Table of contents 目次

  1. Summary 概要
    1. Meaning of words 言葉の意味
  2. News ニュース
  3. Reserved numbers and submitted numbers 予約されている数と投稿された数
  4. Composite numbers that are hoped to be factored 分解が期待される合成数
  5. How to contribute your prime factors 素因数の投稿の仕方
  6. Contributed factorization results 投稿された素因数分解の結果
  7. Graphs グラフ
  8. Records 記録
  9. Factor tables 素因数分解表
    1. Repunit レピュニット (Repunit)
    2. Near-repdigit ニアレプディジット (Near-repdigit)
    3. Plateau-and-depression プラトウアンドデプレッション (Plateau-and-depression)
    4. Quasi-repdigit クワージレプディジット (Quasi-repdigit)
    5. Near-repdigit-palindrome ニアレプディジット回文数 (Near-repdigit-palindrome)
    6. List of factor tables classified by the first digit 先頭の数字で分類した素因数分解表のリスト
  10. Near-repdigit-related (probable) prime numbers ニアレプディジット関連の (おそらく) 素数
  11. Primality certifications of near-repdigit-related prime numbers ニアレプディジット関連の素数の素数性証明
  12. Covering set of near-repdigit-related sequences ニアレプディジット関連の数列の被覆集合
  13. Appendix 付録
    1. Primality proving program based on Pocklington's theorem ポクリントンの定理を用いた素数性証明プログラム
    2. Expression generator of near-repdigit-related numbers ニアレプディジット関連の数の数式ジェネレータ
  14. Acknowledgements 謝辞
  15. Links related to near-repdigit ニアレプディジットの関連リンク

1. Summary 概要

I'm making factor tables of near-repdigit-related numbers. Current factoring targets are repunit, near-repdigit which has a different digit on the edge or next to the edge, quasi-repdigit including plateau-and-depression which has different digits on both edge, and near-repdigit-palindrome. このページでは、ニアレプディジット関連の数の素因数分解表を作っています。現在の分解対象はレピュニット、端または端から 2 桁目が他の桁と異なるニアレプディジット、プラトウアンドデプレッションを含む両端が他の桁と異なるクワージレプディジット、およびニアレプディジット回文数です。

1.1. Meaning of words 言葉の意味

Repunit レピュニット (Repunit)

Repunit is an abbreviated word for repeated unit and means a natural number that is composed entirely of 1 such as 1, 11, 111, 1111, 11111. Repunit normally means decimal repunit without any special notice even though it can be defined on non-decimal numbers. レピュニットは repeated unit (反復単位数) の略で、1, 11, 111, 1111, 11111 のような 1 だけから成る自然数を意味します。10 進数以外でも定義できますが、特に断りがなければ普通は 10 進数のレピュニットを指します。

Repdigit レプディジット (Repdigit)

A natural number that is composed entirely of the same digit are called a repdigit, an abbreviated word for repeated digit. Repdigit includes repunit. レピュニットを含む、すべての桁の数字が同じ自然数 (ぞろ目) を repeated digit を縮めてレプディジットと呼びます。

Near-repdigit ニアレプディジット (Near-repdigit)

Near-repdigit is a natural number in which only one digit of a repdigit was replaced with other digit. ニアレプディジットはレプディジットの数字を 1 個だけ他の数字に置き換えた自然数です。

Plateau-and-depression プラトウアンドデプレッション (Plateau-and-depression)

Plateau-and-depression is a quasi-repdigit that has same different digits on both ends. プラトウアンドデプレッション (台地と盆地) は両端に共通の異なる数字を持つクワージレプディジットです。

Quasi-repdigit クワージレプディジット (Quasi-repdigit)

Quasi-repdigit is a natural number in which only two digits of a repdigit were replaced with other digits. クワージレプディジットはレプディジットの数字を 2 個だけ他の数字に置き換えた自然数です。

Near-repdigit-palindrome ニアレプディジット回文数 (Near-repdigit-palindrome)

Near-repdigit-palindrome is a near-repdigit and a palindrome. Its length is odd number and only one digit in the middle is different from others. 桁数が奇数で中央の桁の数字だけが異なるニアレプディジットがニアレプディジット回文数です。

2. News ニュース

April 22, 2024 2024 年 4 月 22 日

Predrag Kurtovic found two k*10^n+1 form prime numbers. Predrag Kurtovicさんがk*10^n+1の形の素数を2個見つけました。

k*10^n+1 form (probable) prime numbers
rankdigitsflabel_nwlabel[:v]:wwclass(probable) prime numberstatust5kcomment
8862,86990001_86286890w1:862867n2 p19×10862,868 + 1prid=137993Predrag Kurtovic / Srsieve, Prime95, LLR / Apr 22, 2024
10823,03890001_82303790w1:823036n2 p19×10823,037 + 1prid=137992Predrag Kurtovic / Srsieve, Prime95, LLR / Apr 22, 2024

