2016
27 April. Added section about using hashing to obtain witness.
2015
10 June. Added historical result by David McAllister.
2014
1 August. Added remarks section (suggested by Todd Lehman).
2013
26 July. New record found: 1050535501 for bases 336781006125, 9639812373923155 by Marcin Panasiuk and Wojciech Izykowski.
27 May. New records found by Steve Worley:
885594169 for bases 725270293939359937, 3569819667048198375
350269456337 for bases 4230279247111683200, 14694767155120705706, 16641139526367750375
23 May. New records found by Steve Worley:
55245642489451 for bases 2, 141889084524735, 1199124725622454117, 11096072698276303650
7999252175582851 for bases 2, 4130806001517, 149795463772692060, 186635894390467037, 3967304179347715805
585226005592931977 for bases 2, 123635709730000, 9233062284813009, 43835965440333360, 761179012939631437, 1263739024124850375
21 May. New record found: 273919523041 for bases 15, 7363882082, 992620450144556 by Dana Jacobsen, Marcin Panasiuk, and Wojciech Izykowski.
18 May. New record found: 242175507817 for bases 15, 7363882082, 211573017068182 by Dana Jacobsen, Marcin Panasiuk, and Wojciech Izykowski.
15 May. New record found: 220146059407 for bases 15, 953185122, 158682512356199 by Dana Jacobsen, Marcin Panasiuk, and Wojciech Izykowski.
10 March. New record found: 716169301 for bases 15, 13393019396194701 by Dana Jacobsen, Marcin Panasiuk, and Wojciech Izykowski.
3 March. New record found: 341531 for base 9345883071009581737 by Steve Worley
28 February. New record found: 624732421 for bases 15, 5511855321103177 by Dana Jacobsen, Marcin Panasiuk, and Wojciech Izykowski.
23 February. New record found: 154639673381 for bases 15, 176006322, 4221622697 by Marcin Panasiuk and Wojciech Izykowski.
8 February. New record found: 291831 for base 126401071349994536 by Marcin Panasiuk and Wojciech Izykowski.
7 February. New record found: 520924141 for bases 15, 750068417525532 by Marcin Panasiuk and Wojciech Izykowski.
30 January. New records found by Steve Worley:
109134866497 for bases 2, 45650740, 3722628058
47636622961201 for bases 2, 2570940, 211991001, 3749873356
3770579582154547 for bases 2, 2570940, 880937, 610386380, 4130785767
23 January. New record found: 272161 for base 62769592775616394 by Dana Jacobsen, Marcin Panasiuk, and Wojciech Izykowski.
14 January. New record found: 218245 for base 34933608779780163 by Dana Jacobsen, Marcin Panasiuk, and Wojciech Izykowski.
2012
3 December. New record found: 466758181 for bases 91869414, 6346128598129234 by Steve Worley.
21 November. New record found: 360018361 for bases 1143370, 2350307676 by Dana Jacobsen, Marcin Panasiuk, and Wojciech Izykowski.
17 October. New record found: 212321 for base 1948244569546278 by Sebastian Jaworowicz from PNT BOINC Team, Marcin Panasiuk, and Wojciech Izykowski.
15 October. New record found: 192001 for base 1769236083487960 by Sebastian Jaworowicz, Marcin Panasiuk, and Wojciech Izykowski.
