁰²-107)/9	December 24, 2012	Ray Chandler
2396	2602	32239	32w39	(29·10²⁶⁰¹+151)/9	December 24, 2012	Ray Chandler
2397	2600		76w99	(23·10²⁵⁹⁹+97)/3	December 24, 2012	Ray Chandler
2398	2600	63349	63w49	(19·10²⁵⁹⁹+47)/3	December 24, 2012	Ray Chandler

Factorizations of 733...33 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 10³⁰.

December 23, 2012

Ray Chandler successfully proved the primality of a 10625-digit prime number Phi(26570,10) by Primo. Congratulations! Certification is available.

December 20, 2012

Ray Chandler certificated 5 near-repdigit prime numbers, 41 quasi-repdigit prime numbers and 131 near-repdigit-related prime numbers by Primo. Certifications are available.

Proven near-repdigit primes
	digits	flabel	wlabel	expression	when	who
504	2557		9w49999	10²⁵⁵⁷-50001	December 20, 2012	Ray Chandler
505	2555	35333	353w	(106·10²⁵⁵³-1)/3	December 20, 2012	Ray Chandler
506	2546		9w299999999	10²⁵⁴⁶-700000001	December 20, 2012	Ray Chandler
508	2526		9w79999	10²⁵²⁶-20001	December 20, 2012	Ray Chandler
510	2514	15111	151w	(136·10²⁵¹²-1)/9	December 20, 2012	Ray Chandler

Proven quasi-repdigit primes (except pd)
	digits	flabel	wlabel	expression	when	who
340	2598	21151	21w51	(19·10²⁵⁹⁷+359)/9	December 20, 2012	Ray Chandler
342	2594	49919	49w19	5·10²⁵⁹³-81	December 20, 2012	Ray Chandler
343	2594	44423	4w23	(4·10²⁵⁹⁴-193)/9	December 20, 2012	Ray Chandler
344	2593	45443	454w3	(409·10²⁵⁹¹-13)/9	December 20, 2012	Ray Chandler
345	2592	64447	64w7	(58·10²⁵⁹¹+23)/9	December 20, 2012	Ray Chandler
346	2590	79779	797w9	(718·10²⁵⁸⁸+11)/9	December 20, 2012	Ray Chandler
348	2586	17113	171w3	(154·10²⁵⁸⁴+17)/9	December 20, 2012	Ray Chandler
349	2583	87757	87w57	(79·10²⁵⁸²-187)/9	December 20, 2012	Ray Chandler
350	2581	99901	9w01	10²⁵⁸¹-99	December 20, 2012	Ray Chandler
352	2581	23777	237w	(214·10²⁵⁷⁹-7)/9	December 20, 2012	Ray Chandler
353	2573	22247	2w47	(2·10²⁵⁷³+223)/9	December 20, 2012	Ray Chandler
354	2571	66601	6w01	(2·10²⁵⁷¹-197)/3	December 20, 2012	Ray Chandler
355	2571	25777	257w	(232·10²⁵⁶⁹-7)/9	December 20, 2012	Ray Chandler
357	2565	44431	4w31	(4·10²⁵⁶⁵-121)/9	December 20, 2012	Ray Chandler
358	2564	49991	49w1	5·10²⁵⁶³-9	December 20, 2012	Ray Chandler
360	2563	92221	92w1	(83·10²⁵⁶²-11)/9	December 20, 2012	Ray Chandler
362	2556	83353	83w53	(25·10²⁵⁵⁵+59)/3	December 20, 2012	Ray Chandler
363	2555	74449	74w9	(67·10²⁵⁵⁴+41)/9	December 20, 2012	Ray Chandler
364	2554	53393	53w93	(16·10²⁵⁵³+179)/3	December 20, 2012	Ray Chandler
365	2554	10119	101w9	(91·10²⁵⁵²+71)/9	December 20, 2012	Ray Chandler
366	2547	75551	75w1	(68·10²⁵⁴⁶-41)/9	December 20, 2012	Ray Chandler
367	2546	54559	545w9	(491·10²⁵⁴⁴+31)/9	December 20, 2012	Ray Chandler
368	2545	95111	951w	(856·10²⁵⁴³-1)/9	December 20, 2012	Ray Chandler
369	2542	97333	973w	(292·10²⁵⁴⁰-1)/3	December 20, 2012	Ray Chandler
370	2540	63373	63w73	(19·10²⁵³⁹+119)/3	December 20, 2012	Ray Chandler
372	2533	70333	703w	(211·10²⁵³¹-1)/3	December 20, 2012	Ray Chandler
373	2533	55521	5w21	(5·10²⁵³³-311)/9	December 20, 2012	Ray Chandler
374	2532	63661	636w1	(191·10²⁵³⁰-17)/3	December 20, 2012	Ray Chandler
375	2532	40449	404w9	(364·10²⁵³⁰+41)/9	December 20, 2012	Ray Chandler
376	2529	11137	1w37	(10²⁵²⁹+233)/9	December 20, 2012	Ray Chandler
377	2524	16113	161w3	(145·10²⁵²²+17)/9	December 20, 2012	Ray Chandler
378	2519	59909	59w09	6·10²⁵¹⁸-91	December 20, 2012	Ray Chandler
379	2519	31777	317w	(286·10²⁵¹⁷-7)/9	December 20, 2012	Ray Chandler
380	2516	85559	85w9	(77·10²⁵¹⁵+31)/9	December 20, 2012	Ray Chandler
381	2514	27727	27w27	(25·10²⁵¹³-457)/9	December 20, 2012	Ray Chandler
384	2508	64443	64w3	(58·10²⁵⁰⁷-13)/9	December 20, 2012	Ray Chandler
385	2508	48777	487w	(439·10²⁵⁰⁶-7)/9	December 20, 2012	Ray Chandler
386	2506	22231	2w31	(2·10²⁵⁰⁶+79)/9	December 20, 2012	Ray Chandler
387	2503	37707	37w07	(34·10²⁵⁰²-637)/9	December 20, 2012	Ray Chandler
388	2502	71121	71w21	(64·10²⁵⁰¹+89)/9	December 20, 2012	Ray Chandler
389	2500	20229	202w9	(182·10²⁴⁹⁸+61)/9	December 20, 2012	Ray Chandler

Proven near-repdigit-related primes (except ru/nr/pd/qr)
	digits	flabel	wlabel	expression	when	who
2255	2598		48w33	(44·10²⁵⁹⁷-503)/9	December 20, 2012	Ray Chandler
2256	2597	78839	78w39	(71·10²⁵⁹⁶-449)/9	December 20, 2012	Ray Chandler
2257	2597	64483	64w83	(58·10²⁵⁹⁶+347)/9	December 20, 2012	Ray Chandler
2258	2596	48897	48w97	(44·10²⁵⁹⁵+73)/9	December 20, 2012	Ray Chandler
2259	2595	90053	90w53	9·10²⁵⁹⁴+53	December 20, 2012	Ray Chandler
2260	2595	87709	87w09	(79·10²⁵⁹⁴-619)/9	December 20, 2012	Ray Chandler
2261	2595	60017	60w17	6·10²⁵⁹⁴+17	December 20, 2012	Ray Chandler
2263	2595		48w99	(44·10²⁵⁹⁴+91)/9	December 20, 2012	Ray Chandler
2265	2594		52w11	(47·10²⁵⁹³-101)/9	December 20, 2012	Ray Chandler
2267	2593	97763	97w63	(88·10²⁵⁹²-133)/9	December 20, 2012	Ray Chandler
2268	2593	94437	94w37	(85·10²⁵⁹²-67)/9	December 20, 2012	Ray Chandler
2269	2593	74469	74w69	(67·10²⁵⁹²+221)/9	December 20, 2012	Ray Chandler
2270	2593	71127	71w27	(64·10²⁵⁹²+143)/9	December 20, 2012	Ray Chandler
2271	2593	60073	60w73	6·10²⁵⁹²+73	December 20, 2012	Ray Chandler
2272	2592		117w9	(106·10²⁵⁹⁰+11)/9	December 20, 2012	Ray Chandler
2273	2591	79927	79w27	8·10²⁵⁹⁰-73	December 20, 2012	Ray Chandler
2274	2591	78829	78w29	(71·10²⁵⁹⁰-539)/9	December 20, 2012	Ray Chandler
2275	2591	46687	46w87	(14·10²⁵⁹⁰+61)/3	December 20, 2012	Ray Chandler
2276	2590	94419	94w19	(85·10²⁵⁸⁹-229)/9	December 20, 2012	Ray Chandler
2277	2590	75571	75w71	(68·10²⁵⁸⁹+139)/9	December 20, 2012	Ray Chandler
2278	2589	83357	83w57	(25·10²⁵⁸⁸+71)/3	December 20, 2012	Ray Chandler
2279	2589	78813	78w13	(71·10²⁵⁸⁸-683)/9	December 20, 2012	Ray Chandler
2280	2589	34417	34w17	(31·10²⁵⁸⁸-247)/9	December 20, 2012	Ray Chandler
2281	2589		28w77	(26·10²⁵⁸⁸-107)/9	December 20, 2012	Ray Chandler
2284	2586	74493	74w93	(67·10²⁵⁸⁵+437)/9	December 20, 2012	Ray Chandler
2285	2585	39901	39w01	4·10²⁵⁸⁴-99	December 20, 2012	Ray Chandler
2287	2584	62289	62w89	(56·10²⁵⁸³+601)/9	December 20, 2012	Ray Chandler
2289	2583	89957	89w57	9·10²⁵⁸²-43	December 20, 2012	Ray Chandler
2290	2583	31137	31w37	(28·10²⁵⁸²+233)/9	December 20, 2012	Ray Chandler
2291	2582	31109	31w09	(28·10²⁵⁸¹-19)/9	December 20, 2012	Ray Chandler
2293	2581	42291	42w91	(38·10²⁵⁸⁰+619)/9	December 20, 2012	Ray Chandler
2294	2581	19927	19w27	2·10²⁵⁸⁰-73	December 20, 2012	Ray Chandler
2297	2578	70081	70w81	7·10²⁵⁷⁷+81	December 20, 2012	Ray Chandler
2298	2578	45567	45w67	(41·10²⁵⁷⁷+103)/9	December 20, 2012	Ray Chandler
2299	2578	17763	17w63	(16·10²⁵⁷⁷-133)/9	December 20, 2012	Ray Chandler
2300	2578	14489	14w89	(13·10²⁵⁷⁷+401)/9	December 20, 2012	Ray Chandler
2301	2578	10061	10w61	10²⁵⁷⁷+61	December 20, 2012	Ray Chandler
2302	2577		36w11	(11·10²⁵⁷⁶-167)/3	December 20, 2012	Ray Chandler
2304	2576	97751	97w51	(88·10²⁵⁷⁵-241)/9	December 20, 2012	Ray Chandler
2306	2574	15579	15w79	(14·10²⁵⁷³+211)/9	December 20, 2012	Ray Chandler
2308	2572	50081	50w81	5·10²⁵⁷¹+81	December 20, 2012	Ray Chandler
2309	2572	35547	35w47	(32·10²⁵⁷¹-77)/9	December 20, 2012	Ray Chandler
2312	2570	39913	39w13	4·10²⁵⁶⁹-87	December 20, 2012	Ray Chandler
2313	2570		34w99	(31·10²⁵⁶⁹+491)/9	December 20, 2012	Ray Chandler
2314	2569	56681	56w81	(17·10²⁵⁶⁸+43)/3	December 20, 2012	Ray Chandler
2315	2568	58859	58w59	(53·10²⁵⁶⁷-269)/9	December 20, 2012	Ray Chandler
2318	2567	98851	98w51	(89·10²⁵⁶⁶-341)/9	December 20, 2012	Ray Chandler
2320	2566	53351	53w51	(16·10²⁵⁶⁵+53)/3	December 20, 2012	Ray Chandler
2322	2566		25w33	(23·10²⁵⁶⁵-203)/9	December 20, 2012	Ray Chandler
2323	2566	24489	24w89	(22·10²⁵⁶⁵+401)/9	December 20, 2012	Ray Chandler
2324	2565	90019	90w19	9·10²⁵⁶⁴+19	December 20, 2012	Ray Chandler
2325	2564	90089	90w89	9·10²⁵⁶³+89	December 20, 2012	Ray Chandler
2327	2561	18869	18w69	(17·10²⁵⁶⁰-179)/9	December 20, 2012	Ray Chandler
2329	2560	45519	45w19	(41·10²⁵⁵⁹-329)/9	December 20, 2012	Ray Chandler
2332	2559	32207	32w07	(29·10²⁵⁵⁸-137)/9	December 20, 2012	Ray Chandler
2334	2558	43387	43w87	(13·10²⁵⁵⁷+161)/3	December 20, 2012	Ray Chandler
2335	2557	79903	79w03	8·10²⁵⁵⁶-97	December 20, 2012	Ray Chandler
2336	2556	76693	76w93	(23·10²⁵⁵⁵+79)/3	December 20, 2012	Ray Chandler
2337	2556	61159	61w59	(55·10²⁵⁵⁵+431)/9	December 20, 2012	Ray Chandler
2338	2555		94w99	(85·10²⁵⁵⁴+491)/9	December 20, 2012	Ray Chandler
2339	2554		996w7	(299·10²⁵⁵²+1)/3	December 20, 2012	Ray Chandler
2340	2554		89w77	9·10²⁵⁵³-23	December 20, 2012	Ray Chandler
2341	2554		52w33	(47·10²⁵⁵³+97)/9	December 20, 2012	Ray Chandler
2342	2554	30037	30w37	3·10²⁵⁵³+37	December 20, 2012	Ray Chandler
2343	2553		448w3	(404·10²⁵⁵¹-53)/9	December 20, 2012	Ray Chandler
2345	2549		334w3	(301·10²⁵⁴⁷-13)/9	December 20, 2012	Ray Chandler
2347	2548		94w33	(85·10²⁵⁴⁷-103)/9	December 20, 2012	Ray Chandler
2348	2548	34401	34w01	(31·10²⁵⁴⁷-391)/9	December 20, 2012	Ray Chandler
2349	2548		227w3	(205·10²⁵⁴⁶-43)/9	December 20, 2012	Ray Chandler
2350	2548	13361	13w61	(4·10²⁵⁴⁷+83)/3	December 20, 2012	Ray Chandler
2351	2547	96641	96w41	(29·10²⁵⁴⁶-77)/3	December 20, 2012	Ray Chandler
2352	2547	45509	45w09	(41·10²⁵⁴⁶-419)/9	December 20, 2012	Ray Chandler
2353	2547	34437	34w37	(31·10²⁵⁴⁶-67)/9	December 20, 2012	Ray Chandler
2355	2546	65569	65w69	(59·10²⁵⁴⁵+121)/9	December 20, 2012	Ray Chandler
2357	2545	78801	78w01	(71·10²⁵⁴⁴-791)/9	December 20, 2012	Ray Chandler
2358	2545	13379	13w79	(4·10²⁵⁴⁴+137)/3	December 20, 2012	Ray Chandler
2359	2544	15587	15w87	(14·10²⁵⁴³+283)/9	December 20, 2012	Ray Chandler
2360	2543	91129	91w29	(82·10²⁵⁴²+161)/9	December 20, 2012	Ray Chandler
2361	2542	63359	63w59	(19·10²⁵⁴¹+77)/3	December 20, 2012	Ray Chandler
2363	2541	85583	85w83	(77·10²⁵⁴⁰+247)/9	December 20, 2012	Ray Chandler
2364	2541	35573	35w73	(32·10²⁵⁴⁰+157)/9	December 20, 2012	Ray Chandler
2365	2541	20089	20w89	2·10²⁵⁴⁰+89	December 20, 2012	Ray Chandler
2366	2539		772w7	(695·10²⁵³⁷+43)/9	December 20, 2012	Ray Chandler
2367	2539	23347	23w47	(7·10²⁵³⁸+41)/3	December 20, 2012	Ray Chandler
2369	2538	52293	52w93	(47·10²⁵³⁷+637)/9	December 20, 2012	Ray Chandler
2370	2538	42269	42w69	(38·10²⁵³⁷+421)/9	December 20, 2012	Ray Chandler
2371	2536	45547	45w47	(41·10²⁵³⁵-77)/9	December 20, 2012	Ray Chandler
2372	2535	17703	17w03	(16·10²⁵³⁴-673)/9	December 20, 2012	Ray Chandler
2373	2535	14493	14w93	(13·10²⁵³⁴+437)/9	December 20, 2012	Ray Chandler
2374	2534	95513	95w13	(86·10²⁵³³-383)/9	December 20, 2012	Ray Chandler
2375	2534	39913	39w13	4·10²⁵³³-87	December 20, 2012	Ray Chandler
2376	2533	80059	80w59	8·10²⁵³²+59	December 20, 2012	Ray Chandler
2377	2533		771w7	(694·10²⁵³¹+53)/9	December 20, 2012	Ray Chandler
2379	2531	75563	75w63	(68·10²⁵³⁰+67)/9	December 20, 2012	Ray Chandler
2380	2528	28859	28w59	(26·10²⁵²⁷-269)/9	December 20, 2012	Ray Chandler
2381	2527	56641	56w41	(17·10²⁵²⁶-77)/3	December 20, 2012	Ray Chandler
2382	2527		110w9	11·10²⁵²⁵+9	December 20, 2012	Ray Chandler
2383	2526	89923	89w23	9·10²⁵²⁵-77	December 20, 2012	Ray Chandler
2384	2526	72201	72w01	(65·10²⁵²⁵-191)/9	December 20, 2012	Ray Chandler
2385	2526	58851	58w51	(53·10²⁵²⁵-341)/9	December 20, 2012	Ray Chandler
2386	2525	43361	43w61	(13·10²⁵²⁴+83)/3	December 20, 2012	Ray Chandler
2387	2524		53w99	(16·10²⁵²³+197)/3	December 20, 2012	Ray Chandler
2388	2523		336w7	(101·10²⁵²¹+1)/3	December 20, 2012	Ray Chandler
2389	2522	82243	82w43	(74·10²⁵²¹+187)/9	December 20, 2012	Ray Chandler
2391	2522	21149	21w49	(19·10²⁵²¹+341)/9	December 20, 2012	Ray Chandler
2393	2521	42213	42w13	(38·10²⁵²⁰-83)/9	December 20, 2012	Ray Chandler
2394	2521	34457	34w57	(31·10²⁵²⁰+113)/9	December 20, 2012	Ray Chandler
2395	2520	70057	70w57	7·10²⁵¹⁹+57	December 20, 2012	Ray Chandler
2396	2518	37713	37w13	(34·10²⁵¹⁷-583)/9	December 20, 2012	Ray Chandler
2397	2516		97w11	(88·10²⁵¹⁵-601)/9	December 20, 2012	Ray Chandler
2398	2515	37751	37w51	(34·10²⁵¹⁴-241)/9	December 20, 2012	Ray Chandler
2399	2513	97793	97w93	(88·10²⁵¹²+137)/9	December 20, 2012	Ray Chandler
2400	2513	58879	58w79	(53·10²⁵¹²-89)/9	December 20, 2012	Ray Chandler
2401	2513	14429	14w29	(13·10²⁵¹²-139)/9	December 20, 2012	Ray Chandler
2402	2512		95w11	(86·10²⁵¹¹-401)/9	December 20, 2012	Ray Chandler
2403	2512	73351	73w51	(22·10²⁵¹¹+53)/3	December 20, 2012	Ray Chandler
2404	2512	72243	72w43	(65·10²⁵¹¹+187)/9	December 20, 2012	Ray Chandler
2405	2511		83w99	(25·10²⁵¹⁰+197)/3	December 20, 2012	Ray Chandler
2406	2511	74419	74w19	(67·10²⁵¹⁰-229)/9	December 20, 2012	Ray Chandler
2407	2511	62253	62w53	(56·10²⁵¹⁰+277)/9	December 20, 2012	Ray Chandler
2408	2510	87763	87w63	(79·10²⁵⁰⁹-133)/9	December 20, 2012	Ray Chandler
2409	2510		440w3	44·10²⁵⁰⁸+3	December 20, 2012	Ray Chandler
2412	2508		664w1	(598·10²⁵⁰⁶-31)/9	December 20, 2012	Ray Chandler
2413	2508	43357	43w57	(13·10²⁵⁰⁷+71)/3	December 20, 2012	Ray Chandler
2414	2507	39967	39w67	4·10²⁵⁰⁶-33	December 20, 2012	Ray Chandler
2415	2504	27781	27w81	(25·10²⁵⁰³+29)/9	December 20, 2012	Ray Chandler
2416	2503	78841	78w41	(71·10²⁵⁰²-431)/9	December 20, 2012	Ray Chandler
2417	2503		50w77	5·10²⁵⁰²+77	December 20, 2012	Ray Chandler
2419	2501	60083	60w83	6·10²⁵⁰⁰+83	December 20, 2012	Ray Chandler
2420	2501	13397	13w97	(4·10²⁵⁰⁰+191)/3	December 20, 2012	Ray Chandler
2422	2500	13307	13w07	(4·10²⁴⁹⁹-79)/3	December 20, 2012	Ray Chandler

Factorizations of 722...227 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 10³⁰.

