Sierpinski/Riesel Base 5 Problem

This project is an extension of the original Sierpinski/Riesel problems (SoB/TRP). It is attempting to solve the Sierpinski/Riesel problems for base 5 by determining the smallest Sierpinski/Riesel numbers. Therefore, primes of the form k*5^n+/-1 are being sought for even k's.


 *  Sierpinski Base 5  - The smallest even Sierpinski base 5 number is suggested to be k=159986. To prove this, it is sufficient to show that k*5^n+1 is prime for each even k < 159986. This has currently been achieved for all even k, with the exception of the following 30 values (as of 2 July 2020):


 * k = 6436, 7528, 10918, 26798, 29914, 31712, 36412, 41738, 44348, 44738, 45748, 51208, 58642, 60394, 62698, 64258, 67612, 67748, 71492, 74632, 76724, 83936, 84284, 90056, 92906, 93484, 105464, 126134, 139196, 152588


 *  Riesel Base 5  - The smallest even Riesel base 5 number is suggested to be k=346802. To prove this, it is sufficient to show that k*5^n-1 is prime for each even k < 346802. This has currently been achieved for all even k, with the exception of the following 62 values (as of 14th August 2020):


 * k = 3622, 4906, 23906, 26222, 35248, 52922, 63838, 64598, 68132, 71146, 76354, 81134, 92936, 102818, 102952, 109238, 109862, 127174, 131848, 134266, 136804, 143632, 145462, 145484, 146756, 147844, 151042, 152428, 154844, 159388, 164852, 170386, 170908, 177742, 182398, 187916, 189766, 190334, 195872, 201778, 204394, 206894, 213988, 231674, 239062, 239342, 246238, 248546, 259072, 265702, 267298, 271162, 273662, 285598, 285728, 298442, 304004, 313126, 318278, 325922, 335414, 338866

 History  Robert Smith originally presented the idea of a Sierpinski/Riesel base 5 search on 17 September 2004, in the primeform yahoo group. Using {3,7,13,31,601} as the covering set, he proposed that k=346802 is the smallest Riesel base 5 number. Shortly afterwards, Guido Smetrijns proposed that k=159986 is the smallest Sierpinski base 5 number.

After doing most of the initial work himself, Robert posted in the mersenneforum.org on 28 September 2004, and thus, the distributed effort began. Other principle players in the development, management, and growth of the project are Lars Dausch, Geoff Reynolds, Anand S Nair, and Thomas Masser.

During the first couple of years, the project remained very active. Both sieving and primality testing were handled through manual reservations in the Mersenne.

On a side note, it is within this project that Geoffrey Reynolds created his srsieve to support the Sierpinski/Riesel problems. His initial post (27 Apr 2006) can be found here. Thus began his illustrious career in providing excellent sieving software for the prime finding community. His programs continue to be widely used by prime seekers today. His collaboration with Ken Brazier helped produce PPsieve, which revolutionized GPU sieving and established deeply sieved files for both Riesel and Proth prime forms. These files currently provide support for the Riesel Prime Search and Proth Prime Search projects.

On 29 Aug 2006 the project officially launched its LLRNet. This provided for automatic distribution and primality testing of candidates. Manual reservations were continued on an individual basis. Participation continued to be healthy. However, over the next 4 years, interest waned. Interest remained low until March 2010 when a lively discussion took place to determine the project’s future.

For the next few months, participation remained high. On 28 May 2010 manual reservations were ceased for primality testing and all remaining ranges were reserved for SR5’s LLRNet. Soon participation dropped again. In the fall of 2010, PrimeGird started reserving ranges to test in its PRPNet server. Testing among PrimeGrid users remained healthy.

Finally, in December 2010, PrimeGrid hosted an end of year Mini Challenge on it’s PRPNet server benefiting the SR5 project. The last 10 days of 2010 (21 Dec - 31 Dec) was devoted to helping the Sierpinski/Riesel base 5 project remain active. The goal of the Challenge was to help the the SR5 project make 2010 the HIGHEST scoring year of the project in regards to primes found. The Mini Challenge was a huge success with PrimeGrid users finding 5 SR5 primes.

Thus, on 7 January 2011, a collaboration was officially announced between SR5 and PrimeGrid. It remained in PrimeGrid’s PRPNet until 14 Jun 2013 when it was moved to BOINC.