April 18, 2024 2024 年 4 月 18 日

Predrag Kurtovic found a k*10^n+1 form prime number. Predrag Kurtovicさんがk*10^n+1の形の素数を見つけました。

k*10^n+1 form (probable) prime numbers
rankdigitsflabel_nwlabel[:v]:wwclass(probable) prime numberstatust5kcomment
11719,05690001_71905590w1:719054n2 p19×10719,055 + 1prid=137983Predrag Kurtovic / Srsieve, Prime95, LLR / Apr 18, 2024

April 11, 2024 2024 年 4 月 11 日

Tyler Busby found 17 k*10^n-1 form prime numbers, 11 k*10^n+1 form prime numbers, 8 10^n-k form probable prime numbers, 12 near-near-repdigit(quasi-repdigit) probable prime numbers and 200 near-near-near-repdigit (probable) prime numbers. Tyler Busbyさんが 17個のk*10^n-1の形の素数、 11個のk*10^n+1の形の素数、 8個の10^n-kの形のおそらく素数、 12個のニアニアレプディジット(クワージレプディジット)のおそらく素数および 200個のニアニアニアレプディジットのおそらく素数を見つけました。

k*10^n-1 form (probable) prime numbers
rankdigitsflabel_nwlabel[:v]:wwclass(probable) prime numberstatust5kcomment
41446,2081889w:46205n3 m1189×1046,205 − 1prTyler Busby / Apr 11, 2024
45743,40899999979w:43401nr m19,999,998×1043,401 − 1prTyler Busby / Apr 11, 2024
48741,94199999949w:41934nr m19,999,995×1041,934 − 1prTyler Busby / Apr 11, 2024
54339,2031889w:39200n3 m1189×1039,200 − 1prTyler Busby / Apr 11, 2024
64934,5294992379w:34523m1499,238×1034,523 − 1prTyler Busby / Apr 11, 2024
82927,6621889w:27659n3 m1189×1027,659 − 1prTyler Busby / Apr 11, 2024
92525,0451889w:25042n3 m1189×1025,042 − 1prTyler Busby / Apr 11, 2024
108520,5281889w:20525n3 m1189×1020,525 − 1prTyler Busby / Apr 11, 2024
131915,3791889w:15376n3 m1189×1015,376 − 1prTyler Busby / Apr 11, 2024
132315,3231889w:15320n3 m1189×1015,320 − 1prTyler Busby / Apr 11, 2024
138914,1684992379w:14162m1499,238×1014,162 − 1prTyler Busby / Apr 11, 2024
148412,9671889w:12964n3 m1189×1012,964 − 1prTyler Busby / Apr 11, 2024
157711,6441889w:11641n3 m1189×1011,641 − 1prTyler Busby / Apr 11, 2024
158811,4531889w:11450n3 m1189×1011,450 − 1prTyler Busby / Apr 11, 2024
165510,7284992379w:10722m1499,238×1010,722 − 1prTyler Busby / Apr 11, 2024
17589,3864992379w:9380m1499,238×109,380 − 1prTyler Busby / Apr 11, 2024
20007,1634992379w:7157m1499,238×107,157 − 1prTyler Busby / Apr 11, 2024
k*10^n+1 form (probable) prime numbers
rankdigitsflabel_nwlabel[:v]:wwclass(probable) prime numberstatust5kcomment
13948,5683630w1:48564p1363×1048,565 + 1prTyler Busby / Apr 11, 2024
14248,3633169030w1:48356p1316,903×1048,357 + 1prTyler Busby / Apr 11, 2024
15245,2712077770w1:45264p1207,777×1045,265 + 1prTyler Busby / Apr 11, 2024
15544,252980350w1:44246p198,035×1044,247 + 1prTyler Busby / Apr 11, 2024
16541,87821610w1:41873p12,161×1041,874 + 1prTyler Busby / Apr 11, 2024
16840,99721610w1:40992p12,161×1040,993 + 1prTyler Busby / Apr 11, 2024
18635,964880w1:35961n3 p188×1035,962 + 1prTyler Busby / Apr 11, 2024
22722,4243169030w1:22417p1316,903×1022,418 + 1prTyler Busby / Apr 11, 2024
22922,1353169030w1:22128p1316,903×1022,129 + 1prTyler Busby / Apr 11, 2024
25019,2833169030w1:19276p1316,903×1019,277 + 1prTyler Busby / Apr 11, 2024
31611,0983169030w1:11091p1316,903×1011,092 + 1prTyler Busby / Apr 11, 2024