December 17, 2012

Ray Chandler certificated 7 near-repdigit prime numbers, 42 quasi-repdigit prime numbers and 111 near-repdigit-related prime numbers by Primo. Certifications are available.

Proven near-repdigit primes
	digits	flabel	wlabel	expression	when	who
512	2495		9w59999999	10²⁴⁹⁵-40000001	December 17, 2012	Ray Chandler
513	2494	77757	7w57	(7·10²⁴⁹⁴-187)/9	December 17, 2012	Ray Chandler
516	2475		9w599	10²⁴⁷⁵-401	December 17, 2012	Ray Chandler
518	2444		9w59999	10²⁴⁴⁴-40001	December 17, 2012	Ray Chandler
520	2438		9w7999	10²⁴³⁸-2001	December 17, 2012	Ray Chandler
521	2420		9w79999999	10²⁴²⁰-20000001	December 17, 2012	Ray Chandler
523	2400		9w5999999	10²⁴⁰⁰-4000001	December 17, 2012	Ray Chandler

Proven quasi-repdigit primes (except pd)
	digits	flabel	wlabel	expression	when	who
349	2497		4w11	(4·10²⁴⁹⁷-301)/9	December 17, 2012	Ray Chandler
350	2496	54111	541w	(487·10²⁴⁹⁴-1)/9	December 17, 2012	Ray Chandler
351	2495	61661	616w1	(185·10²⁴⁹³-17)/3	December 17, 2012	Ray Chandler
352	2494	78883	78w3	(71·10²⁴⁹³-53)/9	December 17, 2012	Ray Chandler
353	2492	64441	64w1	(58·10²⁴⁹¹-31)/9	December 17, 2012	Ray Chandler
355	2486	84883	848w3	(764·10²⁴⁸⁴-53)/9	December 17, 2012	Ray Chandler
356	2486	62777	627w	(565·10²⁴⁸⁴-7)/9	December 17, 2012	Ray Chandler
357	2485	85887	858w7	(773·10²⁴⁸³-17)/9	December 17, 2012	Ray Chandler
359	2482	33349	3w49	(10²⁴⁸²+47)/3	December 17, 2012	Ray Chandler
360	2479	33349	3w49	(10²⁴⁷⁹+47)/3	December 17, 2012	Ray Chandler
361	2478	73363	73w63	(22·10²⁴⁷⁷+89)/3	December 17, 2012	Ray Chandler
364	2476	66689	6w89	(2·10²⁴⁷⁶+67)/3	December 17, 2012	Ray Chandler
366	2472	20229	202w9	(182·10²⁴⁷⁰+61)/9	December 17, 2012	Ray Chandler
367	2469	82887	828w7	(746·10²⁴⁶⁷-17)/9	December 17, 2012	Ray Chandler
368	2467	12117	121w7	(109·10²⁴⁶⁵+53)/9	December 17, 2012	Ray Chandler
371	2464	30111	301w	(271·10²⁴⁶²-1)/9	December 17, 2012	Ray Chandler
372	2461		771w	(694·10²⁴⁵⁹-1)/9	December 17, 2012	Ray Chandler
373	2460	52777	527w	(475·10²⁴⁵⁸-7)/9	December 17, 2012	Ray Chandler
375	2457	36777	367w	(331·10²⁴⁵⁵-7)/9	December 17, 2012	Ray Chandler
376	2456	64777	647w	(583·10²⁴⁵⁴-7)/9	December 17, 2012	Ray Chandler
378	2447	59989	59w89	6·10²⁴⁴⁶-11	December 17, 2012	Ray Chandler
379	2445	55593	5w93	(5·10²⁴⁴⁵+337)/9	December 17, 2012	Ray Chandler
381	2443	19919	19w19	2·10²⁴⁴²-81	December 17, 2012	Ray Chandler
382	2442	71181	71w81	(64·10²⁴⁴¹+629)/9	December 17, 2012	Ray Chandler
383	2442	36777	367w	(331·10²⁴⁴⁰-7)/9	December 17, 2012	Ray Chandler
384	2442	22251	2w51	(2·10²⁴⁴²+259)/9	December 17, 2012	Ray Chandler
385	2439	31331	313w1	(94·10²⁴³⁷-7)/3	December 17, 2012	Ray Chandler
386	2437		1w001	(10²⁴³⁷-991)/9	December 17, 2012	Ray Chandler
388	2433	55593	5w93	(5·10²⁴³³+337)/9	December 17, 2012	Ray Chandler
390	2432	22267	2w67	(2·10²⁴³²+403)/9	December 17, 2012	Ray Chandler
391	2430	66619	6w19	(2·10²⁴³⁰-143)/3	December 17, 2012	Ray Chandler
392	2429	95993	959w3	96·10²⁴²⁷-7	December 17, 2012	Ray Chandler
393	2429	17113	171w3	(154·10²⁴²⁷+17)/9	December 17, 2012	Ray Chandler
396	2425	69959	69w59	7·10²⁴²⁴-41	December 17, 2012	Ray Chandler
398	2423	29959	29w59	3·10²⁴²²-41	December 17, 2012	Ray Chandler
399	2419		667w	(601·10²⁴¹⁷-7)/9	December 17, 2012	Ray Chandler
401	2418	11193	1w93	(10²⁴¹⁸+737)/9	December 17, 2012	Ray Chandler
402	2416	57717	57w17	(52·10²⁴¹⁵-547)/9	December 17, 2012	Ray Chandler
403	2414	79949	79w49	8·10²⁴¹³-51	December 17, 2012	Ray Chandler
406	2403	67767	67w67	(61·10²⁴⁰²-97)/9	December 17, 2012	Ray Chandler
407	2401	70773	707w3	(637·10²³⁹⁹-43)/9	December 17, 2012	Ray Chandler
408	2400	85883	858w3	(773·10²³⁹⁸-53)/9	December 17, 2012	Ray Chandler

Proven near-repdigit-related primes (except ru/nr/pd/qr)
	digits	flabel	wlabel	expression	when	who
2292	2499		662w7	(596·10²⁴⁹⁷+43)/9	December 17, 2012	Ray Chandler
2293	2499		552w7	(497·10²⁴⁹⁷+43)/9	December 17, 2012	Ray Chandler
2294	2498	84407	84w07	(76·10²⁴⁹⁷-337)/9	December 17, 2012	Ray Chandler
2296	2498		330w7	33·10²⁴⁹⁶+7	December 17, 2012	Ray Chandler
2298	2497	48853	48w53	(44·10²⁴⁹⁶-323)/9	December 17, 2012	Ray Chandler
2299	2496	21157	21w57	(19·10²⁴⁹⁵+413)/9	December 17, 2012	Ray Chandler
2301	2495	85573	85w73	(77·10²⁴⁹⁴+157)/9	December 17, 2012	Ray Chandler
2302	2494	12289	12w89	(11·10²⁴⁹³+601)/9	December 17, 2012	Ray Chandler
2303	2492	97789	97w89	(88·10²⁴⁹¹+101)/9	December 17, 2012	Ray Chandler
2304	2492	40013	40w13	4·10²⁴⁹¹+13	December 17, 2012	Ray Chandler
2305	2491	54497	54w97	(49·10²⁴⁹⁰+473)/9	December 17, 2012	Ray Chandler
2306	2489	20021	20w21	2·10²⁴⁸⁸+21	December 17, 2012	Ray Chandler
2307	2487	24457	24w57	(22·10²⁴⁸⁶+113)/9	December 17, 2012	Ray Chandler
2308	2487	21163	21w63	(19·10²⁴⁸⁶+467)/9	December 17, 2012	Ray Chandler
2309	2486	26657	26w57	(8·10²⁴⁸⁵-29)/3	December 17, 2012	Ray Chandler
2310	2485	76601	76w01	(23·10²⁴⁸⁴-197)/3	December 17, 2012	Ray Chandler
2311	2485	60073	60w73	6·10²⁴⁸⁴+73	December 17, 2012	Ray Chandler
2312	2485	39937	39w37	4·10²⁴⁸⁴-63	December 17, 2012	Ray Chandler
2313	2484		883w1	(265·10²⁴⁸²-7)/3	December 17, 2012	Ray Chandler
2314	2484	36673	36w73	(11·10²⁴⁸³+19)/3	December 17, 2012	Ray Chandler
2315	2481	86683	86w83	(26·10²⁴⁸⁰+49)/3	December 17, 2012	Ray Chandler
2316	2480		94w11	(85·10²⁴⁷⁹-301)/9	December 17, 2012	Ray Chandler
2318	2479	82267	82w67	(74·10²⁴⁷⁸+403)/9	December 17, 2012	Ray Chandler
2320	2478	35517	35w17	(32·10²⁴⁷⁷-347)/9	December 17, 2012	Ray Chandler
2321	2477	69941	69w41	7·10²⁴⁷⁶-59	December 17, 2012	Ray Chandler
2322	2476	91197	91w97	(82·10²⁴⁷⁵+773)/9	December 17, 2012	Ray Chandler
2324	2475		559w7	56·10²⁴⁷³-3	December 17, 2012	Ray Chandler
2325	2475	50021	50w21	5·10²⁴⁷⁴+21	December 17, 2012	Ray Chandler
2326	2474	94481	94w81	(85·10²⁴⁷³+329)/9	December 17, 2012	Ray Chandler
2327	2474	75509	75w09	(68·10²⁴⁷³-419)/9	December 17, 2012	Ray Chandler
2330	2472	24417	24w17	(22·10²⁴⁷¹-247)/9	December 17, 2012	Ray Chandler
2331	2471	95539	95w39	(86·10²⁴⁷⁰-149)/9	December 17, 2012	Ray Chandler
2333	2471		117w9	(106·10²⁴⁶⁹+11)/9	December 17, 2012	Ray Chandler
2334	2470	51189	51w89	(46·10²⁴⁶⁹+701)/9	December 17, 2012	Ray Chandler
2335	2469	61173	61w73	(55·10²⁴⁶⁸+557)/9	December 17, 2012	Ray Chandler
2337	2468	95567	95w67	(86·10²⁴⁶⁷+103)/9	December 17, 2012	Ray Chandler
2338	2468	72287	72w87	(65·10²⁴⁶⁷+583)/9	December 17, 2012	Ray Chandler
2339	2468		446w9	(134·10²⁴⁶⁶+7)/3	December 17, 2012	Ray Chandler
2341	2466	48849	48w49	(44·10²⁴⁶⁵-359)/9	December 17, 2012	Ray Chandler
2342	2466		115w3	(104·10²⁴⁶⁴-23)/9	December 17, 2012	Ray Chandler
2344	2463	80083	80w83	8·10²⁴⁶²+83	December 17, 2012	Ray Chandler
2347	2462	41143	41w43	(37·10²⁴⁶¹+287)/9	December 17, 2012	Ray Chandler
2348	2461		61w99	(55·10²⁴⁶⁰+791)/9	December 17, 2012	Ray Chandler
2349	2460		112w3	(101·10²⁴⁵⁸+7)/9	December 17, 2012	Ray Chandler
2351	2459	96671	96w71	(29·10²⁴⁵⁸+13)/3	December 17, 2012	Ray Chandler
2352	2459		445w7	(401·10²⁴⁵⁷+13)/9	December 17, 2012	Ray Chandler
2353	2458	70093	70w93	7·10²⁴⁵⁷+93	December 17, 2012	Ray Chandler
2354	2458	30067	30w67	3·10²⁴⁵⁷+67	December 17, 2012	Ray Chandler
2358	2456	24403	24w03	(22·10²⁴⁵⁵-373)/9	December 17, 2012	Ray Chandler
2359	2456	13301	13w01	(4·10²⁴⁵⁵-97)/3	December 17, 2012	Ray Chandler
2360	2455		23w77	(7·10²⁴⁵⁴+131)/3	December 17, 2012	Ray Chandler
2362	2454	94473	94w73	(85·10²⁴⁵³+257)/9	December 17, 2012	Ray Chandler
2363	2454	70081	70w81	7·10²⁴⁵³+81	December 17, 2012	Ray Chandler
2364	2453	94483	94w83	(85·10²⁴⁵²+347)/9	December 17, 2012	Ray Chandler
2365	2453	81167	81w67	(73·10²⁴⁵²+503)/9	December 17, 2012	Ray Chandler
2366	2453	46609	46w09	(14·10²⁴⁵²-173)/3	December 17, 2012	Ray Chandler
2368	2452		17w33	(16·10²⁴⁵¹-403)/9	December 17, 2012	Ray Chandler
2369	2452	13367	13w67	(4·10²⁴⁵¹+101)/3	December 17, 2012	Ray Chandler
2370	2450	81109	81w09	(73·10²⁴⁴⁹-19)/9	December 17, 2012	Ray Chandler
2371	2450	80071	80w71	8·10²⁴⁴⁹+71	December 17, 2012	Ray Chandler
2372	2450	79961	79w61	8·10²⁴⁴⁹-39	December 17, 2012	Ray Chandler
2373	2449		86w11	(26·10²⁴⁴⁸-167)/3	December 17, 2012	Ray Chandler
2374	2449	70057	70w57	7·10²⁴⁴⁸+57	December 17, 2012	Ray Chandler
2375	2448		30w77	3·10²⁴⁴⁷+77	December 17, 2012	Ray Chandler
2376	2447		35w99	(32·10²⁴⁴⁶+391)/9	December 17, 2012	Ray Chandler
2379	2444	56683	56w83	(17·10²⁴⁴³+49)/3	December 17, 2012	Ray Chandler
2380	2443	73327	73w27	(22·10²⁴⁴²-19)/3	December 17, 2012	Ray Chandler
2381	2443	64481	64w81	(58·10²⁴⁴²+329)/9	December 17, 2012	Ray Chandler
2383	2441		61w33	(55·10²⁴⁴⁰+197)/9	December 17, 2012	Ray Chandler
2384	2441	56621	56w21	(17·10²⁴⁴⁰-137)/3	December 17, 2012	Ray Chandler
2385	2441	24403	24w03	(22·10²⁴⁴⁰-373)/9	December 17, 2012	Ray Chandler
2387	2439	52263	52w63	(47·10²⁴³⁸+367)/9	December 17, 2012	Ray Chandler
2388	2439		38w11	(35·10²⁴³⁸-701)/9	December 17, 2012	Ray Chandler
2389	2438	71197	71w97	(64·10²⁴³⁷+773)/9	December 17, 2012	Ray Chandler
2392	2437	82281	82w81	(74·10²⁴³⁶+529)/9	December 17, 2012	Ray Chandler
2395	2435	79901	79w01	8·10²⁴³⁴-99	December 17, 2012	Ray Chandler
2396	2435	26681	26w81	(8·10²⁴³⁴+43)/3	December 17, 2012	Ray Chandler
2398	2434		74w77	(67·10²⁴³³+293)/9	December 17, 2012	Ray Chandler
2399	2434	43379	43w79	(13·10²⁴³³+137)/3	December 17, 2012	Ray Chandler
2403	2432	98897	98w97	(89·10²⁴³¹+73)/9	December 17, 2012	Ray Chandler
2404	2432	96617	96w17	(29·10²⁴³¹-149)/3	December 17, 2012	Ray Chandler
2405	2432	86653	86w53	(26·10²⁴³¹-41)/3	December 17, 2012	Ray Chandler
2407	2431	71193	71w93	(64·10²⁴³⁰+737)/9	December 17, 2012	Ray Chandler
2408	2431		29w77	3·10²⁴³⁰-23	December 17, 2012	Ray Chandler
2410	2428	85527	85w27	(77·10²⁴²⁷-257)/9	December 17, 2012	Ray Chandler
2411	2427	85527	85w27	(77·10²⁴²⁶-257)/9	December 17, 2012	Ray Chandler
2412	2427	16627	16w27	(5·10²⁴²⁶-119)/3	December 17, 2012	Ray Chandler
2413	2426	96649	96w49	(29·10²⁴²⁵-53)/3	December 17, 2012	Ray Chandler
2415	2426		76w33	(23·10²⁴²⁵-101)/3	December 17, 2012	Ray Chandler
2417	2425	26617	26w17	(8·10²⁴²⁴-149)/3	December 17, 2012	Ray Chandler
2418	2424	67713	67w13	(61·10²⁴²³-583)/9	December 17, 2012	Ray Chandler
2420	2422		882w1	(794·10²⁴²⁰-11)/9	December 17, 2012	Ray Chandler
2421	2421	86609	86w09	(26·10²⁴²⁰-173)/3	December 17, 2012	Ray Chandler
2422	2421	76657	76w57	(23·10²⁴²⁰-29)/3	December 17, 2012	Ray Chandler
2423	2417	24487	24w87	(22·10²⁴¹⁶+383)/9	December 17, 2012	Ray Chandler
2424	2415		53w77	(16·10²⁴¹⁴+131)/3	December 17, 2012	Ray Chandler
2426	2414	86627	86w27	(26·10²⁴¹³-119)/3	December 17, 2012	Ray Chandler
2427	2414	63301	63w01	(19·10²⁴¹³-97)/3	December 17, 2012	Ray Chandler
2428	2412		37w11	(34·10²⁴¹¹-601)/9	December 17, 2012	Ray Chandler
2431	2410	98857	98w57	(89·10²⁴⁰⁹-287)/9	December 17, 2012	Ray Chandler
2432	2409	84459	84w59	(76·10²⁴⁰⁸+131)/9	December 17, 2012	Ray Chandler
2433	2409	14439	14w39	(13·10²⁴⁰⁸-49)/9	December 17, 2012	Ray Chandler
2435	2407	82213	82w13	(74·10²⁴⁰⁶-83)/9	December 17, 2012	Ray Chandler
2436	2407		76w99	(23·10²⁴⁰⁶+97)/3	December 17, 2012	Ray Chandler
2439	2405		90w11	9·10²⁴⁰⁴+11	December 17, 2012	Ray Chandler
2441	2402	87709	87w09	(79·10²⁴⁰¹-619)/9	December 17, 2012	Ray Chandler
2442	2402	47789	47w89	(43·10²⁴⁰¹+101)/9	December 17, 2012	Ray Chandler
2443	2402	28879	28w79	(26·10²⁴⁰¹-89)/9	December 17, 2012	Ray Chandler
2444	2402		13w99	(4·10²⁴⁰¹+197)/3	December 17, 2012	Ray Chandler
2445	2400	75569	75w69	(68·10²³⁹⁹+121)/9	December 17, 2012	Ray Chandler
2446	2400	71157	71w57	(64·10²³⁹⁹+413)/9	December 17, 2012	Ray Chandler

Factorizations of 700...009 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 10³⁰.