10 July. If you participate in distributed SPRP search, you have the limited choice which record to beat. See here.
2 July. New record found: 161701 for base 64390572806844 by Marcin Panasiuk and Wojciech Izykowski.
10 June. More user-friendly solution checker.
29 May. You can now participate in SPRP search. See details here.
2011
6 September. Added solution checker for 3, 4 and 5 bases (limited to solutions where the first base equals 2).
18 August. Added RSS feed with news.
8 August. Added solution checker for 1 and 2 bases.
8 August. The website has been moved to http://miller-rabin.appspot.com - please update your bookmarks.
23 July. Added historical Jaeschke's result for 1 base.
21 July. Added historical Jaeschke's result for 4 bases.
4 July. Added link to Jan Feitsma's SPSP database.
28 June. Added result for 7 bases by Jim Sinclair.
28 June. First version of this webpage, published at http://priv.ckp.pl/wizykowski/sprp.php
count | date | best solution | bases | discoverer |
---|---|---|---|---|
1 | 03-03-2013 | 341531 | 9345883071009581737 | Steve Worley |
2 | 26-07-2013 | 1050535501 | 336781006125, 9639812373923155 | Wojciech Izykowski, Marcin Panasiuk |
3 | 27-05-2013 | 350269456337 | 4230279247111683200, 14694767155120705706, 16641139526367750375 | Steve Worley |
4 | 23-05-2013 | 55245642489451 | 2, 141889084524735, 1199124725622454117, 11096072698276303650 | Steve Worley |
5 | 23-05-2013 | 7999252175582851 | 2, 4130806001517, 149795463772692060, 186635894390467037, 3967304179347715805 | Steve Worley |
6 | 23-05-2013 | 585226005592931977 | 2, 123635709730000, 9233062284813009, 43835965440333360, 761179012939631437, 1263739024124850375 | Steve Worley |
7 | 20-04-2011 | at least 264 | 2, 325, 9375, 28178, 450775, 9780504, 1795265022 | Jim Sinclair |
date | best solution | base | discoverer |
---|---|---|---|
03-03-2013 | 341531 | 9345883071009581737 | Steve Worley |
08-02-2013 | 291831 | 126401071349994536 | Wojciech Izykowski, Marcin Panasiuk |
23-01-2013 | 272161 | 62769592775616394 | Dana Jacobsen, Wojciech Izykowski, Marcin Panasiuk |
14-01-2013 | 218245 | 34933608779780163 | Dana Jacobsen, Wojciech Izykowski, Marcin Panasiuk |
17-10-2012 | 212321 | 1948244569546278 | Sebastian Jaworowicz, Wojciech Izykowski, Marcin Panasiuk |
15-10-2012 | 192001 | 1769236083487960 | Sebastian Jaworowicz, Wojciech Izykowski, Marcin Panasiuk |
02-07-2012 | 161701 | 64390572806844 | Wojciech Izykowski, Marcin Panasiuk |
12-02-2011 | 132239 | 814494960528 | Wojciech Izykowski, Marcin Panasiuk |
12-02-2011 | 49141 | 921211727 * | Wojciech Izykowski, Marcin Panasiuk |
1993 | 5329 | 377687 | Gerhard Jaeschke |
date | best solution | bases | discoverer |
---|---|---|---|
26-07-2013 | 1050535501 | 336781006125, 9639812373923155 | Wojciech Izykowski, Marcin Panasiuk |
27-05-2013 | 885594169 | 725270293939359937, 3569819667048198375 | Steve Worley |
10-03-2013 | 716169301 | 15, 13393019396194701 | Dana Jacobsen, Wojciech Izykowski, Marcin Panasiuk |
28-02-2013 | 624732421 | 15, 5511855321103177 | Dana Jacobsen, Wojciech Izykowski, Marcin Panasiuk |
07-02-2013 | 520924141 | 15, 750068417525532 | Wojciech Izykowski, Marcin Panasiuk |
03-12-2012 | 466758181 | 91869414, 6346128598129234 | Steve Worley |
21-11-2012 | 360018361 | 1143370, 2350307676 | Dana Jacobsen, Wojciech Izykowski, Marcin Panasiuk |
10-03-2011 | 316349281 | 11000544, 31481107 | Jim Sinclair |
12-02-2011 | 227132641 | 660, 56928287 | Wojciech Izykowski, Marcin Panasiuk |
08-09-2009 | 176609441 | 2346211568, 3056093627 | David McAllister |
2005 | 38010307 | 2, 9332593 | Charles Greathouse |
1993 | 19471033 | 2, 299417 | Gerhard Jaeschke |
date | best solution | bases | discoverer |
---|---|---|---|
27-05-2013 | 350269456337 | 4230279247111683200, 14694767155120705706, 16641139526367750375 | Steve Worley |
21-05-2013 | 273919523041 | 15, 7363882082, 992620450144556 | Dana Jacobsen, Wojciech Izykowski, Marcin Panasiuk |
18-05-2013 | 242175507817 | 15, 7363882082, 211573017068182 | Dana Jacobsen, Wojciech Izykowski, Marcin Panasiuk |
15-05-2013 | 220146059407 | 15, 953185122, 158682512356199 | Dana Jacobsen, Wojciech Izykowski, Marcin Panasiuk |
23-02-2013 | 154639673381 | 15, 176006322, 4221622697 | Wojciech Izykowski, Marcin Panasiuk |
30-01-2013 | 109134866497 | 2, 45650740, 3722628058 | Steve Worley |
12-02-2011 | 105936894253 | 2, 1005905886, 1340600841 | Wojciech Izykowski, Marcin Panasiuk |
2009 | 75792980677 | 2, 379215, 457083754 | Steve Worley |
1993 | 4759123141 | 2, 7, 61 | Gerhard Jaeschke |
date | best solution | bases | discoverer |
---|---|---|---|
23-05-2013 | 55245642489451 | 2, 141889084524735, 1199124725622454117, 11096072698276303650 | Steve Worley |
30-01-2013 | 47636622961201 | 2, 2570940, 211991001, 3749873356 | Steve Worley |
12-02-2011 | 31858317218647 | 2, 642735, 553174392, 3046413974 | Wojciech Izykowski, Marcin Panasiuk |
2009 | 21652684502221 | 2, 1215, 34862, 574237825 | Steve Worley |
1993 | 1122004669633 | 2, 13, 23, 1662803 | Gerhard Jaeschke |
date | best solution | bases | discoverer |
---|---|---|---|
23-05-2013 | 7999252175582851 | 2, 4130806001517, 149795463772692060, 186635894390467037, 3967304179347715805 | Steve Worley |
30-01-2013 | 3770579582154547 | 2, 2570940, 880937, 610386380, 4130785767 | Steve Worley |
12-02-2011 | 3071837692357849 | 2, 75088, 642735, 203659041, 3613982119 | Wojciech Izykowski, Marcin Panasiuk |
date | best solution | bases | discoverer |
---|---|---|---|
23-05-2013 | 585226005592931977 | 2, 123635709730000, 9233062284813009, 43835965440333360, 761179012939631437, 1263739024124850375 | Steve Worley |
date | best solution | bases | discoverer |
---|---|---|---|
20-04-2011 | at least 264 | 2, 325, 9375, 28178, 450775, 9780504, 1795265022 | Jim Sinclair |
By using hashing we can reduce number of witnesses needed to perform deterministic test. The idea is to compute witnesses for every composite by using a small (not using too much memory) and fast function. It is also important for this function to be small to be fast, because we should spare precious cache memory.
Download link | Size | Checksums |
---|---|---|
2-SPRP-2-to-64.zip | 203,889,146 bytes | [MD5 ] 1bdbd72be1b6e104f8c3d08d05ee6bf4 [SHA1 ] f219614e04e2e9bf0e6d4dbc786c79e5ed1f2d99 [SHA-256] a8db0d43c9b04cb1f9d19fc9a87da779c420a6d88f6c2c7b87cde377a7e1f7fe |