10^n-k form (probable) prime numbers
rankdigitsflabel_nwlabel[:v]:wwclass(probable) prime numberstatust5kcomment
9946,8479w5999:46843nr mk1046,847 − 4,001Tyler Busby / Apr 11, 2024
10146,0019w5999:45997nr mk1046,001 − 4,001Tyler Busby / Apr 11, 2024
10941,1409w7999:41136nr mk1041,140 − 2,001Tyler Busby / Apr 11, 2024
11040,9279w19999:40922nr mk1040,927 − 80,001Tyler Busby / Apr 11, 2024
11937,4789w7999999999:37468nr mk1037,478 − 2,000,000,001Tyler Busby / Apr 11, 2024
12237,0139w7999999:37006nr mk1037,013 − 2,000,001Tyler Busby / Apr 11, 2024
13633,5659w799:33562nr mk1033,565 − 201Tyler Busby / Apr 11, 2024
14031,9769w7999:31972nr mk1031,976 − 2,001Tyler Busby / Apr 11, 2024
Near-near-repdigit(quasi-repdigit) (probable) prime numbers
rankdigitsflabel_nwlabel[:v]:wwclass(probable) prime numberstatust5kcomment
113749,251883w:49249n2265×1049,249 − 13Tyler Busby / Apr 11, 2024
126245,45833379_454583w79:45456n21045,458 + 1373Tyler Busby / Apr 11, 2024
126345,4534w99:45451n24×1045,453 + 4919Tyler Busby / Apr 11, 2024
129544,243443w:44241n2133×1044,241 − 13Tyler Busby / Apr 11, 2024
130643,791223w:43789n267×1043,789 − 13Tyler Busby / Apr 11, 2024
139542,0855w33:42083n25×1042,085 − 2039Tyler Busby / Apr 11, 2024
148139,509771w:39507n2694×1039,507 − 19Tyler Busby / Apr 11, 2024
159936,4332w99:36431n22×1036,433 + 6919Tyler Busby / Apr 11, 2024
161036,1375w11:36135n25×1036,137 − 4019Tyler Busby / Apr 11, 2024
164535,291441w:35289n2397×1035,289 − 19Tyler Busby / Apr 11, 2024
178532,425667w:32423n2601×1032,423 − 79Tyler Busby / Apr 11, 2024
187330,5537w99:30551n27×1030,553 + 1919Tyler Busby / Apr 11, 2024
Near-near-near-repdigit (probable) prime numbers
rankdigitsflabel_nwlabel[:v]:wwclass(probable) prime numberstatust5kcomment
233049,87962w11:49876n356×1049,878 − 1019Tyler Busby / Apr 11, 2024
233449,83334w11:49830n331×1049,832 − 3019Tyler Busby / Apr 11, 2024
233849,68134w33:49678n331×1049,680 − 1039Tyler Busby / Apr 11, 2024
236849,09435w99:49091n332×1049,093 + 3919Tyler Busby / Apr 11, 2024
237648,995774w3:48992n3697×1048,993 − 139Tyler Busby / Apr 11, 2024
238548,85485w77:48851n377×1048,853 + 1939Tyler Busby / Apr 11, 2024
238648,843885w7:48840n3797×1048,841 + 139Tyler Busby / Apr 11, 2024
239248,76281w77:48759n373×1048,761 + 5939Tyler Busby / Apr 11, 2024
239748,61552w99:48612n347×1048,614 + 6919Tyler Busby / Apr 11, 2024
240148,54081w99:48537n373×1048,539 + 7919Tyler Busby / Apr 11, 2024
241248,370775w3:48367n3698×1048,368 − 239Tyler Busby / Apr 11, 2024
243448,06387w11:48060n379×1048,062 − 6019Tyler Busby / Apr 11, 2024
243548,05183w77:48048n325×1048,050 + 1313Tyler Busby / Apr 11, 2024
244147,98219w33:47979n32×1047,981 − 67Tyler Busby / Apr 11, 2024
245147,82768w77:47824n362×1047,826 − 1079Tyler Busby / Apr 11, 2024
245547,76917w99:47766n316×1047,768 + 1919Tyler Busby / Apr 11, 2024
246947,589337w1:47586n3304×1047,587 − 619Tyler Busby / Apr 11, 2024
247247,57262w33:47569n356×1047,571 + 979Tyler Busby / Apr 11, 2024
248247,334881w9:47331n3793×1047,332 + 719Tyler Busby / Apr 11, 2024