December 15, 2012

Ray Chandler certificated 8 near-repdigit prime numbers, 44 quasi-repdigit prime numbers and 117 near-repdigit-related prime numbers by Primo. Certifications are available.

Proven near-repdigit primes
	digits	flabel	wlabel	expression	when	who
517	2388		9w199	10²³⁸⁸-801	December 15, 2012	Ray Chandler
518	2388		9w19999	10²³⁸⁸-80001	December 15, 2012	Ray Chandler
524	2350		9w799999999	10²³⁵⁰-200000001	December 15, 2012	Ray Chandler
525	2331	15111	151w	(136·10²³²⁹-1)/9	December 15, 2012	Ray Chandler
526	2329	77717	7w17	(7·10²³²⁹-547)/9	December 15, 2012	Ray Chandler
527	2328	99979	9w79	10²³²⁸-21	December 15, 2012	Ray Chandler
528	2324	34333	343w	(103·10²³²²-1)/3	December 15, 2012	Ray Chandler
529	2311		9w1999	10²³¹¹-8001	December 15, 2012	Ray Chandler

Proven quasi-repdigit primes (except pd)
	digits	flabel	wlabel	expression	when	who
368	2399	22213	2w13	(2·10²³⁹⁹-83)/9	December 15, 2012	Ray Chandler
369	2398	54559	545w9	(491·10²³⁹⁶+31)/9	December 15, 2012	Ray Chandler
370	2397	66607	6w07	(2·10²³⁹⁷-179)/3	December 15, 2012	Ray Chandler
371	2395	78773	787w3	(709·10²³⁹³-43)/9	December 15, 2012	Ray Chandler
372	2395	43393	43w93	(13·10²³⁹⁴+179)/3	December 15, 2012	Ray Chandler
373	2393	53353	53w53	(16·10²³⁹²+59)/3	December 15, 2012	Ray Chandler
374	2387		4w77	(4·10²³⁸⁷+293)/9	December 15, 2012	Ray Chandler
376	2380	97787	97w87	(88·10²³⁷⁹+83)/9	December 15, 2012	Ray Chandler
377	2380	46333	463w	(139·10²³⁷⁸-1)/3	December 15, 2012	Ray Chandler
380	2374	55567	5w67	(5·10²³⁷⁴+103)/9	December 15, 2012	Ray Chandler
381	2373	43393	43w93	(13·10²³⁷²+179)/3	December 15, 2012	Ray Chandler
382	2372	61669	616w9	(185·10²³⁷⁰+7)/3	December 15, 2012	Ray Chandler
383	2370	54111	541w	(487·10²³⁶⁸-1)/9	December 15, 2012	Ray Chandler
384	2368	99913	9w13	10²³⁶⁸-87	December 15, 2012	Ray Chandler
385	2368	31181	31w81	(28·10²³⁶⁷+629)/9	December 15, 2012	Ray Chandler
386	2365	79949	79w49	8·10²³⁶⁴-51	December 15, 2012	Ray Chandler
387	2364	58551	585w1	(527·10²³⁶²-41)/9	December 15, 2012	Ray Chandler
388	2353	85887	858w7	(773·10²³⁵¹-17)/9	December 15, 2012	Ray Chandler
389	2352	46449	464w9	(418·10²³⁵⁰+41)/9	December 15, 2012	Ray Chandler
391	2349		9w11	10²³⁴⁹-89	December 15, 2012	Ray Chandler
392	2348	83303	83w03	(25·10²³⁴⁷-91)/3	December 15, 2012	Ray Chandler
393	2346	91993	919w3	92·10²³⁴⁴-7	December 15, 2012	Ray Chandler
394	2345	91991	919w1	92·10²³⁴³-9	December 15, 2012	Ray Chandler
397	2340	52777	527w	(475·10²³³⁸-7)/9	December 15, 2012	Ray Chandler
398	2337	97707	97w07	(88·10²³³⁶-637)/9	December 15, 2012	Ray Chandler
399	2337	11157	1w57	(10²³³⁷+413)/9	December 15, 2012	Ray Chandler
400	2333	99907	9w07	10²³³³-93	December 15, 2012	Ray Chandler
401	2329	24223	242w3	(218·10²³²⁷+7)/9	December 15, 2012	Ray Chandler
402	2327	22273	2w73	(2·10²³²⁷+457)/9	December 15, 2012	Ray Chandler
403	2324	66629	6w29	(2·10²³²⁴-113)/3	December 15, 2012	Ray Chandler
405	2324	29777	297w	(268·10²³²²-7)/9	December 15, 2012	Ray Chandler
406	2322	91333	913w	(274·10²³²⁰-1)/3	December 15, 2012	Ray Chandler
407	2322	22263	2w63	(2·10²³²²+367)/9	December 15, 2012	Ray Chandler
408	2321	43313	43w13	(13·10²³²⁰-61)/3	December 15, 2012	Ray Chandler
409	2319	46447	464w7	(418·10²³¹⁷+23)/9	December 15, 2012	Ray Chandler
410	2319	11173	1w73	(10²³¹⁹+557)/9	December 15, 2012	Ray Chandler
411	2317	88849	8w49	(8·10²³¹⁷-359)/9	December 15, 2012	Ray Chandler
413	2317	31331	313w1	(94·10²³¹⁵-7)/3	December 15, 2012	Ray Chandler
414	2311	50333	503w	(151·10²³⁰⁹-1)/3	December 15, 2012	Ray Chandler
416	2308	71181	71w81	(64·10²³⁰⁷+629)/9	December 15, 2012	Ray Chandler
417	2307	21181	21w81	(19·10²³⁰⁶+629)/9	December 15, 2012	Ray Chandler
418	2303	51101	51w01	(46·10²³⁰²-91)/9	December 15, 2012	Ray Chandler
420	2302	89929	89w29	9·10²³⁰¹-71	December 15, 2012	Ray Chandler
421	2300	89777	897w	(808·10²²⁹⁸-7)/9	December 15, 2012	Ray Chandler

Proven near-repdigit-related primes (except ru/nr/pd/qr)
	digits	flabel	wlabel	expression	when	who
2336	2399		89w77	9·10²³⁹⁸-23	December 15, 2012	Ray Chandler
2339	2398	27731	27w31	(25·10²³⁹⁷-421)/9	December 15, 2012	Ray Chandler
2341	2396	98893	98w93	(89·10²³⁹⁵+37)/9	December 15, 2012	Ray Chandler
2342	2396		775w1	(698·10²³⁹⁴-41)/9	December 15, 2012	Ray Chandler
2343	2396	51169	51w69	(46·10²³⁹⁵+521)/9	December 15, 2012	Ray Chandler
2344	2396	19901	19w01	2·10²³⁹⁵-99	December 15, 2012	Ray Chandler
2345	2393	70019	70w19	7·10²³⁹²+19	December 15, 2012	Ray Chandler
2347	2392	84467	84w67	(76·10²³⁹¹+203)/9	December 15, 2012	Ray Chandler
2348	2392		80w33	8·10²³⁹¹+33	December 15, 2012	Ray Chandler
2349	2391	96671	96w71	(29·10²³⁹⁰+13)/3	December 15, 2012	Ray Chandler
2353	2390	27709	27w09	(25·10²³⁸⁹-619)/9	December 15, 2012	Ray Chandler
2354	2389	34409	34w09	(31·10²³⁸⁸-319)/9	December 15, 2012	Ray Chandler
2356	2388	72219	72w19	(65·10²³⁸⁷-29)/9	December 15, 2012	Ray Chandler
2359	2387	36679	36w79	(11·10²³⁸⁶+37)/3	December 15, 2012	Ray Chandler
2360	2386		880w7	88·10²³⁸⁴+7	December 15, 2012	Ray Chandler
2361	2386	71123	71w23	(64·10²³⁸⁵+107)/9	December 15, 2012	Ray Chandler
2366	2383	48837	48w37	(44·10²³⁸²-467)/9	December 15, 2012	Ray Chandler
2367	2383	13357	13w57	(4·10²³⁸²+71)/3	December 15, 2012	Ray Chandler
2370	2381		229w3	23·10²³⁷⁹-7	December 15, 2012	Ray Chandler
2371	2380	52237	52w37	(47·10²³⁷⁹+133)/9	December 15, 2012	Ray Chandler
2373	2380	26657	26w57	(8·10²³⁷⁹-29)/3	December 15, 2012	Ray Chandler
2374	2379	80081	80w81	8·10²³⁷⁸+81	December 15, 2012	Ray Chandler
2376	2378	87793	87w93	(79·10²³⁷⁷+137)/9	December 15, 2012	Ray Chandler
2377	2377	34481	34w81	(31·10²³⁷⁶+329)/9	December 15, 2012	Ray Chandler
2379	2376		58w11	(53·10²³⁷⁵-701)/9	December 15, 2012	Ray Chandler
2381	2376	48867	48w67	(44·10²³⁷⁵-197)/9	December 15, 2012	Ray Chandler
2384	2374	53309	53w09	(16·10²³⁷³-73)/3	December 15, 2012	Ray Chandler
2385	2374	27753	27w53	(25·10²³⁷³-223)/9	December 15, 2012	Ray Chandler
2386	2373	36697	36w97	(11·10²³⁷²+91)/3	December 15, 2012	Ray Chandler
2387	2372	65573	65w73	(59·10²³⁷¹+157)/9	December 15, 2012	Ray Chandler
2389	2371		17w99	(16·10²³⁷⁰+191)/9	December 15, 2012	Ray Chandler
2390	2370	94407	94w07	(85·10²³⁶⁹-337)/9	December 15, 2012	Ray Chandler
2391	2370	37759	37w59	(34·10²³⁶⁹-169)/9	December 15, 2012	Ray Chandler
2395	2367	15567	15w67	(14·10²³⁶⁶+103)/9	December 15, 2012	Ray Chandler
2396	2366	94403	94w03	(85·10²³⁶⁵-373)/9	December 15, 2012	Ray Chandler
2397	2363		52w77	(47·10²³⁶²+493)/9	December 15, 2012	Ray Chandler
2399	2360	95569	95w69	(86·10²³⁵⁹+121)/9	December 15, 2012	Ray Chandler
2400	2360	38867	38w67	(35·10²³⁵⁹-197)/9	December 15, 2012	Ray Chandler
2401	2360	30059	30w59	3·10²³⁵⁹+59	December 15, 2012	Ray Chandler
2402	2359	98817	98w17	(89·10²³⁵⁸-647)/9	December 15, 2012	Ray Chandler
2404	2359	80089	80w89	8·10²³⁵⁸+89	December 15, 2012	Ray Chandler
2405	2359	48861	48w61	(44·10²³⁵⁸-251)/9	December 15, 2012	Ray Chandler
2406	2358	32297	32w97	(29·10²³⁵⁷+673)/9	December 15, 2012	Ray Chandler
2407	2357	79901	79w01	8·10²³⁵⁶-99	December 15, 2012	Ray Chandler
2408	2357	78823	78w23	(71·10²³⁵⁶-593)/9	December 15, 2012	Ray Chandler
2409	2357	58819	58w19	(53·10²³⁵⁶-629)/9	December 15, 2012	Ray Chandler
2410	2356	74457	74w57	(67·10²³⁵⁵+113)/9	December 15, 2012	Ray Chandler
2411	2356		36w11	(11·10²³⁵⁵-167)/3	December 15, 2012	Ray Chandler
2412	2356	28897	28w97	(26·10²³⁵⁵+73)/9	December 15, 2012	Ray Chandler
2413	2355	94483	94w83	(85·10²³⁵⁴+347)/9	December 15, 2012	Ray Chandler
2414	2355		668w1	(602·10²³⁵³-71)/9	December 15, 2012	Ray Chandler
2416	2352	90013	90w13	9·10²³⁵¹+13	December 15, 2012	Ray Chandler
2417	2351	85573	85w73	(77·10²³⁵⁰+157)/9	December 15, 2012	Ray Chandler
2419	2351	32267	32w67	(29·10²³⁵⁰+403)/9	December 15, 2012	Ray Chandler
2420	2350	40097	40w97	4·10²³⁴⁹+97	December 15, 2012	Ray Chandler
2421	2349	56657	56w57	(17·10²³⁴⁸-29)/3	December 15, 2012	Ray Chandler
2422	2348		98w99	(89·10²³⁴⁷+91)/9	December 15, 2012	Ray Chandler
2424	2348	58861	58w61	(53·10²³⁴⁷-251)/9	December 15, 2012	Ray Chandler
2426	2346	91153	91w53	(82·10²³⁴⁵+377)/9	December 15, 2012	Ray Chandler
2428	2345	24407	24w07	(22·10²³⁴⁴-337)/9	December 15, 2012	Ray Chandler
2429	2344		447w1	(403·10²³⁴²-61)/9	December 15, 2012	Ray Chandler
2431	2343	25523	25w23	(23·10²³⁴²-293)/9	December 15, 2012	Ray Chandler
2433	2341	76657	76w57	(23·10²³⁴⁰-29)/3	December 15, 2012	Ray Chandler
2435	2339	89987	89w87	9·10²³³⁸-13	December 15, 2012	Ray Chandler
2436	2339	73387	73w87	(22·10²³³⁸+161)/3	December 15, 2012	Ray Chandler
2437	2339	50087	50w87	5·10²³³⁸+87	December 15, 2012	Ray Chandler
2438	2339	26623	26w23	(8·10²³³⁸-131)/3	December 15, 2012	Ray Chandler
2439	2338	29927	29w27	3·10²³³⁷-73	December 15, 2012	Ray Chandler
2440	2337		220w3	22·10²³³⁵+3	December 15, 2012	Ray Chandler
2441	2336	70067	70w67	7·10²³³⁵+67	December 15, 2012	Ray Chandler
2443	2335	59923	59w23	6·10²³³⁴-77	December 15, 2012	Ray Chandler
2445	2334		776w3	(233·10²³³²-11)/3	December 15, 2012	Ray Chandler
2446	2334	54457	54w57	(49·10²³³³+113)/9	December 15, 2012	Ray Chandler
2447	2332	49981	49w81	5·10²³³¹-19	December 15, 2012	Ray Chandler
2448	2331		559w1	56·10²³²⁹-9	December 15, 2012	Ray Chandler
2449	2331		47w99	(43·10²³³⁰+191)/9	December 15, 2012	Ray Chandler
2450	2331	20069	20w69	2·10²³³⁰+69	December 15, 2012	Ray Chandler
2451	2330	40087	40w87	4·10²³²⁹+87	December 15, 2012	Ray Chandler
2452	2329	28843	28w43	(26·10²³²⁸-413)/9	December 15, 2012	Ray Chandler
2453	2329	19903	19w03	2·10²³²⁸-97	December 15, 2012	Ray Chandler
2455	2326	80069	80w69	8·10²³²⁵+69	December 15, 2012	Ray Chandler
2457	2325	47739	47w39	(43·10²³²⁴-349)/9	December 15, 2012	Ray Chandler
2458	2325		339w7	34·10²³²³-3	December 15, 2012	Ray Chandler
2461	2323	74453	74w53	(67·10²³²²+77)/9	December 15, 2012	Ray Chandler
2462	2323	42271	42w71	(38·10²³²²+439)/9	December 15, 2012	Ray Chandler
2463	2321	62269	62w69	(56·10²³²⁰+421)/9	December 15, 2012	Ray Chandler
2464	2321	35513	35w13	(32·10²³²⁰-383)/9	December 15, 2012	Ray Chandler
2465	2320		889w1	89·10²³¹⁸-9	December 15, 2012	Ray Chandler
2467	2319	12251	12w51	(11·10²³¹⁸+259)/9	December 15, 2012	Ray Chandler
2469	2318	56693	56w93	(17·10²³¹⁷+79)/3	December 15, 2012	Ray Chandler
2470	2317	87749	87w49	(79·10²³¹⁶-259)/9	December 15, 2012	Ray Chandler
2471	2317		336w1	(101·10²³¹⁵-17)/3	December 15, 2012	Ray Chandler
2472	2317		227w3	(205·10²³¹⁵-43)/9	December 15, 2012	Ray Chandler
2473	2316	96613	96w13	(29·10²³¹⁵-161)/3	December 15, 2012	Ray Chandler
2474	2316	78897	78w97	(71·10²³¹⁵+73)/9	December 15, 2012	Ray Chandler
2475	2316	62273	62w73	(56·10²³¹⁵+457)/9	December 15, 2012	Ray Chandler
2476	2315		75w77	(68·10²³¹⁴+193)/9	December 15, 2012	Ray Chandler
2477	2315	46691	46w91	(14·10²³¹⁴+73)/3	December 15, 2012	Ray Chandler
2478	2312	98843	98w43	(89·10²³¹¹-413)/9	December 15, 2012	Ray Chandler
2479	2312		83w11	(25·10²³¹¹-67)/3	December 15, 2012	Ray Chandler
2480	2312	71149	71w49	(64·10²³¹¹+341)/9	December 15, 2012	Ray Chandler
2482	2310		668w1	(602·10²³⁰⁸-71)/9	December 15, 2012	Ray Chandler
2484	2308	17709	17w09	(16·10²³⁰⁷-619)/9	December 15, 2012	Ray Chandler
2485	2308	16607	16w07	(5·10²³⁰⁷-179)/3	December 15, 2012	Ray Chandler
2486	2307	92289	92w89	(83·10²³⁰⁶+601)/9	December 15, 2012	Ray Chandler
2487	2307	74401	74w01	(67·10²³⁰⁶-391)/9	December 15, 2012	Ray Chandler
2489	2305		61w99	(55·10²³⁰⁴+791)/9	December 15, 2012	Ray Chandler
2490	2305	12241	12w41	(11·10²³⁰⁴+169)/9	December 15, 2012	Ray Chandler
2491	2304		58w11	(53·10²³⁰³-701)/9	December 15, 2012	Ray Chandler
2493	2304		43w99	(13·10²³⁰³+197)/3	December 15, 2012	Ray Chandler
2494	2304		24w11	(22·10²³⁰³-301)/9	December 15, 2012	Ray Chandler
2495	2303	45593	45w93	(41·10²³⁰²+337)/9	December 15, 2012	Ray Chandler
2496	2303	41159	41w59	(37·10²³⁰²+431)/9	December 15, 2012	Ray Chandler
2497	2303	16673	16w73	(5·10²³⁰²+19)/3	December 15, 2012	Ray Chandler
2498	2302	34427	34w27	(31·10²³⁰¹-157)/9	December 15, 2012	Ray Chandler
2499	2301	31179	31w79	(28·10²³⁰⁰+611)/9	December 15, 2012	Ray Chandler
2502	2300	47713	47w13	(43·10²²⁹⁹-583)/9	December 15, 2012	Ray Chandler

Factorizations of 677...779 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 10³⁰.

