since 21 January 1999 | - 20,000 |
(These results are updating so frequently. Please check every day.)
(To avoid duplication, please check above numbers.)
2012, 2011, 2010, 2009, 2008, 2007, 2006, 2005, 2004, 2003, 2002, 2001, 2000, 1999
φ(n) | n | Cunningham form | last update | unfactored | who are factoring |
---|---|---|---|---|---|
60 | 61 | x61- 1 | Sep. 17, 2012 | Complete !!! | Katsuyuki Okeya, Andy Steward, Masaki Ukai (last number) |
77 | x77- 1 | Mar. 23, 2013 | Complete !!! | Aiichi Yamasaki, Katsuyuki Okeya, Joe Leherbauer, Takahiro Nohara, Tomoya Adachi, Masaki Ukai (last number) | |
93 | x93- 1 | May. 11, 2013 | 118 | Aiichi Yamasaki, Katsuyuki Okeya, Joe Leherbauer, Takahiro Nohara, Tomoya Adachi, Masaki Ukai | |
99 | x99- 1 | Nov. 27, 2012 | Complete !!! | Aiichi Yamasaki, Katsuyuki Okeya, Joe Leherbauer, Takahiro Nohara, Tomoya Adachi (last number) | |
122 | x61+ 1 | Aug. 16, 2012 | Complete !!! | Katsuyuki Okeya, Joe Leherbauer, Takahiro Nohara, Tomoya Adachi (last number) | |
124 | x62+ 1 | Jun. 24, 2012 | Complete !!! | Aiichi Yamasaki, Katsuyuki Okeya, Tomoya Adachi (last number) | |
154 | x77+ 1 | Dec. 13, 2011 | Complete !!! | Aiichi Yamasaki, Hisanori Mishima, Takahiro Nohara, Tomoya Adachi (last number) | |
186 | x93+ 1 | Jul. 25, 2009 | Complete !!! | Aiichi Yamasaki, Hisanori Mishima, Joe Leherbauer, Tomoya Adachi (last number) | |
198 | x99+ 1 | Sep. 15, 2008 | Complete !!! | Aiichi Yamasaki, Hisanori Mishima, Joe Leherbauer, Tomoya Adachi (last number) | |
64 | 85 | x85- 1 | Nov. 27, 2012 | 284 | Tetsuya Kobayashi, Hisanori Mishima |
128 | x64+ 1 | Oct. 09, 2010 | Complete !!! | David A. Miller, Tetsuya Kobayashi, Joe Leherbauer, Hisanori Mishima, Tomoya Adachi (last number) | |
136 | x68+ 1 | Jul. 17, 2012 | 333 | Tetsuya Kobayashi, Hisanori Mishima | |
160 | x80+ 1 | Mar. 04, 2013 | 136 | Tetsuya Kobayashi, Takahiro Nohara | |
170 | x85+ 1 | Jul. 17, 2012 | 362 | Tetsuya Kobayashi, Satoshi Tomabechi, Hisanori Mishima | |
192 | x96+ 1 | Sep. 17, 2012 | 361 | Tetsuya Kobayashi, David A. Miller | |
204 | x102+ 1 | Sep. 17, 2012 | 352 | Tetsuya Kobayashi, Satoshi Tomabechi, Joe Leherbauer, Hisanori Mishima, Tomoya Adachi | |
240 | x120+ 1 | Sep. 17, 2012 | 338 | Tetsuya Kobayashi, Joe Leherbauer, Hisanori Mishima, Tomoya Adachi | |
66 | 67 | x67- 1 | Jan. 29, 2013 | 342 | Sinkiti Sibata, Sean Irvine, Hisanori Mishima, Tomoya Adachi |
134 | x67+ 1 | Sep. 17, 2012 | 381 | Tetsuya Kobayashi, Joe Leherbauer, Hisanori Mishima, Tomoya Adachi | |
70 | 71 | x71- 1 | Dec. 27, 2012 | 395 | Tetsuya Kobayashi, Masaki Ukai, Andy Steward, Sean Irvine, Tomoya Adachi |
142 | x71+ 1 | May 07, 2012 | 310 | Tetsuya Kobayashi, Tomoya Adachi |
φ(n) | n | Cunningham form | last update | unfactored | who's factoring |
---|---|---|---|---|---|
72 | 73 | x73- 1 | Jan. 31, 2013 | 320 | |