248947,239661w9:47236n3595×1047,237 + 719Tyler Busby / Apr 11, 2024
250347,10881w33:47105n373×1047,107 + 1979Tyler Busby / Apr 11, 2024
251446,98390w77:46980n39×1046,982 + 77Tyler Busby / Apr 11, 2024
252146,87231w77:46869n328×1046,871 + 5939Tyler Busby / Apr 11, 2024
253446,755559w1:46752n356×1046,753 − 9Tyler Busby / Apr 11, 2024
253946,58648w99:46583n344×1046,585 + 919Tyler Busby / Apr 11, 2024
254446,53385w77:46530n377×1046,532 + 1939Tyler Busby / Apr 11, 2024
255346,473771w3:46470n3694×1046,471 + 179Tyler Busby / Apr 11, 2024
255646,43631w33:46433n328×1046,435 + 1979Tyler Busby / Apr 11, 2024
255946,418665w3:46415n3599×1046,416 − 239Tyler Busby / Apr 11, 2024
257146,24841w99:46245n337×1046,247 + 7919Tyler Busby / Apr 11, 2024
258146,11534w77:46112n331×1046,114 + 2939Tyler Busby / Apr 11, 2024
259146,013554w1:46010n3499×1046,011 − 319Tyler Busby / Apr 11, 2024
259345,91935w99:45916n332×1045,918 + 3919Tyler Busby / Apr 11, 2024
260945,677662w9:45674n3596×1045,675 + 619Tyler Busby / Apr 11, 2024
262545,502334w9:45499n3301×1045,500 + 419Tyler Busby / Apr 11, 2024
264045,28767w99:45284n361×1045,286 + 1919Tyler Busby / Apr 11, 2024
265045,16572w33:45162n365×1045,164 + 979Tyler Busby / Apr 11, 2024
265645,03742w77:45034n338×1045,036 + 4939Tyler Busby / Apr 11, 2024
265845,006775w9:45003n3698×1045,004 + 319Tyler Busby / Apr 11, 2024
266144,99025w11:44987n323×1044,989 − 4019Tyler Busby / Apr 11, 2024
269744,43857w99:44435n352×1044,437 + 1919Tyler Busby / Apr 11, 2024
270344,40324w33:44400n322×1044,402 − 1039Tyler Busby / Apr 11, 2024
270444,394227w1:44391n3205×1044,392 − 619Tyler Busby / Apr 11, 2024
271544,277447w9:44274n3403×1044,275 + 119Tyler Busby / Apr 11, 2024
271644,27348w99:44270n344×1044,272 + 919Tyler Busby / Apr 11, 2024
272144,229662w7:44226n3596×1044,227 + 439Tyler Busby / Apr 11, 2024
274743,969772w7:43966n3695×1043,967 + 439Tyler Busby / Apr 11, 2024
275243,938551w3:43935n3496×1043,936 + 179Tyler Busby / Apr 11, 2024
276043,83278w11:43829n371×1043,831 − 7019Tyler Busby / Apr 11, 2024
276443,79891w33:43795n382×1043,797 + 1979Tyler Busby / Apr 11, 2024
276643,74295w33:43739n386×1043,741 − 2039Tyler Busby / Apr 11, 2024
278043,41438w33:43411n335×1043,413 − 5039Tyler Busby / Apr 11, 2024
279543,192665w3:43189n3599×1043,190 − 239Tyler Busby / Apr 11, 2024
282242,97225w11:42969n323×1042,971 − 4019Tyler Busby / Apr 11, 2024
282342,958992w9:42955n3893×1042,956 + 619Tyler Busby / Apr 11, 2024
282942,905442w7:42902n3398×1042,903 + 439Tyler Busby / Apr 11, 2024
283942,75727w11:42754n325×1042,756 − 6019Tyler Busby / Apr 11, 2024
284042,753778w3:42750n3701×1042,751 − 539Tyler Busby / Apr 11, 2024
285142,579882w7:42576n3794×1042,577 + 439Tyler Busby / Apr 11, 2024
285342,559774w1:42556n3697×1042,557 − 319Tyler Busby / Apr 11, 2024
285542,528669w7:42525n367×1042,526 − 3Tyler Busby / Apr 11, 2024
285942,45991w77:42456n382×1042,458 + 5939Tyler Busby / Apr 11, 2024
286942,32658w77:42323n353×1042,325 − 1079Tyler Busby / Apr 11, 2024
289242,11485w11:42111n377×1042,113 − 4019Tyler Busby / Apr 11, 2024
290941,931662w1:41928n3596×1041,929 − 119Tyler Busby / Apr 11, 2024