December 14, 2012

Ray Chandler successfully proved the primality of a 9505-digit prime number Phi(20644,10) by Primo. Congratulations! Certification is available.

December 13, 2012

Ray Chandler certificated 7 near-repdigit prime numbers, 45 quasi-repdigit prime numbers and 148 near-repdigit-related prime numbers by Primo. Certifications are available.

Proven near-repdigit primes
	digits	flabel	wlabel	expression	when	who
522	2295	32333	323w	(97·10²²⁹³-1)/3	December 13, 2012	Ray Chandler
524	2277	18111	181w	(163·10²²⁷⁵-1)/9	December 13, 2012	Ray Chandler
526	2269		9w5999999	10²²⁶⁹-4000001	December 13, 2012	Ray Chandler
527	2268	99979	9w79	10²²⁶⁸-21	December 13, 2012	Ray Chandler
529	2238		9w79999	10²²³⁸-20001	December 13, 2012	Ray Chandler
532	2221		9w19999999	10²²²¹-80000001	December 13, 2012	Ray Chandler
535	2204		9w799999999	10²²⁰⁴-200000001	December 13, 2012	Ray Chandler

Proven quasi-repdigit primes (except pd)
	digits	flabel	wlabel	expression	when	who
377	2297		4w77	(4·10²²⁹⁷+293)/9	December 13, 2012	Ray Chandler
378	2296	85881	858w1	(773·10²²⁹⁴-71)/9	December 13, 2012	Ray Chandler
381	2288	41333	413w	(124·10²²⁸⁶-1)/3	December 13, 2012	Ray Chandler
382	2288	13343	13w43	(4·10²²⁸⁷+29)/3	December 13, 2012	Ray Chandler
383	2286	57551	575w1	(518·10²²⁸⁴-41)/9	December 13, 2012	Ray Chandler
384	2283		661w	(595·10²²⁸¹-1)/9	December 13, 2012	Ray Chandler
385	2283	56553	565w3	(509·10²²⁸¹-23)/9	December 13, 2012	Ray Chandler
386	2282	73373	73w73	(22·10²²⁸¹+119)/3	December 13, 2012	Ray Chandler
387	2282	66659	6w59	(2·10²²⁸²-23)/3	December 13, 2012	Ray Chandler
388	2281		1w99	(10²²⁸¹+791)/9	December 13, 2012	Ray Chandler
389	2280	88893	8w93	(8·10²²⁸⁰+37)/9	December 13, 2012	Ray Chandler
390	2280	49333	493w	(148·10²²⁷⁸-1)/3	December 13, 2012	Ray Chandler
392	2275	11129	1w29	(10²²⁷⁵+161)/9	December 13, 2012	Ray Chandler
393	2269	92333	923w	(277·10²²⁶⁷-1)/3	December 13, 2012	Ray Chandler
394	2267	33347	3w47	(10²²⁶⁷+41)/3	December 13, 2012	Ray Chandler
395	2264	94777	947w	(853·10²²⁶²-7)/9	December 13, 2012	Ray Chandler
396	2262	63313	63w13	(19·10²²⁶¹-61)/3	December 13, 2012	Ray Chandler
398	2261	27227	272w7	(245·10²²⁵⁹+43)/9	December 13, 2012	Ray Chandler
399	2260	41333	413w	(124·10²²⁵⁸-1)/3	December 13, 2012	Ray Chandler
400	2257	28227	282w7	(254·10²²⁵⁵+43)/9	December 13, 2012	Ray Chandler
401	2252	41443	414w3	(373·10²²⁵⁰-13)/9	December 13, 2012	Ray Chandler
403	2250	54777	547w	(493·10²²⁴⁸-7)/9	December 13, 2012	Ray Chandler
404	2246	55571	5w71	(5·10²²⁴⁶+139)/9	December 13, 2012	Ray Chandler
406	2243	22273	2w73	(2·10²²⁴³+457)/9	December 13, 2012	Ray Chandler
407	2238	47787	47w87	(43·10²²³⁷+83)/9	December 13, 2012	Ray Chandler
409	2236	37767	37w67	(34·10²²³⁵-97)/9	December 13, 2012	Ray Chandler
410	2235	43363	43w63	(13·10²²³⁴+89)/3	December 13, 2012	Ray Chandler
411	2230	17333	173w	(52·10²²²⁸-1)/3	December 13, 2012	Ray Chandler
412	2229	88809	8w09	(8·10²²²⁹-719)/9	December 13, 2012	Ray Chandler
413	2227	76779	767w9	(691·10²²²⁵+11)/9	December 13, 2012	Ray Chandler
414	2223	36111	361w	(325·10²²²¹-1)/9	December 13, 2012	Ray Chandler
415	2223	17797	17w97	(16·10²²²²+173)/9	December 13, 2012	Ray Chandler
417	2222	19333	193w	(58·10²²²⁰-1)/3	December 13, 2012	Ray Chandler
418	2219	87887	878w7	(791·10²²¹⁷-17)/9	December 13, 2012	Ray Chandler
419	2216	99971	9w71	10²²¹⁶-29	December 13, 2012	Ray Chandler
420	2216	79949	79w49	8·10²²¹⁵-51	December 13, 2012	Ray Chandler
422	2215	79949	79w49	8·10²²¹⁴-51	December 13, 2012	Ray Chandler
423	2215	66629	6w29	(2·10²²¹⁵-113)/3	December 13, 2012	Ray Chandler
425	2213	44423	4w23	(4·10²²¹³-193)/9	December 13, 2012	Ray Chandler
427	2212	15777	157w	(142·10²²¹⁰-7)/9	December 13, 2012	Ray Chandler
428	2210	61777	617w	(556·10²²⁰⁸-7)/9	December 13, 2012	Ray Chandler
429	2210	19949	19w49	2·10²²⁰⁹-51	December 13, 2012	Ray Chandler
431	2208	15117	151w7	(136·10²²⁰⁶+53)/9	December 13, 2012	Ray Chandler
432	2206	41777	417w	(376·10²²⁰⁴-7)/9	December 13, 2012	Ray Chandler
433	2206	26221	262w1	(236·10²²⁰⁴-11)/9	December 13, 2012	Ray Chandler

Proven near-repdigit-related primes (except ru/nr/pd/qr)
	digits	flabel	wlabel	expression	when	who
2385	2299	86687	86w87	(26·10²²⁹⁸+61)/3	December 13, 2012	Ray Chandler
2387	2299		556w3	(167·10²²⁹⁷-11)/3	December 13, 2012	Ray Chandler
2388	2298		81w33	(73·10²²⁹⁷+197)/9	December 13, 2012	Ray Chandler
2391	2297	48863	48w63	(44·10²²⁹⁶-233)/9	December 13, 2012	Ray Chandler
2393	2296	46679	46w79	(14·10²²⁹⁵+37)/3	December 13, 2012	Ray Chandler
2394	2296	43349	43w49	(13·10²²⁹⁵+47)/3	December 13, 2012	Ray Chandler
2397	2294		889w1	89·10²²⁹²-9	December 13, 2012	Ray Chandler
2398	2294	78809	78w09	(71·10²²⁹³-719)/9	December 13, 2012	Ray Chandler
2399	2294	61139	61w39	(55·10²²⁹³+251)/9	December 13, 2012	Ray Chandler
2400	2293	93391	93w91	(28·10²²⁹²+173)/3	December 13, 2012	Ray Chandler
2401	2293	79987	79w87	8·10²²⁹²-13	December 13, 2012	Ray Chandler
2404	2292	17743	17w43	(16·10²²⁹¹-313)/9	December 13, 2012	Ray Chandler
2405	2291	56657	56w57	(17·10²²⁹⁰-29)/3	December 13, 2012	Ray Chandler
2406	2290	63367	63w67	(19·10²²⁸⁹+101)/3	December 13, 2012	Ray Chandler
2407	2288	96629	96w29	(29·10²²⁸⁷-113)/3	December 13, 2012	Ray Chandler
2408	2288	52213	52w13	(47·10²²⁸⁷-83)/9	December 13, 2012	Ray Chandler
2409	2288		335w3	(302·10²²⁸⁶-23)/9	December 13, 2012	Ray Chandler
2410	2287		51w77	(46·10²²⁸⁶+593)/9	December 13, 2012	Ray Chandler
2412	2287	28861	28w61	(26·10²²⁸⁶-251)/9	December 13, 2012	Ray Chandler
2414	2284	76649	76w49	(23·10²²⁸³-53)/3	December 13, 2012	Ray Chandler
2415	2284	56641	56w41	(17·10²²⁸³-77)/3	December 13, 2012	Ray Chandler
2417	2283	38891	38w91	(35·10²²⁸²+19)/9	December 13, 2012	Ray Chandler
2418	2282	68863	68w63	(62·10²²⁸¹-233)/9	December 13, 2012	Ray Chandler
2419	2281		62w33	(56·10²²⁸⁰+97)/9	December 13, 2012	Ray Chandler
2420	2281	40013	40w13	4·10²²⁸⁰+13	December 13, 2012	Ray Chandler
2422	2280	58839	58w39	(53·10²²⁷⁹-449)/9	December 13, 2012	Ray Chandler
2424	2279		84w99	(76·10²²⁷⁸+491)/9	December 13, 2012	Ray Chandler
2425	2279	81167	81w67	(73·10²²⁷⁸+503)/9	December 13, 2012	Ray Chandler
2426	2279	18859	18w59	(17·10²²⁷⁸-269)/9	December 13, 2012	Ray Chandler
2427	2279	14489	14w89	(13·10²²⁷⁸+401)/9	December 13, 2012	Ray Chandler
2428	2277	98871	98w71	(89·10²²⁷⁶-161)/9	December 13, 2012	Ray Chandler
2432	2277	16639	16w39	(5·10²²⁷⁶-83)/3	December 13, 2012	Ray Chandler
2433	2276	84497	84w97	(76·10²²⁷⁵+473)/9	December 13, 2012	Ray Chandler
2434	2274	43361	43w61	(13·10²²⁷³+83)/3	December 13, 2012	Ray Chandler
2435	2273	75503	75w03	(68·10²²⁷²-473)/9	December 13, 2012	Ray Chandler
2436	2273	57713	57w13	(52·10²²⁷²-583)/9	December 13, 2012	Ray Chandler
2437	2270	73319	73w19	(22·10²²⁶⁹-43)/3	December 13, 2012	Ray Chandler
2438	2270	54487	54w87	(49·10²²⁶⁹+383)/9	December 13, 2012	Ray Chandler
2439	2269	83371	83w71	(25·10²²⁶⁸+113)/3	December 13, 2012	Ray Chandler
2440	2268	95523	95w23	(86·10²²⁶⁷-293)/9	December 13, 2012	Ray Chandler
2441	2268	94459	94w59	(85·10²²⁶⁷+131)/9	December 13, 2012	Ray Chandler
2442	2268		330w7	33·10²²⁶⁶+7	December 13, 2012	Ray Chandler
2444	2267	85573	85w73	(77·10²²⁶⁶+157)/9	December 13, 2012	Ray Chandler
2445	2266	62271	62w71	(56·10²²⁶⁵+439)/9	December 13, 2012	Ray Chandler
2446	2265	84427	84w27	(76·10²²⁶⁴-157)/9	December 13, 2012	Ray Chandler
2447	2265	56693	56w93	(17·10²²⁶⁴+79)/3	December 13, 2012	Ray Chandler
2449	2264	63371	63w71	(19·10²²⁶³+113)/3	December 13, 2012	Ray Chandler
2450	2264	35561	35w61	(32·10²²⁶³+49)/9	December 13, 2012	Ray Chandler
2451	2264	13381	13w81	(4·10²²⁶³+143)/3	December 13, 2012	Ray Chandler
2453	2263	53327	53w27	(16·10²²⁶²-19)/3	December 13, 2012	Ray Chandler
2455	2263	17751	17w51	(16·10²²⁶²-241)/9	December 13, 2012	Ray Chandler
2456	2262	23347	23w47	(7·10²²⁶¹+41)/3	December 13, 2012	Ray Chandler
2457	2261	82259	82w59	(74·10²²⁶⁰+331)/9	December 13, 2012	Ray Chandler
2460	2258	92269	92w69	(83·10²²⁵⁷+421)/9	December 13, 2012	Ray Chandler
2461	2258	70039	70w39	7·10²²⁵⁷+39	December 13, 2012	Ray Chandler
2462	2258	40021	40w21	4·10²²⁵⁷+21	December 13, 2012	Ray Chandler
2464	2256	74413	74w13	(67·10²²⁵⁵-283)/9	December 13, 2012	Ray Chandler
2465	2256		335w7	(302·10²²⁵⁴+13)/9	December 13, 2012	Ray Chandler
2468	2255	67759	67w59	(61·10²²⁵⁴-169)/9	December 13, 2012	Ray Chandler
2469	2255	42293	42w93	(38·10²²⁵⁴+637)/9	December 13, 2012	Ray Chandler
2470	2255	10081	10w81	10²²⁵⁴+81	December 13, 2012	Ray Chandler
2471	2254	91193	91w93	(82·10²²⁵³+737)/9	December 13, 2012	Ray Chandler
2473	2254		45w77	(41·10²²⁵³+193)/9	December 13, 2012	Ray Chandler
2474	2254	40051	40w51	4·10²²⁵³+51	December 13, 2012	Ray Chandler
2476	2253	81127	81w27	(73·10²²⁵²+143)/9	December 13, 2012	Ray Chandler
2477	2253	25581	25w81	(23·10²²⁵²+229)/9	December 13, 2012	Ray Chandler
2478	2252	21187	21w87	(19·10²²⁵¹+683)/9	December 13, 2012	Ray Chandler
2480	2251	61197	61w97	(55·10²²⁵⁰+773)/9	December 13, 2012	Ray Chandler
2481	2251	16631	16w31	(5·10²²⁵⁰-107)/3	December 13, 2012	Ray Chandler
2482	2250	96673	96w73	(29·10²²⁴⁹+19)/3	December 13, 2012	Ray Chandler
2483	2250		64w77	(58·10²²⁴⁹+293)/9	December 13, 2012	Ray Chandler
2484	2250	20047	20w47	2·10²²⁴⁹+47	December 13, 2012	Ray Chandler
2485	2248	68841	68w41	(62·10²²⁴⁷-431)/9	December 13, 2012	Ray Chandler
2486	2248		10w33	10²²⁴⁷+33	December 13, 2012	Ray Chandler
2487	2247	85529	85w29	(77·10²²⁴⁶-239)/9	December 13, 2012	Ray Chandler
2489	2247		556w1	(167·10²²⁴⁵-17)/3	December 13, 2012	Ray Chandler
2490	2246	79937	79w37	8·10²²⁴⁵-63	December 13, 2012	Ray Chandler
2491	2246	42293	42w93	(38·10²²⁴⁵+637)/9	December 13, 2012	Ray Chandler
2492	2245	58893	58w93	(53·10²²⁴⁴+37)/9	December 13, 2012	Ray Chandler
2493	2245	32239	32w39	(29·10²²⁴⁴+151)/9	December 13, 2012	Ray Chandler
2494	2245	31179	31w79	(28·10²²⁴⁴+611)/9	December 13, 2012	Ray Chandler
2495	2245	21107	21w07	(19·10²²⁴⁴-37)/9	December 13, 2012	Ray Chandler
2496	2244		89w33	9·10²²⁴³-67	December 13, 2012	Ray Chandler
2497	2244	70039	70w39	7·10²²⁴³+39	December 13, 2012	Ray Chandler
2498	2244		663w1	(199·10²²⁴²-7)/3	December 13, 2012	Ray Chandler
2499	2243	86627	86w27	(26·10²²⁴²-119)/3	December 13, 2012	Ray Chandler
2500	2243	69917	69w17	7·10²²⁴²-83	December 13, 2012	Ray Chandler
2502	2241	34423	34w23	(31·10²²⁴⁰-193)/9	December 13, 2012	Ray Chandler
2503	2239	59927	59w27	6·10²²³⁸-73	December 13, 2012	Ray Chandler
2504	2239	10037	10w37	10²²³⁸+37	December 13, 2012	Ray Chandler
2505	2238	96673	96w73	(29·10²²³⁷+19)/3	December 13, 2012	Ray Chandler
2506	2238	85527	85w27	(77·10²²³⁷-257)/9	December 13, 2012	Ray Chandler
2507	2238	62247	62w47	(56·10²²³⁷+223)/9	December 13, 2012	Ray Chandler
2508	2238	54409	54w09	(49·10²²³⁷-319)/9	December 13, 2012	Ray Chandler
2509	2237	82237	82w37	(74·10²²³⁶+133)/9	December 13, 2012	Ray Chandler
2510	2237	29921	29w21	3·10²²³⁶-79	December 13, 2012	Ray Chandler
2511	2236	50041	50w41	5·10²²³⁵+41	December 13, 2012	Ray Chandler
2512	2235	86681	86w81	(26·10²²³⁴+43)/3	December 13, 2012	Ray Chandler
2514	2235	17763	17w63	(16·10²²³⁴-133)/9	December 13, 2012	Ray Chandler
2515	2234	75563	75w63	(68·10²²³³+67)/9	December 13, 2012	Ray Chandler
2517	2233	60053	60w53	6·10²²³²+53	December 13, 2012	Ray Chandler
2518	2231	26647	26w47	(8·10²²³⁰-59)/3	December 13, 2012	Ray Chandler
2520	2230	70097	70w97	7·10²²²⁹+97	December 13, 2012	Ray Chandler
2521	2229	93361	93w61	(28·10²²²⁸+83)/3	December 13, 2012	Ray Chandler
2522	2229	82283	82w83	(74·10²²²⁸+547)/9	December 13, 2012	Ray Chandler
2524	2228	68837	68w37	(62·10²²²⁷-467)/9	December 13, 2012	Ray Chandler
2525	2228	32251	32w51	(29·10²²²⁷+259)/9	December 13, 2012	Ray Chandler
2527	2226	74439	74w39	(67·10²²²⁵-49)/9	December 13, 2012	Ray Chandler
2528	2226	35501	35w01	(32·10²²²⁵-491)/9	December 13, 2012	Ray Chandler
2529	2226	10069	10w69	10²²²⁵+69	December 13, 2012	Ray Chandler
2531	2225		64w99	(58·10²²²⁴+491)/9	December 13, 2012	Ray Chandler
2532	2224		880w9	88·10²²²²+9	December 13, 2012	Ray Chandler
2535	2223	65519	65w19	(59·10²²²²-329)/9	December 13, 2012	Ray Chandler
2536	2221	60073	60w73	6·10²²²⁰+73	December 13, 2012	Ray Chandler
2538	2220	31197	31w97	(28·10²²¹⁹+773)/9	December 13, 2012	Ray Chandler
2540	2218	95587	95w87	(86·10²²¹⁷+283)/9	December 13, 2012	Ray Chandler
2542	2218	73349	73w49	(22·10²²¹⁷+47)/3	December 13, 2012	Ray Chandler
2543	2218	40049	40w49	4·10²²¹⁷+49	December 13, 2012	Ray Chandler
2545	2217	64497	64w97	(58·10²²¹⁶+473)/9	December 13, 2012	Ray Chandler
2546	2217	32253	32w53	(29·10²²¹⁶+277)/9	December 13, 2012	Ray Chandler
2547	2217		119w3	12·10²²¹⁵-7	December 13, 2012	Ray Chandler
2548	2216	81169	81w69	(73·10²²¹⁵+521)/9	December 13, 2012	Ray Chandler
2549	2216		556w9	(167·10²²¹⁴+7)/3	December 13, 2012	Ray Chandler
2550	2215	36671	36w71	(11·10²²¹⁴+13)/3	December 13, 2012	Ray Chandler
2551	2214	51123	51w23	(46·10²²¹³+107)/9	December 13, 2012	Ray Chandler
2552	2213	41159	41w59	(37·10²²¹²+431)/9	December 13, 2012	Ray Chandler
2553	2213		26w99	(8·10²²¹²+97)/3	December 13, 2012	Ray Chandler
2554	2212	95593	95w93	(86·10²²¹¹+337)/9	December 13, 2012	Ray Chandler
2555	2212	38823	38w23	(35·10²²¹¹-593)/9	December 13, 2012	Ray Chandler
2556	2211	62259	62w59	(56·10²²¹⁰+331)/9	December 13, 2012	Ray Chandler
2558	2209	37793	37w93	(34·10²²⁰⁸+137)/9	December 13, 2012	Ray Chandler
2559	2209	13309	13w09	(4·10²²⁰⁸-73)/3	December 13, 2012	Ray Chandler
2560	2208	82271	82w71	(74·10²²⁰⁷+439)/9	December 13, 2012	Ray Chandler
2561	2208		26w33	(8·10²²⁰⁷-101)/3	December 13, 2012	Ray Chandler
2562	2207	90059	90w59	9·10²²⁰⁶+59	December 13, 2012	Ray Chandler
2563	2207		42w99	(38·10²²⁰⁶+691)/9	December 13, 2012	Ray Chandler
2564	2207	36607	36w07	(11·10²²⁰⁶-179)/3	December 13, 2012	Ray Chandler
2565	2206	84483	84w83	(76·10²²⁰⁵+347)/9	December 13, 2012	Ray Chandler
2567	2206		72w11	(65·10²²⁰⁵-101)/9	December 13, 2012	Ray Chandler
2568	2206	59927	59w27	6·10²²⁰⁵-73	December 13, 2012	Ray Chandler
2570	2205	94483	94w83	(85·10²²⁰⁴+347)/9	December 13, 2012	Ray Chandler
2571	2205	35523	35w23	(32·10²²⁰⁴-293)/9	December 13, 2012	Ray Chandler
2573	2205	15573	15w73	(14·10²²⁰⁴+157)/9	December 13, 2012	Ray Chandler
2575	2204		64w11	(58·10²²⁰³-301)/9	December 13, 2012	Ray Chandler
2576	2204	30037	30w37	3·10²²⁰³+37	December 13, 2012	Ray Chandler
2577	2204		117w1	(106·10²²⁰²-61)/9	December 13, 2012	Ray Chandler
2579	2202	27769	27w69	(25·10²²⁰¹-79)/9	December 13, 2012	Ray Chandler
2580	2201	48827	48w27	(44·10²²⁰⁰-557)/9	December 13, 2012	Ray Chandler