91 | x91- 1 | Sep. 17, 2012 | 452 | ||
95 | x95- 1 | Sep. 17, 2012 | 439 | ||
111 | x111- 1 | Sep. 17, 2012 | 394 | ||
117 | x117- 1 | Sep. 17, 2012 | 402 | ||
135 | x135- 1 | Apr. 17, 2013 | 441 | ||
146 | x73+ 1 | Sep. 17, 2012 | 386 | ||
148 | x74+ 1 | Sep. 17, 2012 | 473 | ||
152 | x76+ 1 | Sep. 17, 2012 | 485 | ||
182 | x91+ 1 | May 07, 2012 | 466 | ||
190 | x95+ 1 | Sep. 17, 2012 | 490 | ||
216 | x108+ 1 | Sep. 17, 2012 | 523 | ||
222 | x111+ 1 | Nov. 04, 2008 | 514 | ||
228 | x114+ 1 | Sep. 17, 2012 | 436 | ||
234 | x117+ 1 | Sep. 17, 2012 | 495 | ||
252 | x126+ 1 | Sep. 17, 2012 | 509 | ||
270 | x135+ 1 | Sep. 17, 2012 | 520 | ||
78 | 79 | x79- 1 | Sep. 17, 2012 | 520 | |
158 | x79+ 1 | Sep. 17, 2012 | 552 | ||
80 | 123 | x123- 1 | Sep. 17, 2012 | 577 | |
164 | x82+ 1 | Nov. 23, 2011 | 543 | ||
165 | x165- 1 | Nov. 23, 2011 | 502 | ||
176 | x88+ 1 | Sep. 17, 2012 | 517 | ||
200 | x100+ 1 | Sep. 17, 2012 | 587 | ||
220 | x110+ 1 | Sep. 17, 2012 | 531 | ||
246 | x123+ 1 | Nov. 23, 2011 | 548 | ||
264 | x132+ 1 | May 07, 2012 | 583 | ||
300 | x150+ 1 | Sep. 17, 2012 | 561 | ||
330 | x165+ 1 | Nov. 23, 2011 | 576 |
φ(n) | n | Cunningham form | last update | unfactored | who's factoring |
---|---|---|---|---|---|
82 | 83 | x83- 1 | Jan. 07, 2013 | 479 | |
166 | x83+ 1 | Sep. 17, 2012 | 539 | ||
84 | 129 | x129- 1 | May 11, 2013 | 588 | |
147 | x147- 1 | May 11, 2013 | 565 | ||
172 | x86+ 1 | May 11, 2013 | 534 | ||
196 | x98+ 1 | May 11, 2013 | 558 | ||
258 | x129+ 1 | May 11, 2013 | 570 | ||
294 | x147+ 1 | May 11, 2013 | 612 | ||
88 | 89 | x89- 1 | Aug. 09, 2012 | 612 | |
115 | x115- 1 | Dec. 27, 2012 | 674 | ||
178 | x89+ 1 | Sep. 17, 2012 | 647 | ||
184 | x92+ 1 | Nov. 23, 2011 | 621 | ||
230 | x115+ 1 | Nov. 23, 2011 | 677 | ||
276 | x138+ 1 | Nov. 23, 2011 | 637 | ||
92 | 141 | x141- 1 | Nov. 23, 2011 | 615 | |
188 | x94+ 1 | Nov. 23, 2011 | 617 | ||
282 | x141+ 1 | Nov. 23, 2011 | 638 | ||
96 | 97 | x97- 1 | May 16, 2013 | 634 | |
119 | x119- 1 | Dec. 27, 2012 | 631 | ||
153 | x153- 1 | Nov. 23, 2011 | 638 | ||
194 | x97+ 1 | Jul. 04, 2011 | 630 | ||
195 | x195- 1 | Nov. 17, 2008 | 655 | ||
208 | x104+ 1 | Nov. 23, 2011 | 646 | ||
224 | x112+ 1 | Oct. 18, 2010 | 642 | ||
238 | x119+ 1 | Dec. 25, 2011 | 655 | ||
260 | x130+ 1 | Nov. 23, 2011 | 638 | ||
280 | x140+ 1 | Nov. 23, 2011 | 678 | ||
288 | x144+ 1 | Nov. 17, 2008 | 665 | ||
306 | x153+ 1 | Aug. 16, 2012 | 631 | ||
312 | x156+ 1 | May 07, 2012 | 676 | ||
336 | x168+ 1 | Nov. 23, 2011 | 680 | ||
360 | x180+ 1 | Nov. 23, 2011 | 665 | ||
390 | x195+ 1 | May 07, 2012 | 663 | ||
420 | x210+ 1 | Jun. 15, 2010 | 626 | ||
100 | 101 | x101- 1 | Feb. 04, 2013 | 609 | |
125 | x125- 1 | Dec. 27, 2012 | 631 | ||
202 | x101+ 1 | Nov. 17, 2008 | 649 | ||
250 | x125+ 1 | May 07, 2012 | 657 |
(alphabetical order of last name : 50 members are now challenging.)