291041,916442w9:41913n3398×1041,914 + 619Tyler Busby / Apr 11, 2024
291141,91361w77:41910n355×1041,912 + 5939Tyler Busby / Apr 11, 2024
291941,78658w77:41783n353×1041,785 − 1079Tyler Busby / Apr 11, 2024
292241,705882w9:41702n3794×1041,703 + 619Tyler Busby / Apr 11, 2024
294341,425445w9:41422n3401×1041,423 + 319Tyler Busby / Apr 11, 2024
295141,32014w33:41317n313×1041,319 − 1039Tyler Busby / Apr 11, 2024
296341,150114w1:41147n3103×1041,148 − 319Tyler Busby / Apr 11, 2024
298340,901557w1:40898n3502×1040,899 − 619Tyler Busby / Apr 11, 2024
300440,58692w33:40583n383×1040,585 + 979Tyler Busby / Apr 11, 2024
301040,54114w11:40538n313×1040,540 − 3019Tyler Busby / Apr 11, 2024
302540,34149w33:40338n35×1040,340 − 67Tyler Busby / Apr 11, 2024
304840,04891w33:40045n382×1040,047 + 1979Tyler Busby / Apr 11, 2024
309939,43362w33:39430n356×1039,432 + 979Tyler Busby / Apr 11, 2024
310639,38132w11:39378n329×1039,380 − 1019Tyler Busby / Apr 11, 2024
310739,376334w9:39373n3301×1039,374 + 419Tyler Busby / Apr 11, 2024
310939,343442w7:39340n3398×1039,341 + 439Tyler Busby / Apr 11, 2024
311539,31556w99:39312n317×1039,314 + 973Tyler Busby / Apr 11, 2024
312539,203884w7:39200n3796×1039,201 + 239Tyler Busby / Apr 11, 2024
312739,198884w7:39195n3796×1039,196 + 239Tyler Busby / Apr 11, 2024
316438,731442w7:38728n3398×1038,729 + 439Tyler Busby / Apr 11, 2024
317538,622882w7:38619n3794×1038,620 + 439Tyler Busby / Apr 11, 2024
318138,570669w7:38567n367×1038,568 − 3Tyler Busby / Apr 11, 2024
320438,32864w11:38325n358×1038,327 − 3019Tyler Busby / Apr 11, 2024
321838,15126w77:38148n38×1038,150 + 313Tyler Busby / Apr 11, 2024
321938,13554w33:38132n349×1038,134 − 1039Tyler Busby / Apr 11, 2024
323937,895771w3:37892n3694×1037,893 + 179Tyler Busby / Apr 11, 2024
324037,89512w11:37892n311×1037,894 − 1019Tyler Busby / Apr 11, 2024
325037,76518w77:37762n317×1037,764 − 1079Tyler Busby / Apr 11, 2024
325137,73052w11:37727n347×1037,729 − 1019Tyler Busby / Apr 11, 2024
325537,64261w33:37639n355×1037,641 + 1979Tyler Busby / Apr 11, 2024
325837,60532w11:37602n329×1037,604 − 1019Tyler Busby / Apr 11, 2024
326437,55286w99:37549n326×1037,551 + 973Tyler Busby / Apr 11, 2024
328237,352332w3:37349n3299×1037,350 + 79Tyler Busby / Apr 11, 2024
328437,308225w9:37305n3203×1037,306 + 319Tyler Busby / Apr 11, 2024
328737,265664w9:37262n3598×1037,263 + 419Tyler Busby / Apr 11, 2024
329837,157994w3:37154n3895×1037,155 − 139Tyler Busby / Apr 11, 2024
330537,04252w33:37039n347×1037,041 + 979Tyler Busby / Apr 11, 2024
330637,032225w1:37029n3203×1037,030 − 419Tyler Busby / Apr 11, 2024
331136,947221w7:36944n3199×1036,945 + 539Tyler Busby / Apr 11, 2024
331836,825117w3:36822n3106×1036,823 − 439Tyler Busby / Apr 11, 2024
332336,755770w9:36752n377×1036,753 + 9Tyler Busby / Apr 11, 2024
334036,581557w1:36578n3502×1036,579 − 619Tyler Busby / Apr 11, 2024
334236,52887w11:36525n379×1036,527 − 6019Tyler Busby / Apr 11, 2024
334536,503775w1:36500n3698×1036,501 − 419Tyler Busby / Apr 11, 2024
334836,48245w99:36479n341×1036,481 + 3919Tyler Busby / Apr 11, 2024