December 12, 2012

Factorizations of 677...77 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 10³⁰.

December 11, 2012

Ray Chandler certificated 9 near-repdigit prime numbers, 39 quasi-repdigit prime numbers and 129 near-repdigit-related prime numbers by Primo. Certifications are available.

Proven near-repdigit primes
	digits	flabel	wlabel	expression	when	who
529	2192		9w1999999999	10²¹⁹²-8000000001	December 11, 2012	Ray Chandler
530	2189		9w79999	10²¹⁸⁹-20001	December 11, 2012	Ray Chandler
532	2175		9w79999	10²¹⁷⁵-20001	December 11, 2012	Ray Chandler
534	2169		9w5999999	10²¹⁶⁹-4000001	December 11, 2012	Ray Chandler
535	2168		9w4999999	10²¹⁶⁸-5000001	December 11, 2012	Ray Chandler
538	2151		9w8999999	10²¹⁵¹-1000001	December 11, 2012	Ray Chandler
539	2146	99929	9w29	10²¹⁴⁶-71	December 11, 2012	Ray Chandler
540	2140	33323	3w23	(10²¹⁴⁰-31)/3	December 11, 2012	Ray Chandler
541	2130		9w499999	10²¹³⁰-500001	December 11, 2012	Ray Chandler

Proven quasi-repdigit primes (except pd)
	digits	flabel	wlabel	expression	when	who
393	2196	11143	1w43	(10²¹⁹⁶+287)/9	December 11, 2012	Ray Chandler
395	2195	53111	531w	(478·10²¹⁹³-1)/9	December 11, 2012	Ray Chandler
396	2195	27221	272w1	(245·10²¹⁹³-11)/9	December 11, 2012	Ray Chandler
397	2194	10113	101w3	(91·10²¹⁹²+17)/9	December 11, 2012	Ray Chandler
398	2193	90777	907w	(817·10²¹⁹¹-7)/9	December 11, 2012	Ray Chandler
400	2189	59557	595w7	(536·10²¹⁸⁷+13)/9	December 11, 2012	Ray Chandler
401	2188	38777	387w	(349·10²¹⁸⁶-7)/9	December 11, 2012	Ray Chandler
402	2187		337w	(304·10²¹⁸⁵-7)/9	December 11, 2012	Ray Chandler
403	2183	24229	242w9	(218·10²¹⁸¹+61)/9	December 11, 2012	Ray Chandler
404	2181	50559	505w9	(455·10²¹⁷⁹+31)/9	December 11, 2012	Ray Chandler
406	2180	22241	2w41	(2·10²¹⁸⁰+169)/9	December 11, 2012	Ray Chandler
408	2175	83393	83w93	(25·10²¹⁷⁴+179)/3	December 11, 2012	Ray Chandler
409	2173	89959	89w59	9·10²¹⁷²-41	December 11, 2012	Ray Chandler
411	2170	77741	7w41	(7·10²¹⁷⁰-331)/9	December 11, 2012	Ray Chandler
412	2169	10333	103w	(31·10²¹⁶⁷-1)/3	December 11, 2012	Ray Chandler
413	2165	79939	79w39	8·10²¹⁶⁴-61	December 11, 2012	Ray Chandler
414	2165	50111	501w	(451·10²¹⁶³-1)/9	December 11, 2012	Ray Chandler
417	2161	44483	4w83	(4·10²¹⁶¹+347)/9	December 11, 2012	Ray Chandler
420	2158	61669	616w9	(185·10²¹⁵⁶+7)/3	December 11, 2012	Ray Chandler
423	2150	88867	8w67	(8·10²¹⁵⁰-197)/9	December 11, 2012	Ray Chandler
424	2149	55597	5w97	(5·10²¹⁴⁹+373)/9	December 11, 2012	Ray Chandler
427	2147	20333	203w	(61·10²¹⁴⁵-1)/3	December 11, 2012	Ray Chandler
428	2141	17119	171w9	(154·10²¹³⁹+71)/9	December 11, 2012	Ray Chandler
431	2138	59959	59w59	6·10²¹³⁷-41	December 11, 2012	Ray Chandler
433	2134	66637	6w37	(2·10²¹³⁴-89)/3	December 11, 2012	Ray Chandler
435	2132	14113	141w3	(127·10²¹³⁰+17)/9	December 11, 2012	Ray Chandler
436	2128	13343	13w43	(4·10²¹²⁷+29)/3	December 11, 2012	Ray Chandler
437	2127	55569	5w69	(5·10²¹²⁷+121)/9	December 11, 2012	Ray Chandler
438	2124	68663	686w3	(206·10²¹²²-11)/3	December 11, 2012	Ray Chandler
439	2123	55513	5w13	(5·10²¹²³-383)/9	December 11, 2012	Ray Chandler
442	2118	61131	61w31	(55·10²¹¹⁷+179)/9	December 11, 2012	Ray Chandler
443	2117	88807	8w07	(8·10²¹¹⁷-737)/9	December 11, 2012	Ray Chandler
445	2115	66601	6w01	(2·10²¹¹⁵-197)/3	December 11, 2012	Ray Chandler
446	2115	46447	464w7	(418·10²¹¹³+23)/9	December 11, 2012	Ray Chandler
447	2114	59111	591w	(532·10²¹¹²-1)/9	December 11, 2012	Ray Chandler
448	2112	13303	13w03	(4·10²¹¹¹-91)/3	December 11, 2012	Ray Chandler
449	2111	61667	616w7	(185·10²¹⁰⁹+1)/3	December 11, 2012	Ray Chandler
450	2111	28229	282w9	(254·10²¹⁰⁹+61)/9	December 11, 2012	Ray Chandler
453	2106	41443	414w3	(373·10²¹⁰⁴-13)/9	December 11, 2012	Ray Chandler

Proven near-repdigit-related primes (except ru/nr/pd/qr)
	digits	flabel	wlabel	expression	when	who
2433	2199	39973	39w73	4·10²¹⁹⁸-27	December 11, 2012	Ray Chandler
2434	2198	93307	93w07	(28·10²¹⁹⁷-79)/3	December 11, 2012	Ray Chandler
2435	2198	31189	31w89	(28·10²¹⁹⁷+701)/9	December 11, 2012	Ray Chandler
2436	2197		663w7	(199·10²¹⁹⁵+11)/3	December 11, 2012	Ray Chandler
2437	2197	61103	61w03	(55·10²¹⁹⁶-73)/9	December 11, 2012	Ray Chandler
2439	2196	25509	25w09	(23·10²¹⁹⁵-419)/9	December 11, 2012	Ray Chandler
2440	2195		64w99	(58·10²¹⁹⁴+491)/9	December 11, 2012	Ray Chandler
2441	2195	28817	28w17	(26·10²¹⁹⁴-647)/9	December 11, 2012	Ray Chandler
2442	2193	15531	15w31	(14·10²¹⁹²-221)/9	December 11, 2012	Ray Chandler
2444	2192	48869	48w69	(44·10²¹⁹¹-179)/9	December 11, 2012	Ray Chandler
2445	2190	43327	43w27	(13·10²¹⁸⁹-19)/3	December 11, 2012	Ray Chandler
2446	2189	95569	95w69	(86·10²¹⁸⁸+121)/9	December 11, 2012	Ray Chandler
2447	2189	61169	61w69	(55·10²¹⁸⁸+521)/9	December 11, 2012	Ray Chandler
2448	2188	69913	69w13	7·10²¹⁸⁷-87	December 11, 2012	Ray Chandler
2449	2188	65509	65w09	(59·10²¹⁸⁷-419)/9	December 11, 2012	Ray Chandler
2450	2188	52297	52w97	(47·10²¹⁸⁷+673)/9	December 11, 2012	Ray Chandler
2451	2188	16627	16w27	(5·10²¹⁸⁷-119)/3	December 11, 2012	Ray Chandler
2452	2187	24469	24w69	(22·10²¹⁸⁶+221)/9	December 11, 2012	Ray Chandler
2454	2186	61153	61w53	(55·10²¹⁸⁵+377)/9	December 11, 2012	Ray Chandler
2455	2184	83389	83w89	(25·10²¹⁸³+167)/3	December 11, 2012	Ray Chandler
2456	2184		58w77	(53·10²¹⁸³-107)/9	December 11, 2012	Ray Chandler
2457	2184	34401	34w01	(31·10²¹⁸³-391)/9	December 11, 2012	Ray Chandler
2458	2184	14497	14w97	(13·10²¹⁸³+473)/9	December 11, 2012	Ray Chandler
2460	2181		81w99	(73·10²¹⁸⁰+791)/9	December 11, 2012	Ray Chandler
2462	2180	47783	47w83	(43·10²¹⁷⁹+47)/9	December 11, 2012	Ray Chandler
2464	2180	24451	24w51	(22·10²¹⁷⁹+59)/9	December 11, 2012	Ray Chandler
2465	2180	15571	15w71	(14·10²¹⁷⁹+139)/9	December 11, 2012	Ray Chandler
2466	2179	80017	80w17	8·10²¹⁷⁸+17	December 11, 2012	Ray Chandler
2467	2179		770w3	77·10²¹⁷⁷+3	December 11, 2012	Ray Chandler
2468	2179	69983	69w83	7·10²¹⁷⁸-17	December 11, 2012	Ray Chandler
2470	2177	23321	23w21	(7·10²¹⁷⁶-37)/3	December 11, 2012	Ray Chandler
2472	2175	98861	98w61	(89·10²¹⁷⁴-251)/9	December 11, 2012	Ray Chandler
2474	2175	48821	48w21	(44·10²¹⁷⁴-611)/9	December 11, 2012	Ray Chandler
2475	2174	94459	94w59	(85·10²¹⁷³+131)/9	December 11, 2012	Ray Chandler
2476	2174	13361	13w61	(4·10²¹⁷³+83)/3	December 11, 2012	Ray Chandler
2477	2173	56657	56w57	(17·10²¹⁷²-29)/3	December 11, 2012	Ray Chandler
2478	2171	98851	98w51	(89·10²¹⁷⁰-341)/9	December 11, 2012	Ray Chandler
2479	2170	96617	96w17	(29·10²¹⁶⁹-149)/3	December 11, 2012	Ray Chandler
2482	2169		883w1	(265·10²¹⁶⁷-7)/3	December 11, 2012	Ray Chandler
2484	2169	40043	40w43	4·10²¹⁶⁸+43	December 11, 2012	Ray Chandler
2485	2167	28839	28w39	(26·10²¹⁶⁶-449)/9	December 11, 2012	Ray Chandler
2486	2166	91129	91w29	(82·10²¹⁶⁵+161)/9	December 11, 2012	Ray Chandler
2487	2166	69953	69w53	7·10²¹⁶⁵-47	December 11, 2012	Ray Chandler
2488	2166	45579	45w79	(41·10²¹⁶⁵+211)/9	December 11, 2012	Ray Chandler
2489	2165	74453	74w53	(67·10²¹⁶⁴+77)/9	December 11, 2012	Ray Chandler
2490	2165		50w77	5·10²¹⁶⁴+77	December 11, 2012	Ray Chandler
2491	2164	46657	46w57	(14·10²¹⁶³-29)/3	December 11, 2012	Ray Chandler
2492	2164	38847	38w47	(35·10²¹⁶³-377)/9	December 11, 2012	Ray Chandler
2493	2163		668w7	(602·10²¹⁶¹-17)/9	December 11, 2012	Ray Chandler
2495	2162	61129	61w29	(55·10²¹⁶¹+161)/9	December 11, 2012	Ray Chandler
2498	2159	96671	96w71	(29·10²¹⁵⁸+13)/3	December 11, 2012	Ray Chandler
2499	2159	69941	69w41	7·10²¹⁵⁸-59	December 11, 2012	Ray Chandler
2500	2159	17749	17w49	(16·10²¹⁵⁸-259)/9	December 11, 2012	Ray Chandler
2501	2158	79951	79w51	8·10²¹⁵⁷-49	December 11, 2012	Ray Chandler
2503	2157	27769	27w69	(25·10²¹⁵⁶-79)/9	December 11, 2012	Ray Chandler
2504	2156		62w33	(56·10²¹⁵⁵+97)/9	December 11, 2012	Ray Chandler
2505	2156	12269	12w69	(11·10²¹⁵⁵+421)/9	December 11, 2012	Ray Chandler
2509	2155	15523	15w23	(14·10²¹⁵⁴-293)/9	December 11, 2012	Ray Chandler
2512	2153	16631	16w31	(5·10²¹⁵²-107)/3	December 11, 2012	Ray Chandler
2514	2153	13327	13w27	(4·10²¹⁵²-19)/3	December 11, 2012	Ray Chandler
2516	2152	89923	89w23	9·10²¹⁵¹-77	December 11, 2012	Ray Chandler
2517	2152	27731	27w31	(25·10²¹⁵¹-421)/9	December 11, 2012	Ray Chandler
2518	2151	38879	38w79	(35·10²¹⁵⁰-89)/9	December 11, 2012	Ray Chandler
2519	2151		34w11	(31·10²¹⁵⁰-301)/9	December 11, 2012	Ray Chandler
2520	2151	28841	28w41	(26·10²¹⁵⁰-431)/9	December 11, 2012	Ray Chandler
2521	2151	24457	24w57	(22·10²¹⁵⁰+113)/9	December 11, 2012	Ray Chandler
2523	2150	30037	30w37	3·10²¹⁴⁹+37	December 11, 2012	Ray Chandler
2524	2150	10057	10w57	10²¹⁴⁹+57	December 11, 2012	Ray Chandler
2525	2149	25503	25w03	(23·10²¹⁴⁸-473)/9	December 11, 2012	Ray Chandler
2526	2149	24471	24w71	(22·10²¹⁴⁸+239)/9	December 11, 2012	Ray Chandler
2527	2148	86623	86w23	(26·10²¹⁴⁷-131)/3	December 11, 2012	Ray Chandler
2529	2145	86681	86w81	(26·10²¹⁴⁴+43)/3	December 11, 2012	Ray Chandler
2530	2145	43391	43w91	(13·10²¹⁴⁴+173)/3	December 11, 2012	Ray Chandler
2531	2145		118w3	(107·10²¹⁴³-53)/9	December 11, 2012	Ray Chandler
2533	2143		449w3	45·10²¹⁴¹-7	December 11, 2012	Ray Chandler
2534	2142	84421	84w21	(76·10²¹⁴¹-211)/9	December 11, 2012	Ray Chandler
2535	2142		82w33	(74·10²¹⁴¹+97)/9	December 11, 2012	Ray Chandler
2537	2142	76637	76w37	(23·10²¹⁴¹-89)/3	December 11, 2012	Ray Chandler
2538	2142	45501	45w01	(41·10²¹⁴¹-491)/9	December 11, 2012	Ray Chandler
2539	2142	26621	26w21	(8·10²¹⁴¹-137)/3	December 11, 2012	Ray Chandler
2540	2141	95509	95w09	(86·10²¹⁴⁰-419)/9	December 11, 2012	Ray Chandler
2541	2141		880w3	88·10²¹³⁹+3	December 11, 2012	Ray Chandler
2542	2141	81143	81w43	(73·10²¹⁴⁰+287)/9	December 11, 2012	Ray Chandler
2544	2141	35513	35w13	(32·10²¹⁴⁰-383)/9	December 11, 2012	Ray Chandler
2545	2140		93w77	(28·10²¹³⁹+131)/3	December 11, 2012	Ray Chandler
2546	2140	46649	46w49	(14·10²¹³⁹-53)/3	December 11, 2012	Ray Chandler
2547	2140		19w33	2·10²¹³⁹-67	December 11, 2012	Ray Chandler
2548	2140	16643	16w43	(5·10²¹³⁹-71)/3	December 11, 2012	Ray Chandler
2549	2139	47749	47w49	(43·10²¹³⁸-259)/9	December 11, 2012	Ray Chandler
2550	2139	36653	36w53	(11·10²¹³⁸-41)/3	December 11, 2012	Ray Chandler
2551	2138	96679	96w79	(29·10²¹³⁷+37)/3	December 11, 2012	Ray Chandler
2552	2138		64w33	(58·10²¹³⁷-103)/9	December 11, 2012	Ray Chandler
2553	2138		37w11	(34·10²¹³⁷-601)/9	December 11, 2012	Ray Chandler
2554	2138	29951	29w51	3·10²¹³⁷-49	December 11, 2012	Ray Chandler
2555	2137	53387	53w87	(16·10²¹³⁶+161)/3	December 11, 2012	Ray Chandler
2559	2134	52237	52w37	(47·10²¹³³+133)/9	December 11, 2012	Ray Chandler
2560	2134		223w7	(67·10²¹³²+11)/3	December 11, 2012	Ray Chandler
2561	2133	68847	68w47	(62·10²¹³²-377)/9	December 11, 2012	Ray Chandler
2562	2133		54w99	(49·10²¹³²+491)/9	December 11, 2012	Ray Chandler
2564	2132	78829	78w29	(71·10²¹³¹-539)/9	December 11, 2012	Ray Chandler
2565	2132	64487	64w87	(58·10²¹³¹+383)/9	December 11, 2012	Ray Chandler
2567	2130		552w1	(497·10²¹²⁸-11)/9	December 11, 2012	Ray Chandler
2568	2130		15w99	(14·10²¹²⁹+391)/9	December 11, 2012	Ray Chandler
2569	2129		64w33	(58·10²¹²⁸-103)/9	December 11, 2012	Ray Chandler
2570	2129	14479	14w79	(13·10²¹²⁸+311)/9	December 11, 2012	Ray Chandler
2571	2128	37709	37w09	(34·10²¹²⁷-619)/9	December 11, 2012	Ray Chandler
2572	2127	25523	25w23	(23·10²¹²⁶-293)/9	December 11, 2012	Ray Chandler
2575	2125	68829	68w29	(62·10²¹²⁴-539)/9	December 11, 2012	Ray Chandler
2576	2124	61173	61w73	(55·10²¹²³+557)/9	December 11, 2012	Ray Chandler
2577	2124	37719	37w19	(34·10²¹²³-529)/9	December 11, 2012	Ray Chandler
2579	2123	92273	92w73	(83·10²¹²²+457)/9	December 11, 2012	Ray Chandler
2580	2122	74417	74w17	(67·10²¹²¹-247)/9	December 11, 2012	Ray Chandler
2581	2122	62239	62w39	(56·10²¹²¹+151)/9	December 11, 2012	Ray Chandler
2582	2121	74487	74w87	(67·10²¹²⁰+383)/9	December 11, 2012	Ray Chandler
2584	2120	73387	73w87	(22·10²¹¹⁹+161)/3	December 11, 2012	Ray Chandler
2588	2115	97729	97w29	(88·10²¹¹⁴-439)/9	December 11, 2012	Ray Chandler
2589	2115		883w7	(265·10²¹¹³+11)/3	December 11, 2012	Ray Chandler
2590	2115	62283	62w83	(56·10²¹¹⁴+547)/9	December 11, 2012	Ray Chandler
2591	2115	58821	58w21	(53·10²¹¹⁴-611)/9	December 11, 2012	Ray Chandler
2592	2115	54493	54w93	(49·10²¹¹⁴+437)/9	December 11, 2012	Ray Chandler
2595	2113	26659	26w59	(8·10²¹¹²-23)/3	December 11, 2012	Ray Chandler
2596	2112	86623	86w23	(26·10²¹¹¹-131)/3	December 11, 2012	Ray Chandler
2599	2111	42209	42w09	(38·10²¹¹⁰-119)/9	December 11, 2012	Ray Chandler
2600	2110		72w11	(65·10²¹⁰⁹-101)/9	December 11, 2012	Ray Chandler
2601	2110	69913	69w13	7·10²¹⁰⁹-87	December 11, 2012	Ray Chandler
2602	2109	41157	41w57	(37·10²¹⁰⁸+413)/9	December 11, 2012	Ray Chandler
2603	2109	32213	32w13	(29·10²¹⁰⁸-83)/9	December 11, 2012	Ray Chandler
2604	2108	71123	71w23	(64·10²¹⁰⁷+107)/9	December 11, 2012	Ray Chandler
2611	2102	72253	72w53	(65·10²¹⁰¹+277)/9	December 11, 2012	Ray Chandler