No. | Name | Factoring Numbers | Program |
---|---|---|---|
1 | Richard Brent | Brent-Montgomery-te Riele tables xn +/- 1 (n=13..99) | GMP-ecm, snfs (original), ppmpqs (original) |
2 | Robert Backstrom | ||
3 | Conrad Curry | ||
4 | Nicolas Daminelli | ||
5 | Jens Franke | ||
6 | Sean Irvine | ||
7 | Joe Leherbauer | ||
8 | David A. Miller | ||
9 | Gerhard Niklasch | ||
10 | Henrik Olsen | ||
11 | Carsten Pedersen | ||
12 | Warut Roonguthai | ||
13 | Jo Yeong Uk | ||
14 | Andy Steward | Generalised Repunits (xn-1)/(x-1) n=41,43,47,49,53,61, ... up to 99 | ecm (original), ppmpqs, p-1 (original) |
15 | Tomoya Adachi | 104 | GMP-ecm, ppsiqs |
16 | Mark Belangee | 57, 63, 108, 114, 126 | MPQS (in Pari) |
17 | Marco Bodrato | 360, 420 | GMP-ecm |
18 | Tom Cage | all (from small digits) | MPQS |
19 | Greg Childers | 53, 87 | GMP-ecm, ppsiqs |
20 | Jun Eto | 92 | GMP-ecm, ppmpqs |
21 | Sander Hoogendoorn | all | GMP-ecm |
22 | Tetsuya Izu | 41, 132, 150 | ecm (GMP and original), ppmpqs, snfs |
23 | Yuji Kida | φ(n) > 46 and large digits | ecm (original), ppmpqs (original), snfs (original) |
24 | Toshifusa Kinsho | 142 | GMP-ecm, snfs |
25 | Thorsten Kleinjung | 150 | snfs |
26 | Tetsuya Kobayashi | 57, 63, 75, 150, 69, 92, 138, 94 | GMP-ecm, ppmpqs |
27 | Alexander Kruppa | 86 | mpqs4 (Jens Franke) |
28 | Shusuke Kubota | all | GMP-ecm |
29 | Hisanori Mishima | 114, 126, 100, all Table 2 by ecm | GMP-ecm, ppmpqs, snfs |
30 | Kunihiko Miyazaki | 49 | GMP-ecm, ppmpqs |
31 | Mitsuo Morimoto | φ(n) > 46 | ecm, ppmpqs, snfs |
32 | Tim Morrow | φ(165), φ(n)=100 | GMP-ecm |
33 | Souichi Murata | all | GMP-ecm |
34 | Takahiro Nohara | 69, 59 | ecm, ppmpqs, snfs |
35 | Katsuyuki Okeya | 82, 88, 75, 61, 77, 93, 122, 124 | snfs (Kida), ppmpqs |
36 | Igor Schein | all (from small digits) | MPQS (in Pari) |
37 | Frank Schickel | 83 | GMP-ecm |
38 | Sinkiti Sibata | 59, 67, 81 | GMP-ecm, snfs |
39 | Philippe Strohl | 180 | PPSIQS |
40 | Tetsuya Taniguchi | 65 | GMP-ecm |
41 | Satoshi Tomabechi | 82, 100, 49 | snfs (original), ppmpqs (original) |
42 | Yasunobu Torii | 63, 108, 126 | snfs (original) |
43 | Masaki Ukai | all by GMP-ecm | GMP-ecm, ppmpqs |
44 | Steven Whitaker | 100, 104 | ppmpqs |
45 | Thomas Wu | all (from small digits) | GMP-ecm |
46 | Aiichi Yamasaki | 57, 63, 114, 126 | ecm, ppmpqs, snfs |
47-50 | Maksym Voznyy, Lesya, Anton & Roman | 87 | GMP-ecm |
Up to φ(n) ≤ 58 are completely factored (Table 1, Table 2).