336436,33620w99:36333n32×1036,335 + 99Tyler Busby / Apr 11, 2024
336836,309442w9:36306n3398×1036,307 + 619Tyler Busby / Apr 11, 2024
337736,23783w77:36234n325×1036,236 + 1313Tyler Busby / Apr 11, 2024
338636,152771w9:36149n3694×1036,150 + 719Tyler Busby / Apr 11, 2024
338936,10787w99:36104n379×1036,106 + 1919Tyler Busby / Apr 11, 2024
339136,10147w11:36098n343×1036,100 − 6019Tyler Busby / Apr 11, 2024
340735,943998w1:35940n3899×1035,941 − 719Tyler Busby / Apr 11, 2024
340835,934994w7:35931n3895×1035,932 + 239Tyler Busby / Apr 11, 2024
341035,89641w33:35893n337×1035,895 + 1979Tyler Busby / Apr 11, 2024
341235,846667w3:35843n3601×1035,844 − 439Tyler Busby / Apr 11, 2024
344535,48214w11:35479n313×1035,481 − 3019Tyler Busby / Apr 11, 2024
344635,477885w9:35474n3797×1035,475 + 319Tyler Busby / Apr 11, 2024
345035,45052w11:35447n347×1035,449 − 1019Tyler Busby / Apr 11, 2024
345535,397115w3:35394n3104×1035,395 − 239Tyler Busby / Apr 11, 2024
346135,36045w99:35357n341×1035,359 + 3919Tyler Busby / Apr 11, 2024
347035,26557w99:35262n352×1035,264 + 1919Tyler Busby / Apr 11, 2024
347535,21018w11:35207n317×1035,209 − 7019Tyler Busby / Apr 11, 2024
348035,17641w77:35173n337×1035,175 + 5939Tyler Busby / Apr 11, 2024
348235,154775w3:35151n3698×1035,152 − 239Tyler Busby / Apr 11, 2024
348335,15459w33:35151n36×1035,153 − 67Tyler Busby / Apr 11, 2024
349035,068661w9:35065n3595×1035,066 + 719Tyler Busby / Apr 11, 2024
349135,06848w77:35065n344×1035,067 − 1079Tyler Busby / Apr 11, 2024
350534,88535w99:34882n332×1034,884 + 3919Tyler Busby / Apr 11, 2024
350734,86148w11:34858n344×1034,860 − 7019Tyler Busby / Apr 11, 2024
351534,778551w7:34775n3496×1034,776 + 539Tyler Busby / Apr 11, 2024
351734,75731w77:34754n328×1034,756 + 5939Tyler Busby / Apr 11, 2024
351834,75359w11:34750n36×1034,752 − 89Tyler Busby / Apr 11, 2024
352334,733662w9:34730n3596×1034,731 + 619Tyler Busby / Apr 11, 2024
354834,430669w7:34427n367×1034,428 − 3Tyler Busby / Apr 11, 2024
354934,429448w1:34426n3404×1034,427 − 719Tyler Busby / Apr 11, 2024
355034,40591w33:34402n382×1034,404 + 1979Tyler Busby / Apr 11, 2024
355134,33614w99:34333n313×1034,335 + 4919Tyler Busby / Apr 11, 2024
356634,15431w77:34151n328×1034,153 + 5939Tyler Busby / Apr 11, 2024
358133,977998w1:33974n3899×1033,975 − 719Tyler Busby / Apr 11, 2024
358233,96028w11:33957n326×1033,959 − 7019Tyler Busby / Apr 11, 2024
358833,92724w11:33924n322×1033,926 − 3019Tyler Busby / Apr 11, 2024
359533,892992w9:33889n3893×1033,890 + 619Tyler Busby / Apr 11, 2024
361333,734667w3:33731n3601×1033,732 − 439Tyler Busby / Apr 11, 2024
362333,650117w1:33647n3106×1033,648 − 619Tyler Busby / Apr 11, 2024
362633,58581w77:33582n373×1033,584 + 5939Tyler Busby / Apr 11, 2024
363233,475887w3:33472n3799×1033,473 − 439Tyler Busby / Apr 11, 2024
363533,465225w9:33462n3203×1033,463 + 319Tyler Busby / Apr 11, 2024
363633,456669w7:33453n367×1033,454 − 3Tyler Busby / Apr 11, 2024
363833,454338w3:33451n3305×1033,452 − 539Tyler Busby / Apr 11, 2024
364333,41865w11:33415n359×1033,417 − 4019Tyler Busby / Apr 11, 2024