December 10, 2012

Ray Chandler certificated 5 near-repdigit prime numbers, 39 quasi-repdigit prime numbers and 121 near-repdigit-related prime numbers by Primo. Certifications are available.

Proven near-repdigit primes
	digits	flabel	wlabel	expression	when	who
538	2051	31333	313w	(94·10²⁰⁴⁹-1)/3	December 10, 2012	Ray Chandler
539	2048		9w59999999	10²⁰⁴⁸-40000001	December 10, 2012	Ray Chandler
543	2021		9w299999999	10²⁰²¹-700000001	December 10, 2012	Ray Chandler
550	2006		9w8999999999	10²⁰⁰⁶-1000000001	December 10, 2012	Ray Chandler
551	2006	33323	3w23	(10²⁰⁰⁶-31)/3	December 10, 2012	Ray Chandler

Proven quasi-repdigit primes (except pd)
	digits	flabel	wlabel	expression	when	who
416	2098	59553	595w3	(536·10²⁰⁹⁶-23)/9	December 10, 2012	Ray Chandler
419	2092	44481	4w81	(4·10²⁰⁹²+329)/9	December 10, 2012	Ray Chandler
421	2092	29909	29w09	3·10²⁰⁹¹-91	December 10, 2012	Ray Chandler
422	2091	37737	37w37	(34·10²⁰⁹⁰-367)/9	December 10, 2012	Ray Chandler
423	2086	88807	8w07	(8·10²⁰⁸⁶-737)/9	December 10, 2012	Ray Chandler
425	2083	44469	4w69	(4·10²⁰⁸³+221)/9	December 10, 2012	Ray Chandler
429	2072	88829	8w29	(8·10²⁰⁷²-539)/9	December 10, 2012	Ray Chandler
433	2068	66679	6w79	(2·10²⁰⁶⁸+37)/3	December 10, 2012	Ray Chandler
434	2067	94777	947w	(853·10²⁰⁶⁵-7)/9	December 10, 2012	Ray Chandler
436	2067	19333	193w	(58·10²⁰⁶⁵-1)/3	December 10, 2012	Ray Chandler
438	2065	28221	282w1	(254·10²⁰⁶³-11)/9	December 10, 2012	Ray Chandler
440	2063	60667	606w7	(182·10²⁰⁶¹+1)/3	December 10, 2012	Ray Chandler
441	2062	49919	49w19	5·10²⁰⁶¹-81	December 10, 2012	Ray Chandler
442	2061	82881	828w1	(746·10²⁰⁵⁹-71)/9	December 10, 2012	Ray Chandler
443	2061	59989	59w89	6·10²⁰⁶⁰-11	December 10, 2012	Ray Chandler
444	2060	88867	8w67	(8·10²⁰⁶⁰-197)/9	December 10, 2012	Ray Chandler
445	2060	77753	7w53	(7·10²⁰⁶⁰-223)/9	December 10, 2012	Ray Chandler
446	2059	83881	838w1	(755·10²⁰⁵⁷-71)/9	December 10, 2012	Ray Chandler
447	2059	53323	53w23	(16·10²⁰⁵⁸-31)/3	December 10, 2012	Ray Chandler
448	2056	44421	4w21	(4·10²⁰⁵⁶-211)/9	December 10, 2012	Ray Chandler
449	2055	77731	7w31	(7·10²⁰⁵⁵-421)/9	December 10, 2012	Ray Chandler
451	2053	31151	31w51	(28·10²⁰⁵²+359)/9	December 10, 2012	Ray Chandler
452	2052	57111	571w	(514·10²⁰⁵⁰-1)/9	December 10, 2012	Ray Chandler
453	2052	44491	4w91	(4·10²⁰⁵²+419)/9	December 10, 2012	Ray Chandler
454	2050	55563	5w63	(5·10²⁰⁵⁰+67)/9	December 10, 2012	Ray Chandler
455	2048	16777	167w	(151·10²⁰⁴⁶-7)/9	December 10, 2012	Ray Chandler
456	2044	66679	6w79	(2·10²⁰⁴⁴+37)/3	December 10, 2012	Ray Chandler
458	2040	87881	878w1	(791·10²⁰³⁸-71)/9	December 10, 2012	Ray Chandler
459	2040	73363	73w63	(22·10²⁰³⁹+89)/3	December 10, 2012	Ray Chandler
462	2036	63383	63w83	(19·10²⁰³⁵+149)/3	December 10, 2012	Ray Chandler
463	2035	68777	687w	(619·10²⁰³³-7)/9	December 10, 2012	Ray Chandler
464	2034	58111	581w	(523·10²⁰³²-1)/9	December 10, 2012	Ray Chandler
467	2032	63343	63w43	(19·10²⁰³¹+29)/3	December 10, 2012	Ray Chandler
468	2025	69777	697w	(628·10²⁰²³-7)/9	December 10, 2012	Ray Chandler
469	2024	58333	583w	(175·10²⁰²²-1)/3	December 10, 2012	Ray Chandler
470	2024	22297	2w97	(2·10²⁰²⁴+673)/9	December 10, 2012	Ray Chandler
471	2019	53303	53w03	(16·10²⁰¹⁸-91)/3	December 10, 2012	Ray Chandler
483	2006	59777	597w	(538·10²⁰⁰⁴-7)/9	December 10, 2012	Ray Chandler
484	2005		6w77	(2·10²⁰⁰⁵+31)/3	December 10, 2012	Ray Chandler

Proven near-repdigit-related primes (except ru/nr/pd/qr)
	digits	flabel	wlabel	expression	when	who
2482	2098	92281	92w81	(83·10²⁰⁹⁷+529)/9	December 10, 2012	Ray Chandler
2484	2098	25593	25w93	(23·10²⁰⁹⁷+337)/9	December 10, 2012	Ray Chandler
2485	2097	93347	93w47	(28·10²⁰⁹⁶+41)/3	December 10, 2012	Ray Chandler
2486	2097		13w99	(4·10²⁰⁹⁶+197)/3	December 10, 2012	Ray Chandler
2487	2096	98873	98w73	(89·10²⁰⁹⁵-143)/9	December 10, 2012	Ray Chandler
2489	2096	14453	14w53	(13·10²⁰⁹⁵+77)/9	December 10, 2012	Ray Chandler
2491	2094	98829	98w29	(89·10²⁰⁹³-539)/9	December 10, 2012	Ray Chandler
2492	2094	13369	13w69	(4·10²⁰⁹³+107)/3	December 10, 2012	Ray Chandler
2494	2093	35573	35w73	(32·10²⁰⁹²+157)/9	December 10, 2012	Ray Chandler
2495	2092		557w3	(502·10²⁰⁹⁰-43)/9	December 10, 2012	Ray Chandler
2497	2090	76651	76w51	(23·10²⁰⁸⁹-47)/3	December 10, 2012	Ray Chandler
2498	2089	45519	45w19	(41·10²⁰⁸⁸-329)/9	December 10, 2012	Ray Chandler
2499	2089	36617	36w17	(11·10²⁰⁸⁸-149)/3	December 10, 2012	Ray Chandler
2500	2089	34481	34w81	(31·10²⁰⁸⁸+329)/9	December 10, 2012	Ray Chandler
2501	2087	16693	16w93	(5·10²⁰⁸⁶+79)/3	December 10, 2012	Ray Chandler
2502	2086	92263	92w63	(83·10²⁰⁸⁵+367)/9	December 10, 2012	Ray Chandler
2503	2086	54429	54w29	(49·10²⁰⁸⁵-139)/9	December 10, 2012	Ray Chandler
2506	2085	19903	19w03	2·10²⁰⁸⁴-97	December 10, 2012	Ray Chandler
2507	2084	67781	67w81	(61·10²⁰⁸³+29)/9	December 10, 2012	Ray Chandler
2509	2084	28861	28w61	(26·10²⁰⁸³-251)/9	December 10, 2012	Ray Chandler
2510	2084	17743	17w43	(16·10²⁰⁸³-313)/9	December 10, 2012	Ray Chandler
2511	2084	12263	12w63	(11·10²⁰⁸³+367)/9	December 10, 2012	Ray Chandler
2512	2083	12271	12w71	(11·10²⁰⁸²+439)/9	December 10, 2012	Ray Chandler
2513	2082	31147	31w47	(28·10²⁰⁸¹+323)/9	December 10, 2012	Ray Chandler
2514	2081	65567	65w67	(59·10²⁰⁸⁰+103)/9	December 10, 2012	Ray Chandler
2515	2080	94487	94w87	(85·10²⁰⁷⁹+383)/9	December 10, 2012	Ray Chandler
2516	2080	75541	75w41	(68·10²⁰⁷⁹-131)/9	December 10, 2012	Ray Chandler
2517	2080	31169	31w69	(28·10²⁰⁷⁹+521)/9	December 10, 2012	Ray Chandler
2520	2078	65587	65w87	(59·10²⁰⁷⁷+283)/9	December 10, 2012	Ray Chandler
2521	2078	41167	41w67	(37·10²⁰⁷⁷+503)/9	December 10, 2012	Ray Chandler
2522	2077	82237	82w37	(74·10²⁰⁷⁶+133)/9	December 10, 2012	Ray Chandler
2525	2076	82259	82w59	(74·10²⁰⁷⁵+331)/9	December 10, 2012	Ray Chandler
2527	2074		993w1	(298·10²⁰⁷²-7)/3	December 10, 2012	Ray Chandler
2528	2074	71103	71w03	(64·10²⁰⁷³-73)/9	December 10, 2012	Ray Chandler
2529	2073	38837	38w37	(35·10²⁰⁷²-467)/9	December 10, 2012	Ray Chandler
2530	2073		32w11	(29·10²⁰⁷²-101)/9	December 10, 2012	Ray Chandler
2531	2072	82289	82w89	(74·10²⁰⁷¹+601)/9	December 10, 2012	Ray Chandler
2532	2071	15583	15w83	(14·10²⁰⁷⁰+247)/9	December 10, 2012	Ray Chandler
2533	2070	73357	73w57	(22·10²⁰⁶⁹+71)/3	December 10, 2012	Ray Chandler
2534	2069	46603	46w03	(14·10²⁰⁶⁸-191)/3	December 10, 2012	Ray Chandler
2535	2069	21157	21w57	(19·10²⁰⁶⁸+413)/9	December 10, 2012	Ray Chandler
2536	2068		880w3	88·10²⁰⁶⁶+3	December 10, 2012	Ray Chandler
2537	2068	69907	69w07	7·10²⁰⁶⁷-93	December 10, 2012	Ray Chandler
2539	2065		71w33	(64·10²⁰⁶⁴+197)/9	December 10, 2012	Ray Chandler
2540	2065	68863	68w63	(62·10²⁰⁶⁴-233)/9	December 10, 2012	Ray Chandler
2542	2064		776w9	(233·10²⁰⁶²+7)/3	December 10, 2012	Ray Chandler
2543	2064	17701	17w01	(16·10²⁰⁶³-691)/9	December 10, 2012	Ray Chandler
2546	2063	85597	85w97	(77·10²⁰⁶²+373)/9	December 10, 2012	Ray Chandler
2547	2063	75563	75w63	(68·10²⁰⁶²+67)/9	December 10, 2012	Ray Chandler
2548	2063	59971	59w71	6·10²⁰⁶²-29	December 10, 2012	Ray Chandler
2552	2062	15513	15w13	(14·10²⁰⁶¹-383)/9	December 10, 2012	Ray Chandler
2554	2060		220w9	22·10²⁰⁵⁸+9	December 10, 2012	Ray Chandler
2555	2059	70039	70w39	7·10²⁰⁵⁸+39	December 10, 2012	Ray Chandler
2557	2058		993w7	(298·10²⁰⁵⁶+11)/3	December 10, 2012	Ray Chandler
2559	2055	81187	81w87	(73·10²⁰⁵⁴+683)/9	December 10, 2012	Ray Chandler
2560	2055	60053	60w53	6·10²⁰⁵⁴+53	December 10, 2012	Ray Chandler
2561	2054	87749	87w49	(79·10²⁰⁵³-259)/9	December 10, 2012	Ray Chandler
2562	2054	76697	76w97	(23·10²⁰⁵³+91)/3	December 10, 2012	Ray Chandler
2563	2053		779w3	78·10²⁰⁵¹-7	December 10, 2012	Ray Chandler
2564	2053	56629	56w29	(17·10²⁰⁵²-113)/3	December 10, 2012	Ray Chandler
2565	2053	49931	49w31	5·10²⁰⁵²-69	December 10, 2012	Ray Chandler
2566	2053	20027	20w27	2·10²⁰⁵²+27	December 10, 2012	Ray Chandler
2567	2052		62w77	(56·10²⁰⁵¹+493)/9	December 10, 2012	Ray Chandler
2571	2051		338w9	(305·10²⁰⁴⁹+1)/9	December 10, 2012	Ray Chandler
2572	2051	28807	28w07	(26·10²⁰⁵⁰-737)/9	December 10, 2012	Ray Chandler
2573	2051		118w1	(107·10²⁰⁴⁹-71)/9	December 10, 2012	Ray Chandler
2574	2049		775w3	(698·10²⁰⁴⁷-23)/9	December 10, 2012	Ray Chandler
2575	2049	43301	43w01	(13·10²⁰⁴⁸-97)/3	December 10, 2012	Ray Chandler
2576	2048	59983	59w83	6·10²⁰⁴⁷-17	December 10, 2012	Ray Chandler
2579	2047	60073	60w73	6·10²⁰⁴⁶+73	December 10, 2012	Ray Chandler
2580	2047	40021	40w21	4·10²⁰⁴⁶+21	December 10, 2012	Ray Chandler
2581	2045		883w7	(265·10²⁰⁴³+11)/3	December 10, 2012	Ray Chandler
2582	2045	21107	21w07	(19·10²⁰⁴⁴-37)/9	December 10, 2012	Ray Chandler
2583	2044	64473	64w73	(58·10²⁰⁴³+257)/9	December 10, 2012	Ray Chandler
2584	2043		557w1	(502·10²⁰⁴¹-61)/9	December 10, 2012	Ray Chandler
2585	2043		16w99	(5·10²⁰⁴²+97)/3	December 10, 2012	Ray Chandler
2588	2041	56653	56w53	(17·10²⁰⁴⁰-41)/3	December 10, 2012	Ray Chandler
2591	2040		991w7	(892·10²⁰³⁸+53)/9	December 10, 2012	Ray Chandler
2592	2040	67741	67w41	(61·10²⁰³⁹-331)/9	December 10, 2012	Ray Chandler
2594	2039	97759	97w59	(88·10²⁰³⁸-169)/9	December 10, 2012	Ray Chandler
2595	2039	54487	54w87	(49·10²⁰³⁸+383)/9	December 10, 2012	Ray Chandler
2596	2039	31169	31w69	(28·10²⁰³⁸+521)/9	December 10, 2012	Ray Chandler
2598	2038		69w77	7·10²⁰³⁷-23	December 10, 2012	Ray Chandler
2599	2036	86639	86w39	(26·10²⁰³⁵-83)/3	December 10, 2012	Ray Chandler
2603	2035	10093	10w93	10²⁰³⁴+93	December 10, 2012	Ray Chandler
2604	2034	47791	47w91	(43·10²⁰³³+119)/9	December 10, 2012	Ray Chandler
2606	2032	92239	92w39	(83·10²⁰³¹+151)/9	December 10, 2012	Ray Chandler
2607	2032	26621	26w21	(8·10²⁰³¹-137)/3	December 10, 2012	Ray Chandler
2608	2031		76w99	(23·10²⁰³⁰+97)/3	December 10, 2012	Ray Chandler
2609	2031	12279	12w79	(11·10²⁰³⁰+511)/9	December 10, 2012	Ray Chandler
2611	2027		50w77	5·10²⁰²⁶+77	December 10, 2012	Ray Chandler
2612	2027	25549	25w49	(23·10²⁰²⁶-59)/9	December 10, 2012	Ray Chandler
2613	2026		770w3	77·10²⁰²⁴+3	December 10, 2012	Ray Chandler
2614	2026	56641	56w41	(17·10²⁰²⁵-77)/3	December 10, 2012	Ray Chandler
2615	2026	34481	34w81	(31·10²⁰²⁵+329)/9	December 10, 2012	Ray Chandler
2616	2025	92283	92w83	(83·10²⁰²⁴+547)/9	December 10, 2012	Ray Chandler
2618	2025	25563	25w63	(23·10²⁰²⁴+67)/9	December 10, 2012	Ray Chandler
2619	2025	24457	24w57	(22·10²⁰²⁴+113)/9	December 10, 2012	Ray Chandler
2623	2023	85579	85w79	(77·10²⁰²²+211)/9	December 10, 2012	Ray Chandler
2624	2022	86653	86w53	(26·10²⁰²¹-41)/3	December 10, 2012	Ray Chandler
2625	2021		92w33	(83·10²⁰²⁰+97)/9	December 10, 2012	Ray Chandler
2627	2021	73301	73w01	(22·10²⁰²⁰-97)/3	December 10, 2012	Ray Chandler
2629	2020	19913	19w13	2·10²⁰¹⁹-87	December 10, 2012	Ray Chandler
2630	2019		84w11	(76·10²⁰¹⁸-301)/9	December 10, 2012	Ray Chandler
2631	2019	28857	28w57	(26·10²⁰¹⁸-287)/9	December 10, 2012	Ray Chandler
2632	2019	14493	14w93	(13·10²⁰¹⁸+437)/9	December 10, 2012	Ray Chandler
2633	2017	65503	65w03	(59·10²⁰¹⁶-473)/9	December 10, 2012	Ray Chandler
2634	2017	58863	58w63	(53·10²⁰¹⁶-233)/9	December 10, 2012	Ray Chandler
2638	2015		667w9	(601·10²⁰¹³+11)/9	December 10, 2012	Ray Chandler
2639	2015	48857	48w57	(44·10²⁰¹⁴-287)/9	December 10, 2012	Ray Chandler
2644	2009	81149	81w49	(73·10²⁰⁰⁸+341)/9	December 10, 2012	Ray Chandler
2649	2005	73301	73w01	(22·10²⁰⁰⁴-97)/3	December 10, 2012	Ray Chandler
2652	2004	78867	78w67	(71·10²⁰⁰³-197)/9	December 10, 2012	Ray Chandler
2653	2004	69943	69w43	7·10²⁰⁰³-57	December 10, 2012	Ray Chandler
2654	2004	39901	39w01	4·10²⁰⁰³-99	December 10, 2012	Ray Chandler
2655	2004	36623	36w23	(11·10²⁰⁰³-131)/3	December 10, 2012	Ray Chandler
2656	2003	29957	29w57	3·10²⁰⁰²-43	December 10, 2012	Ray Chandler
2657	2003	27761	27w61	(25·10²⁰⁰²-151)/9	December 10, 2012	Ray Chandler
2659	2002		23w99	(7·10²⁰⁰¹+197)/3	December 10, 2012	Ray Chandler
2660	2001	74469	74w69	(67·10²⁰⁰⁰+221)/9	December 10, 2012	Ray Chandler
2663	2001	18863	18w63	(17·10²⁰⁰⁰-233)/9	December 10, 2012	Ray Chandler