102 ≤ φ(n) ≤ 200 are not maintained here.
Please see Table 5, 6 and 7,
Tomoya Adachi's web site for 102 ≤ φ(n) ≤ 120.
and
Prof. Morimoto's web site for 102 ≤ φ(n) ≤ 200.
φ(n) | n |
---|---|
102 | 103, 206 |
104 | 159, 212, 318 |
106 | 107, 214 |
108 | 109, 133, 171, 189, 218, 266, 324, 342, 378 |
110 | 121, 242 |
112 | 113, 145, 226, 232, 290, 348 |
116 | 177, 236, 354 |
120 | 143, 155, 175, 183, 225, 231, 244, 248, 286, 308, 310, 350, 366, 372, 396 |
φ(n) | n |
---|---|
126 | 127, 254 |
128 | 255, 256, 272, 320, 340, 384, 408, 480, 510 |
130 | 131, 262 |
132 | 161, 201, 207, 268, 322, 402, 414 |
136 | 137, 274 |
138 | 139, 278 |
140 | 213, 284, 426 |
144 | 185, 219, 273, 285, 292, 296, 304, 315, 364, 370, 380, 432, 438, 444, 456, 468, 504, 540, 546, 570, 630 |
148 | 149, 298 |
150 | 139, 278 |
156 | 157, 169, 237, 314, 316, 338, 474 |
160 | 187, 205, 328, 352, 374, 400, 410, 440, 492, 528, 600, 660 |
φ(n) | n |
---|---|
162 | 163, 243, 326, 486 |
164 | 249, 332, 498 |
166 | 167, 334 |
168 | 203, 215, 245, 261, 344, 392, 406, 430, 490, 516, 522, 588 |
172 | 173, 346 |
176 | 267, 345, 356, 368, 460, 534, 552, 690 |
178 | 179, 358 |
180 | 181, 209, 217, 279, 297, 362, 418, 434, 558, 594 |
184 | 235, 376, 470, 564 |
190 | 191, 382 |
192 | 193, 221, 291, 357, 386, 388, 416, 442, 448, 476, 520, 560, 576, 582, 612, 624, 672, 714, 720, 780, 840 |
196 | 197, 394 |
198 | 199, 398 |
200 | 275, 303, 375, 404, 500, 550, 606, 750 |
Mint
Mint for Linux (588 KB) |
"Mint" is a library for computing multi-precision integer. It is consisted of header files for representing multi digits numbers and many number theoretic functions. Especially, it includes the source files of PPSIQS and PPMPQS. I'm convinced that this will help many programmers who try to write effective factoring tools. |
PPSIQSVer. 1.1 for Linux (188 KB)(Dec. 17, 2001) Ver. 1.1 for Windows (190 KB) (Nov. 09, 2001) |
PPSIQS is the double large primes procedure variation of the self-intializing quadratic sieve. In general, PPSIQS is faster than PPMPQS. Reference Scott Contini,"Factoring integers with the self-initializing quadratic sieve" ,Performance report of PPSIQS "PPSIQS Version 1.1 of Satoshi Tomabechi: Statistics for 60 Runs", By Tom Hill (January 21, 2003) |
PPMPQSVer. 2.8 for Linux (184 KB)(Dec. 17, 2001) Ver. 2.8 for Windows (185 KB) (Jul. 14, 2001) |
If there remain composite numbers up to around 100 digits, and you convince there are no factors which can be found by ECM, then you should try to use this program. The following documents are attached in the zip files. Average time of factorization using PPMPQS |
factor |
Factorization program for general numbers. It proceeds by rho (x2+1, x2-1, x2+3), p-1 and PPMPQS. Usage is same as the following programs. |
p-1 method | p-1 method |
Factorization of "aba" | Factorization of Various Numbers | Factorization of Partition Numbers |
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