365933,270224w9:33267n3202×1033,268 + 419Tyler Busby / Apr 11, 2024
367433,12474w33:33121n367×1033,123 − 1039Tyler Busby / Apr 11, 2024
368133,02563w11:33022n319×1033,024 − 673Tyler Busby / Apr 11, 2024
370532,85057w99:32847n352×1032,849 + 1919Tyler Busby / Apr 11, 2024
371132,774998w3:32771n3899×1032,772 − 539Tyler Busby / Apr 11, 2024
371832,698664w9:32695n3598×1032,696 + 419Tyler Busby / Apr 11, 2024
372232,654558w3:32651n3503×1032,652 − 539Tyler Busby / Apr 11, 2024
373432,568115w3:32565n3104×1032,566 − 239Tyler Busby / Apr 11, 2024
374332,43878w77:32435n371×1032,437 − 1079Tyler Busby / Apr 11, 2024
374832,372775w1:32369n3698×1032,370 − 419Tyler Busby / Apr 11, 2024
375032,359552w7:32356n3497×1032,357 + 439Tyler Busby / Apr 11, 2024
376032,274445w3:32271n3401×1032,272 − 239Tyler Busby / Apr 11, 2024
377632,09978w33:32096n371×1032,098 − 5039Tyler Busby / Apr 11, 2024
378232,032775w7:32029n3698×1032,030 + 139Tyler Busby / Apr 11, 2024
378532,00931w33:32006n328×1032,008 + 1979Tyler Busby / Apr 11, 2024
380331,828227w3:31825n3205×1031,826 − 439Tyler Busby / Apr 11, 2024
382131,638881w3:31635n3793×1031,636 + 179Tyler Busby / Apr 11, 2024
382331,620445w9:31617n3401×1031,618 + 319Tyler Busby / Apr 11, 2024
382731,607556w3:31604n3167×1031,605 − 113Tyler Busby / Apr 11, 2024
382831,59964w77:31596n358×1031,598 + 2939Tyler Busby / Apr 11, 2024
383131,563881w3:31560n3793×1031,561 + 179Tyler Busby / Apr 11, 2024
383431,54349w33:31540n35×1031,542 − 67Tyler Busby / Apr 11, 2024
383731,50492w99:31501n383×1031,503 + 6919Tyler Busby / Apr 11, 2024
384931,45131w77:31448n328×1031,450 + 5939Tyler Busby / Apr 11, 2024
385631,370552w9:31367n3497×1031,368 + 619Tyler Busby / Apr 11, 2024
386531,29382w11:31290n374×1031,292 − 1019Tyler Busby / Apr 11, 2024
388531,11562w33:31112n356×1031,114 + 979Tyler Busby / Apr 11, 2024
388631,11184w11:31108n376×1031,110 − 3019Tyler Busby / Apr 11, 2024
388731,099442w1:31096n3398×1031,097 − 119Tyler Busby / Apr 11, 2024
388831,092220w9:31089n322×1031,090 + 9Tyler Busby / Apr 11, 2024
389831,00459w11:31001n36×1031,003 − 89Tyler Busby / Apr 11, 2024
390031,00039w77:30997n34×1030,999 − 23Tyler Busby / Apr 11, 2024
390630,96190w77:30958n39×1030,960 + 77Tyler Busby / Apr 11, 2024
391130,94980w33:30946n38×1030,948 + 33Tyler Busby / Apr 11, 2024
391530,920554w7:30917n3499×1030,918 + 239Tyler Busby / Apr 11, 2024
392330,78492w99:30781n383×1030,783 + 6919Tyler Busby / Apr 11, 2024
396730,477228w3:30474n3206×1030,475 − 539Tyler Busby / Apr 11, 2024
397830,407775w7:30404n3698×1030,405 + 139Tyler Busby / Apr 11, 2024
397930,407551w7:30404n3496×1030,405 + 539Tyler Busby / Apr 11, 2024
398130,39215w99:30389n314×1030,391 + 3919Tyler Busby / Apr 11, 2024
398930,35687w33:30353n379×1030,355 − 4039Tyler Busby / Apr 11, 2024
399930,27851w99:30275n346×1030,277 + 7919Tyler Busby / Apr 11, 2024
400030,25742w33:30254n338×1030,256 + 979Tyler Busby / Apr 11, 2024
400430,220442w9:30217n3398×1030,218 + 619Tyler Busby / Apr 11, 2024
401430,107442w7:30104n3398×1030,105 + 439Tyler Busby / Apr 11, 2024