December 9, 2012

Factorizations of 600...007 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 10³⁰.

December 6, 2012

Factorizations of 577...77 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 10³⁰.

December 4, 2012

Factorizations of 499...991 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 10³⁰.

December 2, 2012

Factorizations of 866...663 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 10³⁰.

November 2012

November 30, 2012

Factorizations of 722...223 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 10³⁰.

November 27, 2012

Factorizations of 44...441 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 10³⁰.

November 25, 2012

Factorizations of 400...007 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 10³⁰.

November 24, 2012

Factorizations of 166...661 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 10³⁰.

November 22, 2012

Factorizations of 155...559 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 10³⁰.

November 21, 2012

Factorizations of 588...889 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 10³⁰.

November 20, 2012

Factorizations of 355...559 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 10³⁰.

November 19, 2012

Factorizations of 99...997 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 10³⁰.

November 18, 2012

Factorizations of 844...449 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 10³⁰.

November 16, 2012

Factorizations of 488...881 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 10³⁰.

November 15, 2012

Factorizations of 22...221 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 10³⁰.

November 13, 2012

Factorizations of 422...227 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 10³⁰.

November 12, 2012

Factorizations of 400...003 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 10³⁰.

November 1, 2012

Factorizations of 988...881 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 10³⁰.

October 2012

October 27, 2012

Factorizations of 155...551 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 10³⁰.

October 22, 2012

Factorizations of 822...229 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 10³⁰.

October 15, 2012

Factorizations of 799...997 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 10³⁰.

October 9, 2012

Factorizations of 855...553 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 10³⁰.

October 4, 2012

Factorizations of 388...883 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 10³⁰.

September 2012

September 27, 2012

Markus Tervooren proved primality of 10⁷⁶⁶⁸+3 by ECPP. Certification is available.

Proven quasi-repdigit primes (except pd)
	digits	flabel	wlabel	expression	when	who
176	7669	10003	10w3	10⁷⁶⁶⁸+3	September 27, 2012	Markus Tervooren

September 26, 2012

Factorizations of 177...773 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 10³⁰.

September 21, 2012

Factorizations of 88...883 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 10³⁰.

September 15, 2012

Factorizations of 322...223 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 10³⁰.

September 13, 2012

Alexander Gramolin found the largest known quasi-repdit prime number. Congratulations!

Proven quasi-repdigit primes (except pd)
	digits	flabel	wlabel	expression	when	who
1	665830	30001	30w1	3·10⁶⁶⁵⁸²⁹+1	September 13, 2012	Alexander Gramolin

The Prime Database: 3*10^665829+1 (Chris K. Caldwell)

September 9, 2012

Factorizations of 233...339 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 10³⁰.

September 5, 2012

Stefano D'Urso found the 46th prime number of the form 1003205·10ⁿ-1. It's also the largest known prime number of the form k·10ⁿ-1 where k generates 45 known prime numbers at least. Congratulations!

Prime numbers of the form k·10ⁿ-1 (including 45 known prime numbers at least)
	digits	flabel	wlabel	expression	when	who
1	314712		10032049w	1003205·10³¹⁴⁷⁰⁵-1	September 5, 2012	Stefano D'Urso

The Prime Database: 1003205*10^314705-1 (Chris K. Caldwell)

September 2, 2012

Factorizations of 22...227 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 10³⁰.

August 2012

August 28, 2012

Factorizations of 211...11 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 10³⁰.

August 24, 2012

Stefano D'Urso found the 45th prime number of the form 1003205·10ⁿ-1. It's also the largest known prime number of the form k·10ⁿ-1 where k generates 45 known prime numbers at least. Congratulations!

Prime numbers of the form k·10ⁿ-1 (including 45 known prime numbers at least)
	digits	wlabel	expression	when	who
1	291684	10032049w	1003205·10²⁹¹⁶⁷⁷-1	August 24, 2012	Stefano D'Urso
2	258342	10032049w	1003205·10²⁵⁸³³⁵-1	May 4, 2012	Stefano D'Urso
8	217813	10032049w	1003205·10²¹⁷⁸⁰⁶-1	January 8, 2012	Stefano D'Urso

The Prime Database: 1003205*10^217806-1 (Chris K. Caldwell)
The Prime Database: 1003205*10^258335-1 (Chris K. Caldwell)
The Prime Database: 1003205*10^291677-1 (Chris K. Caldwell)

August 22, 2012

Factorizations of 133...331 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 10³⁰.

August 17, 2012

Factorizations of 100...007 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 10³⁰.

August 14, 2012

Mathew proved 2 near-repdigit primes and 4 quasi-repdigit primes by Primo. Certifications are available.

Proven near-repdigit primes
	digits	flabel	wlabel	expression	when	who
402	4709	33533	3w53w	(10⁴⁷⁰⁹+6·10²³⁵⁴-1)/3	August 10, 2012	Mathew
436	3641	33533	3w53w	(10³⁶⁴¹+6·10¹⁸²⁰-1)/3	August 5, 2012	Mathew

Proven quasi-repdigit primes (except pd)
	digits	flabel	wlabel	expression	when	who
243	4123	49993	49w3	5·10⁴¹²²-7	August 12, 2012	Mathew
268	3473	84443	84w3	(76·10³⁴⁷²-13)/9	August 14, 2012	Mathew
275	3326	49993	49w3	5·10³³²⁵-7	August 12, 2012	Mathew
285	3164	84443	84w3	(76·10³¹⁶³-13)/9	August 13, 2012	Mathew

August 12, 2012

Factorizations of 133...33 have been extended up to n=300. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 10³⁰.

August 8, 2012

Factorizations of 411...119 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 10³⁰.

August 5, 2012

Alexander Gramolin found the largest proven quasi-repdit prime (except pd). Congratulations!

Proven quasi-repdigit primes (except pd)
	digits	flabel	wlabel	expression	when	who
1	618854	30001	30w1	3·10⁶¹⁸⁸⁵³+1	August 5, 2012	Alexander Gramolin

The Prime Database: 3*10^618853+1 (Chris K. Caldwell)

August 1, 2012

Factorizations of 355...557 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 10³⁰.

July 2012

July 29, 2012

Mathew proved a quasi-repdigit prime by Primo. Certifications are available.

Proven quasi-repdigit primes (except pd)
	digits	flabel	wlabel	expression	when	who
285	3111	16667	16w7	(5·10³¹¹⁰+1)/3	July 29, 2012	Mathew

July 27, 2012

Factorizations of 322...229 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 10³⁰.

July 23, 2012

Factorizations of 155...557 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 10³⁰.

July 18, 2012

Factorizations of 911...119 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 10³⁰.

July 14, 2012

Factorizations of 133...337 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 10³⁰.

July 10, 2012

Factorizations of 733...331 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 10³⁰.

July 4, 2012

Factorizations of 955...559 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 10³⁰.

Factorizations of 77...77477...77 have been extended up to n=150. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 10³⁰.

June 26, 2012

Erik Branger pointed out that the Murphy_E score of some SNFS polynomials can be greatly improved by multiplied by a small number. So, I changed the polynomial selection method to new one based on the Murphy_E score. For example, SNFS polynomial of 77677_119 was changed from 700000·(10³⁹)⁶-900·(10³⁹)³-7 to 7·(10⁴⁰)⁶-9·(10⁴⁰)³-70. Its Murphy_E score was increased from 3.597e-13 to 5.537e-13. Sieving time may be shortened but I'm not sure whether the change always brings positive effects.

June 20, 2012

Factorizations of 377...77 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 10³⁰.

June 14, 2012

Factorizations of 922...221 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 10³⁰.

June 11, 2012

Ray Chandler reported that no additional prime number of the form 7347764627675020164·10ⁿ-1 up to n=200000 was found.

June 8, 2012

Factorizations of 211...117 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 10³⁰.

June 4, 2012

The threshold of the wanted list 3, composite numbers which are longer than 97 percent of the corresponding SNFS polynomial, has been raised from 95 percent at the suggestion of Serge Batalov.

June 3, 2012

Please make sure of your mail address before making reservations. Thank you.

June 2, 2012

Factorizations of 966...667 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 10³⁰.

May 2012

May 27, 2012

Factorizations of 944...447 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 10³⁰.

May 22, 2012

Factorizations of 855...557 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 10³⁰.

May 16, 2012

Factorizations of 155...553 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 10³⁰.

May 14, 2012

Erik Branger has finished searching prime numbers of the form 711...11 until 200000 digits.

May 11, 2012

Factorizations of 144...441 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 10³⁰.

May 5, 2012

Factorizations of 122...227 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 10³⁰.

May 1, 2012

Factorizations of 522...223 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 10³⁰.

April 2012

April 24, 2012

Factorizations of 199...997 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 10³⁰.

April 19, 2012

Factorizations of 99...99799...99 have been extended up to n=150. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 10³⁰.

April 16, 2012

History of searching prime numbers of each form is available. e.g. History of searching prime numbers of the form 77...771

April 15, 2012

Erik Branger has finished searching prime numbers of the form 77...771 until 300000 digits.

April 13, 2012

Factorizations of 511...117 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 10³⁰.

April 11, 2012

Darren Bedwell found the largest known near-repdigit-palindrome prime number. Congratulations!

Proven near-repdigit-palindrome primes
	digits	flabel	wlabel	expression	when	who
1	290253	99799	9w79w	10²⁹⁰²⁵³-2·10¹⁴⁵¹²⁶-1	April 11, 2012	Darren Bedwell

The Prime Database: 10^290253-2*10^145126-1 (Chris K. Caldwell)
The Top Twenty: Near-repdigit (Chris K. Caldwell)
The Top Twenty: Palindrome (Chris K. Caldwell)

April 9, 2012

Factorizations of 699...991 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 10³⁰.

April 5, 2012

Factorizations of 911...11 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 10³⁰.

April 2, 2012

Factorizations of 433...331 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 10³⁰.

Ray Chandler found the 62nd prime number of the form 7347764627675020164·10ⁿ-1.

Prime numbers of the form k·10ⁿ-1 (including 45 known prime numbers at least)
	digits	flabel	wlabel	expression	when	who
11	145198		73477646276750201639w	7347764627675020164·10¹⁴⁵¹⁷⁹-1	April 2, 2012	Ray Chandler

March 2012

March 30, 2012

Factorizations of 977...773 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 10³⁰.

March 29, 2012

Erik Branger proved 114 prime cofactors of Phi_n(10) by ECPP. See Primality certifications.

March 27, 2012

Ray Chandler found the 61st prime number of the form 7347764627675020164·10ⁿ-1.

Prime numbers of the form k·10ⁿ-1 (including 45 known prime numbers at least)
	digits	flabel	wlabel	expression	when	who
12	136281		73477646276750201639w	7347764627675020164·10¹³⁶²⁶²-1	March 27, 2012	Ray Chandler

March 26, 2012

Factorizations of 766...661 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 10³⁰.

March 21, 2012

Factorizations of 77...77877...77 have been extended up to n=150. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 10³⁰.

March 15, 2012

Factorizations of 255...557 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 10³⁰.

March 12, 2012

Ray Chandler found 15 prime numbers of the form k·10ⁿ-1 (including 45 known prime numbers at least). 46th-47th of n=1199620156415569595, 48th of n=24255533047620308, 49th of n=248108640286930808, 51st of n=330640210602617363, 46th of n=4155941632109082935, 48th of n=5189395769656459445, 47th of n=529220357182862954, 47th of n=5410621003833542777, 49th of n=5906181743052623648, 50th of n=8058799722014140442, 53rd of n=8861036989751958627 and 50th-52nd of n=9334983988275764.

Prime numbers of the form k·10ⁿ-1 (including 45 known prime numbers at least)
	digits	wlabel	expression	when	who
36	49659	93349839882757639w	9334983988275764·10⁴⁹⁶⁴³-1	March 12, 2012	Ray Chandler
39	49360	93349839882757639w	9334983988275764·10⁴⁹³⁴⁴-1	March 12, 2012	Ray Chandler
42	49236	51893957696564594449w	5189395769656459445·10⁴⁹²¹⁷-1	March 12, 2012	Ray Chandler
59	47345	80587997220141404419w	8058799722014140442·10⁴⁷³²⁶-1	March 12, 2012	Ray Chandler
77	45701	2481086402869308079w	248108640286930808·10⁴⁵⁶⁸³-1	March 12, 2012	Ray Chandler
79	45490	93349839882757639w	9334983988275764·10⁴⁵⁴⁷⁴-1	March 12, 2012	Ray Chandler
80	45473	59061817430526236479w	5906181743052623648·10⁴⁵⁴⁵⁴-1	March 12, 2012	Ray Chandler
84	45137	41559416321090829349w	4155941632109082935·10⁴⁵¹¹⁸-1	March 12, 2012	Ray Chandler
87	44799	5292203571828629539w	529220357182862954·10⁴⁴⁷⁸¹-1	March 12, 2012	Ray Chandler
89	44758	11996201564155695949w	1199620156415569595·10⁴⁴⁷³⁹-1	March 12, 2012	Ray Chandler
90	44649	11996201564155695949w	1199620156415569595·10⁴⁴⁶³⁰-1	March 12, 2012	Ray Chandler
99	43416	242555330476203079w	24255533047620308·10⁴³³⁹⁹-1	March 12, 2012	Ray Chandler
105	42851	54106210038335427769w	5410621003833542777·10⁴²⁸³²-1	March 12, 2012	Ray Chandler
107	42668	3306402106026173629w	330640210602617363·10⁴²⁶⁵⁰-1	March 12, 2012	Ray Chandler
108	42548	88610369897519586269w	8861036989751958627·10⁴²⁵²⁹-1	March 12, 2012	Ray Chandler

Factorizations of 88...881 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 10³⁰.

