RieselSieve
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Riesel Sieve is a Distributed computing project trying to prove the Riesel conjecture. This conjecture says that 509203 is the smallest Riesel number. Seventeen or bust is a similar project for Sierpinski numbers. Riesel Sieve is running partially under the BOINC platform.
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[edit] Proving the conjecture
To prove the Riesel conjecture we must find an n value for every odd k smaller than 509203 so that 
is a prime number is. At the start of the project 101 of these k's were left. Now we're down to 69 possible Riesel numbers. These numbers we're dealing with are huge. The largest prime found by this project is 
. This is a 742,147 digit number.
[edit] LLR
For proving the primality of the numbers , the Lucas-Lehmer-Riesel test has been developed. It is based on the Lucas–Lehmer test for Mersenne numbers. This test can prove the primality of a k-n pair. But it would be very time consuming to LLR every k-n pair. So we need another way to reduce the numbers we have to test.
[edit] Sieving
Instead of primality-testing every k-n pair, we can also take a range of factors and see if any k-n pair has one of these factors. This method is called sieving. If a k-n pair has one of the factors in the range, it can't possibly be prime, so it's removed from the dat-file. So the sieve is unable to find any primes, it can only remove composite numbers.
[edit] Optimized sieving
If your processor supports instruction sets like SSE2 or CMOV7 you can run an optimized application. Not all processors support these instruction sets, so these are not the default applications. For more information on how to use optimized applications, see this forum thread.
[edit] Results
From the 101 Riesel-candidates at the start of the project only these 69 remain:
2293, 9221, 23669, 26773, 31859, 38473, 40597, 46663, 65531, 67117, 74699, 81041, 93839, 97139, 107347, 113983, 121889, 123547, 129007, 141941, 143047, 146561, 161669, 162941, 191249, 192971, 206039, 206231, 215443, 226153, 234343, 245561, 250027, 252191, 273809, 304207, 315929, 319511, 324011, 325123, 327671, 336839, 342673, 342847, 344759, 353159, 362609, 363343, 364903, 365159, 368411, 371893, 384539, 386801, 397027, 398023, 402539, 409753, 415267, 428639, 444637, 469949, 470173, 474491, 477583, 485557, 485767, 494743, 502573.
Right now 26 primes have been found removing 26 candidates.
| User | K | N | Digits | Date |
|---|---|---|---|---|
| botXXX | 275293 | 2335007 | 702913 | 2006-09-21 |
| maefly | 450457 | 2307905 | 694754 | 2006-03-27 |
| bwhite | 114487 | 2198389 | 661786 | 2006-05-23 |
| Auritania | 196597 | 2178109 | 655681 | 2006-05-07 |
| mackerel | 467917 | 1993429 | 600088 | 2005-12-24 |
| frmky | 417643 | 1800787 | 542097 | 2005-10-04 |
| NeoLogic | 357659 | 1779847 | 535793 | 2005-09-24 |
| tekno | 110413 | 1591999 | 479244 | 2005-06-07 |
| Footmaster | 234847 | 1535589 | 462264 | 2005-05-07 |
| tekno | 325627 | 1472117 | 443157 | 2005-04-04 |
| pvh | 149797 | 1414137 | 425703 | 2005-03-13 |
| mercutio | 192089 | 1395688 | 420149 | 2004-05-09 |
| Rseffco | 502541 | 1199930 | 361221 | 2004-12-21 |
| neologic | 71009 | 1185112 | 356759 | 2004-12-06 |
| sean | 350107 | 1144101 | 344414 | 2004-10-23 |
| footmaster | 500621 | 1138518 | 342734 | 2004-10-18 |
| Magnus | 504613 | 1136459 | 342114 | 2004-10-16 |
| SISU | 412717 | 1084409 | 326445 | 2004-08-24 |
| footmaster | 150847 | 1076441 | 324046 | 2004-08-14 |
| hemigrid | 309817 | 901173 | 271286 | 2004-06-07 |
| neologic | 170591 | 866870 | 260959 | 2004-04-15 |
| mercutio | 93997 | 864401 | 260216 | 2004-04-01 |
| neologic | 460139 | 779536 | 234669 | 2004-03-26 |
| spooty | 246299 | 752600 | 226561 | 2004-01-23 |
| sean | 261221 | 689422 | 207542 | 2003-12-22 |
| cipher | 279703 | 616235 | 185511 | 2004-01-06 |