Past news 過去のニュース

3. Reserved numbers and submitted numbers 予約されている数と投稿された数

4. Composite numbers that are hoped to be factored 分解が期待される合成数

5. How to contribute your prime factors 素因数の投稿の仕方

6. Contributed factorization results 投稿された素因数分解の結果

7. Graphs グラフ

8. Records 記録

9. Factor tables 素因数分解表

9.1. Repunit レピュニット (Repunit)

9.2. Near-repdigit ニアレプディジット (Near-repdigit)

9.3. Plateau-and-depression プラトウアンドデプレッション (Plateau-and-depression)

9.4. Quasi-repdigit クワージレプディジット (Quasi-repdigit)

9.5. Near-repdigit-palindrome ニアレプディジット回文数 (Near-repdigit-palindrome)

9.6. List of factor tables classified by the first digit 先頭の数字で分類した素因数分解表のリスト

10. Near-repdigit-related (probable) prime numbers ニアレプディジット関連の (おそらく) 素数

11. Primality certifications of near-repdigit-related prime numbers ニアレプディジット関連の素数の素数性証明

12. Covering set of near-repdigit-related sequences ニアレプディジット関連の数列の被覆集合

13. Appendix 付録

13.1. Primality proving program based on Pocklington's theorem ポクリントンの定理を用いた素数性証明プログラム

13.2. Expression generator of near-repdigit-related numbers ニアレプディジット関連の数の数式ジェネレータ

14. Acknowledgements 謝辞

I am thankful to contributors: 投稿してくださった皆さん、ありがとうございます: 10metreh, A.C., Agnew yoyo, Alessandro Freda, Alexander Mkrtychyan, Alfred Reich, Andreas Enge, Andreas Tete, Andy, Anonymous, Anonymouse, Anton Korobeynikov, apo, axels, Bart Jans, bbd in ep, bbmz, Ben Chaffin, Ben Meekins, Beyond, Bob Backstrom, Bob Price, Bouk de Water, Brad, Bryan Koen, btolksdorf, bundaboy, bur, Caleb Birtwistle, Carlos Pinho, ccc, Cedric Vonck, centylion torun, Chris Monico, Christopher Birkbeck, Crunchers For More Power, Crystal Butler, Crystal Pellet, Cyp, Daniel Jackson, Daniel Morel, Darren Bedwell, David Broadhurst, denjoR, Dennis Bertels, Dmitry, Dmitry Domanov, Domanov Dmitry, Dubslow, Dull Man Real Dull, Dylan Delgado, ebina, Edwin Hall, Egon Olsen, EMK2, ERBrouwer, Eric JEANCOLAS, Erik Branger, Evan Engler, Familie, Florian Baur, Florian Piesker, Fragman, Frank Schickel, Frank Villasenor, frank_0987923, FredOnCyc, Freyn, Friedhelm Baumeister, funecm, funecm2017, G.L.I.S., Gennady Stolyarov II, GRB IV, Greg, Greg Childers, Grotex, Grubix, Grzegorz Roman Granowski, Ha Seok woo, Haran, Harvey Dubner, He Jiahao, honeycrack7, Hugo Platzer, Ian, Ignacio Santos, Ivan Panchenko, ivelive, jafarism, Jamoko, Jan Ptacek, Jane Sullivan, Jarekcz, Jarod McClintock, Jason Parker-Burlingham, jdommer, Jeff Gilchrist, Jeff17, Jens, Jerzy Gieorgijewski, Jiahao He, jje1701, JMB, Jo Yeong Uk, John, John Black, Jon Becker, Jose Pascoa, Joshua2, JPascoa, Julien Peter Benney, juno1369, Justin Card, K, Maemondo, Kai Inouye, Kenichiro Yamaguchi, Kenji Ibusuki, kh9, KTakahashi, Lazarusuk, LegionMammal978, Lionel Debroux, Liuqyn, Luca Dentis, Luigi Morelli, Luminescence, M Vang, Makoto Kamada, Makso, Maksym Voznyy, MarcinGorecki, Markus Tervooren, Marlon Trifunovic, Masaki UKAI, Mathew, matsui, Max Dettweiler, Meharts, mia7077, Michael Peterson, Michael Rao, MicroKraken, mikkovi, Mitchell, Mitchell Dickerman, Morel Daniel, Mr. Hankey, Mr. Ice, msc_nbg, Naoki Yamamoto, Nechaev Sergey, nenym, NFS@Home, NFS@Home Greg Childers, NFS@Home/Serge Batalov, NFSathome, Nicolai Caraibendko, nisba, Nitro, Norbert Schneider, Norman D Powell, Norman Powell, Normsn Powell, NyanCat, NyanCatTW1, Oliver Kruse, Ordi, Patrick Keller, Paul Underwood, Pawel Apostol, Phil, Phil Carmody, Philippe Strohl, Pierre Jammes, Pipao, Polybius, processing-home, pschoefer, Raffi Chaglassian, Ray Chandler, RAZIELakaALIN, Rich Dickerson, Rich Smith, Richard G., RichD, rkillian, Roald, Robert Backstrom, Robert Balfour, Robert Gelhar, RobertS, Rocke Verser, Roman, RSALS, ruffenach timothee, Rytis Slatkevicius, Samuel Chong, Sander Hoogendoorn, SBS, Schildkroete, Scott O, Sean A. Irvine, Sean Wellman, Serge Batalov, Seth Troisi, Shaopu Lin, shauge, shima@engei, shun, Shusuke Kubota, shyguy7129, Sinkiti Sibata, skneo, Sonic@Planet 3DNow!, Stargate38, Stefan Straleger, steinrar, stelf, Steph Lady, suberi, SuikaPredator, Syj, Taiyo Kodama, Takahiro Nohara, Tapio Rajala, TeamFUN, Ted Burton, Tetsuya Kobayashi, Thomas Womack, Thomas Womack for NFS@home, Tom Li, Tomoya Adachi, toms83, ToolboxNL, tor, transtec-AG, Tyler Cadigan, UA_ReMMeR, vanos0512, Victor de Hollander, VictordeHollander, Vladimir, Warut Roonguthai, Wataru Sakai, Wojciech Florek, Yang Hae Hun, yas mat, Yoichi Hanatani, yoshida, Youcef L, Youcef Lemsafer, yoyo, yoyo@Home, Zeta-Flux, zlodeck, [AF>Amis des Lapins] Nabz37, [AF>France] intello222222, [AF>HFR>RR] julien76100, [AF>Le_Pommier>MacADSL.com]Bertrand, [AF>Le_Pommier>MacBidouille.com]m.o.u.s.t.i.c, [boinc.at] Fireman69, [GPU Force] Robert 7NBI, [P3D] Crashtest, [SG-FC] hl, [SG]marodeur6, [TiDC] Chulma, [XTBA>TSA] IvanleFou and [XTBA>TSA]+IvanleFou.

15. Links related to near-repdigit ニアレプディジットの関連リンク