March 7, 2012

Factorizations of 844...441 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 10³⁰.

March 5, 2012

Erik Branger found the third largest known unprovable near-repdigit PRP. Congratulations!

Unprovable near-repdigit PRPs
	digits	flabel	wlabel	expression	when	who
3	271757	77771	7w1	(7·10²⁷¹⁷⁵⁷-61)/9	March 5, 2012	Erik Branger

March 4, 2012

Factorizations of 744...443 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 10³⁰.

February 2012

February 29, 2012

Darren Bedwell found the largest known near-repdigit-palindrome prime number. Congratulations!

Proven near-repdigit-palindrome primes
	digits	flabel	wlabel	expression	when	who
1	269479	99299	9w29w	10²⁶⁹⁴⁷⁹-7·10¹³⁴⁷³⁹-1	February 29, 2012	Darren Bedwell

The Prime Database: 10^269479-7*10^134739-1 (Chris K. Caldwell)
The Top Twenty: Near-repdigit (Chris K. Caldwell)
The Top Twenty: Palindrome (Chris K. Caldwell)

February 28, 2012

Ray Chandler found the 60th prime number of the form 7347764627675020164·10ⁿ-1. Congratulations!

Prime numbers of the form k·10ⁿ-1 (including 45 known prime numbers at least)
	digits	flabel	wlabel	expression	when	who
13	103129		73477646276750201639w	7347764627675020164·10¹⁰³¹¹⁰-1	February 28, 2012	Ray Chandler

Factorizations of 755...559 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 10³⁰.

February 24, 2012

Alexander Gramolin found the second largest proven quasi-repdit prime (except pd). Congratulations!

Proven quasi-repdigit primes (except pd)
	digits	flabel	wlabel	expression	when	who
2	111989	30001	30w1	3·10¹¹¹⁹⁸⁸+1	February 24, 2012	Alexander Gramolin

Factorizations of 933...337 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 10³⁰.

February 22, 2012

Ray Chandler found 24 prime numbers of the form k·10ⁿ-1 (including 45 known prime numbers at least). 45th-46th of n=8461887092138837, 48th-49th of n=9334983988275764, 45th-47th of n=15600468793880159, 48th of n=16337430201479681, 46th-47th of n=24255533047620308, 47th-48th of n=29472578289080199, 48th of n=30895035496936877, 44th of n=35627728454703812, 48th of n=248108640286930808, 50th of n=330640210602617363, 44th of n=1089887362034810066, 52nd-53rd of n=3688107672047143961, 48th of n=3745413626697133958, 46th of n=5410621003833542777, 48th of n=5906181743052623648, 48th-49th of n=8058799722014140442 and 46th-47th of n=8124529194875611707.

Prime numbers of the form k·10ⁿ-1 (including 45 known prime numbers at least)
	digits	wlabel	expression	when	who
106	41913	54106210038335427769w	5410621003833542777·10⁴¹⁸⁹⁴-1	February 22, 2012	Ray Chandler
113	41145	36881076720471439609w	3688107672047143961·10⁴¹¹²⁶-1	February 22, 2012	Ray Chandler
118	40844	294725782890801989w	29472578289080199·10⁴⁰⁸²⁷-1	February 22, 2012	Ray Chandler
119	40829	84618870921388369w	8461887092138837·10⁴⁰⁸¹³-1	February 22, 2012	Ray Chandler
123	40273	156004687938801589w	15600468793880159·10⁴⁰²⁵⁶-1	February 22, 2012	Ray Chandler
131	39537	84618870921388369w	8461887092138837·10³⁹⁵²¹-1	February 22, 2012	Ray Chandler
132	39534	2481086402869308079w	248108640286930808·10³⁹⁵¹⁶-1	February 22, 2012	Ray Chandler
137	39365	93349839882757639w	9334983988275764·10³⁹³⁴⁹-1	February 22, 2012	Ray Chandler
139	39293	242555330476203079w	24255533047620308·10³⁹²⁷⁶-1	February 22, 2012	Ray Chandler
140	39227	81245291948756117069w	8124529194875611707·10³⁹²⁰⁸-1	February 22, 2012	Ray Chandler
141	39068	93349839882757639w	9334983988275764·10³⁹⁰⁵²-1	February 22, 2012	Ray Chandler
145	38699	80587997220141404419w	8058799722014140442·10³⁸⁶⁸⁰-1	February 22, 2012	Ray Chandler
147	38691	156004687938801589w	15600468793880159·10³⁸⁶⁷⁴-1	February 22, 2012	Ray Chandler
155	38100	242555330476203079w	24255533047620308·10³⁸⁰⁸³-1	February 22, 2012	Ray Chandler
156	38049	156004687938801589w	15600468793880159·10³⁸⁰³²-1	February 22, 2012	Ray Chandler
167	37331	59061817430526236479w	5906181743052623648·10³⁷³¹²-1	February 22, 2012	Ray Chandler
172	37060	294725782890801989w	29472578289080199·10³⁷⁰⁴³-1	February 22, 2012	Ray Chandler
185	36230	80587997220141404419w	8058799722014140442·10³⁶²¹¹-1	February 22, 2012	Ray Chandler
187	36124	37454136266971339579w	3745413626697133958·10³⁶¹⁰⁵-1	February 22, 2012	Ray Chandler
189	36058	308950354969368769w	30895035496936877·10³⁶⁰⁴¹-1	February 22, 2012	Ray Chandler
193	35527	81245291948756117069w	8124529194875611707·10³⁵⁵⁰⁸-1	February 22, 2012	Ray Chandler
195	35416	163374302014796809w	16337430201479681·10³⁵³⁹⁹-1	February 22, 2012	Ray Chandler
205	34928	3306402106026173629w	330640210602617363·10³⁴⁹¹⁰-1	February 22, 2012	Ray Chandler
230	33279	36881076720471439609w	3688107672047143961·10³³²⁶⁰-1	February 22, 2012	Ray Chandler

February 21, 2012

Ray Chandler found 18 prime numbers of the form k·10ⁿ-1 (including 45 known prime numbers at least). 50th of n=5849194205932532, 50th of n=10471993823152799, 49th-50th of n=11885302750562514, 50th-52nd of n=13523719823507418, 45th-46th of n=24395082050363864, 47th of n=37731518958711032, 51st of n=2265457412699262446, 45th of n=2960341158972475544, 46th-47th of n=5586437116317036434, 50th-51st of n=6758517141263266764, 45th of n=7270120168119633986 and 49th of n=8953919255802171035.

Prime numbers of the form k·10ⁿ-1 (including 45 known prime numbers at least)
	digits	wlabel	expression	when	who
35	49619	72701201681196339859w	7270120168119633986·10⁴⁹⁶⁰⁰-1	February 21, 2012	Ray Chandler
41	48828	58491942059325319w	5849194205932532·10⁴⁸⁸¹²-1	February 21, 2012	Ray Chandler
47	47963	104719938231527989w	10471993823152799·10⁴⁷⁹⁴⁶-1	February 21, 2012	Ray Chandler
50	47669	118853027505625139w	11885302750562514·10⁴⁷⁶⁵²-1	February 21, 2012	Ray Chandler
59	46852	377315189587110319w	37731518958711032·10⁴⁶⁸³⁵-1	February 21, 2012	Ray Chandler
75	45185	243950820503638639w	24395082050363864·10⁴⁵¹⁶⁸-1	February 21, 2012	Ray Chandler
80	44310	118853027505625139w	11885302750562514·10⁴⁴²⁹³-1	February 21, 2012	Ray Chandler
89	43300	29603411589724755439w	2960341158972475544·10⁴³²⁸¹-1	February 21, 2012	Ray Chandler
94	42534	135237198235074179w	13523719823507418·10⁴²⁵¹⁷-1	February 21, 2012	Ray Chandler
96	42496	89539192558021710349w	8953919255802171035·10⁴²⁴⁷⁷-1	February 21, 2012	Ray Chandler
97	42480	243950820503638639w	24395082050363864·10⁴²⁴⁶³-1	February 21, 2012	Ray Chandler
100	42390	135237198235074179w	13523719823507418·10⁴²³⁷³-1	February 21, 2012	Ray Chandler
114	40967	55864371163170364339w	5586437116317036434·10⁴⁰⁹⁴⁸-1	February 21, 2012	Ray Chandler
117	40748	135237198235074179w	13523719823507418·10⁴⁰⁷³¹-1	February 21, 2012	Ray Chandler
120	40105	55864371163170364339w	5586437116317036434·10⁴⁰⁰⁸⁶-1	February 21, 2012	Ray Chandler
125	39600	67585171412632667639w	6758517141263266764·10³⁹⁵⁸¹-1	February 21, 2012	Ray Chandler
128	39434	22654574126992624459w	2265457412699262446·10³⁹⁴¹⁵-1	February 21, 2012	Ray Chandler
130	39317	67585171412632667639w	6758517141263266764·10³⁹²⁹⁸-1	February 21, 2012	Ray Chandler

Factorizations of 911...117 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 10³⁰.

February 19, 2012

Ray Chandler found 16 prime numbers of the form k·10ⁿ-1 (including 45 known prime numbers at least). 45th-47th of n=1085096464828759446, 47th-48th of n=12627335841170253, 47th of n=1473996556504596663, 45th-46th of n=1770173404019815998, 46th-47th of n=18337020241048446, 44th-45th of n=3074342565732763052, 45th of n=3673162065033455603, 46th of n=3956926644759313113, 49th of n=8849719619597556 and 47th of n=9866995547651697.

Prime numbers of the form k·10ⁿ-1 (including 45 known prime numbers at least)
	digits	wlabel	expression	when	who
36	49357	126273358411702529w	12627335841170253·10⁴⁹³⁴⁰-1	February 19, 2012	Ray Chandler
38	49098	126273358411702529w	12627335841170253·10⁴⁹⁰⁸¹-1	February 19, 2012	Ray Chandler
39	48846	14739965565045966629w	1473996556504596663·10⁴⁸⁸²⁷-1	February 19, 2012	Ray Chandler
45	47908	10850964648287594459w	1085096464828759446·10⁴⁷⁸⁸⁹-1	February 19, 2012	Ray Chandler
47	47621	17701734040198159979w	1770173404019815998·10⁴⁷⁶⁰²-1	February 19, 2012	Ray Chandler
53	46956	36731620650334556029w	3673162065033455603·10⁴⁶⁹³⁷-1	February 19, 2012	Ray Chandler
58	46502	10850964648287594459w	1085096464828759446·10⁴⁶⁴⁸³-1	February 19, 2012	Ray Chandler
59	46328	30743425657327630519w	3074342565732763052·10⁴⁶³⁰⁹-1	February 19, 2012	Ray Chandler
70	45039	30743425657327630519w	3074342565732763052·10⁴⁵⁰²⁰-1	February 19, 2012	Ray Chandler
76	43717	88497196195975559w	8849719619597556·10⁴³⁷⁰¹-1	February 19, 2012	Ray Chandler
84	42798	98669955476516969w	9866995547651697·10⁴²⁷⁸²-1	February 19, 2012	Ray Chandler
86	42526	183370202410484459w	18337020241048446·10⁴²⁵⁰⁹-1	February 19, 2012	Ray Chandler
89	42248	10850964648287594459w	1085096464828759446·10⁴²²²⁹-1	February 19, 2012	Ray Chandler
96	41543	17701734040198159979w	1770173404019815998·10⁴¹⁵²⁴-1	February 19, 2012	Ray Chandler
101	41014	39569266447593131129w	3956926644759313113·10⁴⁰⁹⁹⁵-1	February 19, 2012	Ray Chandler
102	40928	183370202410484459w	18337020241048446·10⁴⁰⁹¹¹-1	February 19, 2012	Ray Chandler

February 18, 2012

Factorizations of 866...669 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 10³⁰.

February 15, 2012

Factorizations of 766...663 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 10³⁰.

February 13, 2012

Factorizations of 822...223 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 10³⁰.

February 11, 2012

Ray Chandler found 4 unprovable near-repdigit PRPs.

Unprovable near-repdigit PRPs
	digits	flabel	wlabel	expression	when	who
12	90212	61111	61w	(55·10⁹⁰²¹¹-1)/9	February 11, 2012	Ray Chandler
27	61098	61111	61w	(55·10⁶¹⁰⁹⁷-1)/9	February 11, 2012	Ray Chandler
43	49170	61111	61w	(55·10⁴⁹¹⁶⁹-1)/9	February 11, 2012	Ray Chandler
66	32633	61111	61w	(55·10³²⁶³²-1)/9	February 11, 2012	Ray Chandler

February 10, 2012

Factorizations of 800...009 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 10³⁰.

February 9, 2012

Ray Chandler found 16 prime numbers of the form k·10ⁿ-1 (including 45 known prime numbers at least). 51st of n=11749536972569333, 50th of n=13651074048698702, 52nd of n=191368947589402968, 53rd-54th of n=2998375267299290424, 50th-51st of n=3752621885794525128, 48th of n=401115243497052, 50th of n=4512565955069796981, 51st of n=4964807464647923921, 46th-47th of n=5294970814496095005, 49th of n=81610032903525693, 46th of n=8681897852553216354 and 48th-49th of n=920700247429683.

Prime numbers of the form k·10ⁿ-1 (including 45 known prime numbers at least)
	digits	wlabel	expression	when	who
36	49306	52949708144960950049w	5294970814496095005·10⁴⁹²⁸⁷-1	February 9, 2012	Ray Chandler
39	48453	37526218857945251279w	3752621885794525128·10⁴⁸⁴³⁴-1	February 9, 2012	Ray Chandler
41	48137	29983752672992904239w	2998375267299290424·10⁴⁸¹¹⁸-1	February 9, 2012	Ray Chandler
45	47534	52949708144960950049w	5294970814496095005·10⁴⁷⁵¹⁵-1	February 9, 2012	Ray Chandler
46	47259	37526218857945251279w	3752621885794525128·10⁴⁷²⁴⁰-1	February 9, 2012	Ray Chandler
48	46926	9207002474296829w	920700247429683·10⁴⁶⁹¹¹-1	February 9, 2012	Ray Chandler
49	46681	816100329035256929w	81610032903525693·10⁴⁶⁶⁶⁴-1	February 9, 2012	Ray Chandler
50	46648	9207002474296829w	920700247429683·10⁴⁶⁶³³-1	February 9, 2012	Ray Chandler
59	45588	29983752672992904239w	2998375267299290424·10⁴⁵⁵⁶⁹-1	February 9, 2012	Ray Chandler
63	44794	117495369725693329w	11749536972569333·10⁴⁴⁷⁷⁷-1	February 9, 2012	Ray Chandler
72	42902	45125659550697969809w	4512565955069796981·10⁴²⁸⁸³-1	February 9, 2012	Ray Chandler
76	42405	4011152434970519w	401115243497052·10⁴²³⁹⁰-1	February 9, 2012	Ray Chandler
77	42153	136510740486987019w	13651074048698702·10⁴²¹³⁶-1	February 9, 2012	Ray Chandler
78	42074	49648074646479239209w	4964807464647923921·10⁴²⁰⁵⁵-1	February 9, 2012	Ray Chandler
84	41419	86818978525532163539w	8681897852553216354·10⁴¹⁴⁰⁰-1	February 9, 2012	Ray Chandler
85	41418	1913689475894029679w	191368947589402968·10⁴¹⁴⁰⁰-1	February 9, 2012	Ray Chandler

February 8, 2012

Edward Trice found the largest known quasi-repdigit prime number of the form k·10ⁿ+1. Congratulations!

Proven quasi-repdigit primes (except pd)
	digits	flabel	wlabel	expression	when	who
1	231618	60001	60w1	6·10²³¹⁶¹⁷+1	February 8, 2012	Edward Trice

Ray Chandler found 1 unprovable near-repdigit PRP.

Unprovable near-repdigit PRPs
	digits	flabel	wlabel	expression	when	who
23	66576	67777	67w	(61·10⁶⁶⁵⁷⁵-7)/9	February 8, 2012	Ray Chandler

February 7, 2012

Factorizations of 799...991 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 10³⁰.

February 5, 2012

Factorizations of 755...557 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 10³⁰.

February 4, 2012

Ray Chandler found an 74254-digit unprovable near-repdigit PRP of the form 21w.

Unprovable near-repdigit PRPs
	digits	flabel	wlabel	expression	when	who
19	74254	21111	21w	(19·10⁷⁴²⁵³-1)/9	February 4, 2012	Ray Chandler

February 2, 2012

Factorizations of 33...33733...33 have been extended up to n=150. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 10³⁰.

Markus Tervooren proved the primality of a 10297-digit near-repdigit number (19·10¹⁰²⁹⁶-1)/9 by Primo.

Proven near-repdigit primes
	digits	flabel	wlabel	expression	when	who
303	10297	21111	21w	(19·10¹⁰²⁹⁶-1)/9	February 2, 2012	Markus Tervooren

Factorizations of 55...553 have been extended up to n=250 by Serge Batalov. Added composite numbers had passed ECM iterations 530 times at the level 30. Most unknown factors are supposed to be greater than 10³⁰.

January 2012

January 30, 2012

Factorizations of 844...443 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 10³⁰.

January 27, 2012

Factorizations of 499...993 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 10³⁰.

January 24, 2012

Factorizations of 299...993 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 10³⁰.

January 22, 2012

Factorizations of 166...669 have been extended up to n=250. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 10³⁰.

January 20, 2012

Factorizations of 99...99299...99 have been extended up to n=150. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 10³⁰.

January 17, 2012

Factorizations of 99...99199...99 have been extended up to n=150. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 10³⁰.

January 14, 2012

Factorizations of 77...77677...77 have been extended up to n=150. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 10³⁰.

January 11, 2012

Factorizations of 33...33533...33 have been extended up to n=150. Added composite numbers had passed ECM iterations 118 times at the level 35. Most unknown factors are supposed to be greater than 10³⁰.

January 10, 2012

Leonid Durman found the second largest known unprovable near-repdigit PRP so far. Congratulations!

Unprovable near-repdigit PRPs
	digits	flabel	wlabel	expression	when	who
2	380976	33331	3w1	(10³⁸⁰⁹⁷⁶-7)/3	January 10, 2012	Leonid Durman

January 9, 2012

Leonid Durman found the largest known unprovable near-repdigit PRP so far. Congratulations!

Unprovable near-repdigit PRPs
	digits	flabel	wlabel	expression	when	who
1	424861	33331	3w1	(10⁴²⁴⁸⁶¹-7)/3	January 9, 2012	Leonid Durman

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