 Primes found by PrimeGrid 

109838*5^3168862-1 found by Erik Veit on 13 August 2020 | Official Announcement

118568*5^3112069+1 found by Honza Cholt on 1 May 2020 | Official Announcement

207494*5^3017502-1 found by Todd Pickering on 16 March 2020 | Official Announcement

238694*5^2979422-1 found by Chris Howell on 12 March 2020 | Official Announcement

146264*5^2953282-1 found by Wolfgang Schwieger on 9 March 2020 | Official Announcement

35816*5^2945294-1 found by Pavel Atnashev on 5 March 2020 | Official Announcement

322498*5^2800819-1 found by Jordan Romaidis on 23 June 2019 | Official Announcement

88444*5^2799269-1 found by Scott Brown on 21 June 2019 | Official Announcement

138514*5^2771922+1 found by Ken Ito on 26 April 2019 | Official Announcement

194368*5^2638045-1 found by Honza Cholt on 15 August 2018 | Official Announcement

66916*5^2628609-1 found by Honza Cholt on 29 July 2018 | Official Announcement

81556*5^2539960+1 found by Jiří Bočan on 20 June 2018 | Official Announcement

327926*5^2542838-1 found by Seiya Tsuji on 19 June 2018 | Official Announcement

301562*5^2408646-1 found by Håkan Lind on 17 September 2017 | Official Announcement

171362*5^2400996-1 found by Frank Schwegler on 25 August 2017 | Official Announcement

180062*5^2249192-1 found by Stefan Larsson on 20 August 2016 | Official Announcement

53546*5^2216664-1 found by Tom Greer on 30 May 2016 | Official Announcement

296024*5^2185270-1 found by Steven Wong on 25 March 2016 | Official Announcement

92158*5^2145024+1 found by Karl Burridge on 15 March 2016 | Official Announcement

77072*5^2139921+1 found by Wolfgang Becker on 6 March 2016 | Official Announcement

306398*5^2112410-1 found by André Ahlfors Dahl on 11 January 2016 | Official Announcement

154222*5^2091432+1 found by Scott Brown on 10 November 2015 | Official Announcement

100186*5^2079747-1 found by Toshitaka Kumagai on 21 October 2015 | Official Announcement

144052*5^2018290+1 found by Wolfgang Schmidt on 23 May 2015 | Official Announcement

109208*5^1816285+1 found by Scott Brown on 18 October 2014 | Official Announcement

325918*5^1803339-1 found by Jörg Meili on 21 September 2014 | Official Announcement

133778*5^1785689+1 found by Guo Hua Miao on 17 August 2014 | Official Announcement

24032*5^1768249+1 found by Hiroyuki Okazaki on 23 July 2014 | Official Announcement

138172*5^1714207-1 found by Walter Darimont on 27 June 2014 | Official Announcement

22478*5^1675150-1 found by Guo Hua Miao on 19 June 2014 | Official Announcement

326834*5^1634978-1 found by Scott Brown on 25 April 2014 | Official Announcement

207394*5^1612573-1 found by Honza Cholt on 9 April 2014 | Official Announcement

104944*5^1610735-1 found by Brian Smith on 9 April 2014 | Official Announcement

330286*5^1584399-1 found by Scott Brown on 21 March 2014 | Official Announcement

22934*5^1536762-1 found by Keishi Toda on 6 February 2014 | Official Announcement

178658*5^1525224-1 found by Keishi Toda on 31 January 2014 | Official Announcement

59912*5^1500861+1 found by Raymond Ottusch on 17 January 2014 | Official Announcement

37292*5^1487989+1 found by Stephen R Cilliers on 29 December 2013 | Official Announcement

173198*5^1457792-1 found by Motohiro Ohno on 4 December 2013 | Official Announcement

245114*5^1424104-1 found by David Yost on 1 November 2013

175124*5^1422646-1 found by David Yost on 31 October 2013

256612*5^1335485-1 found by Wolfgang Schwieger on 4 August 2013

268514*5^1292240-1 found by Raymond Schouten on 16 July 2013

243944*5^1258576-1 found by Tod Slakans on 5 July 2013

97366*5^1259955-1 found by Jörg Meili on 4 July 2013

84466*5^1215373-1 found by Raymond Schouten on 29 June 2013

150344*5^1205508-1 found by Randy Ready on 28 June 2013

1396*5^1146713-1 found by Randy Ready on 23 June 2013

17152*5^1131205-1 found by Bob Benson on 22 June 2013

92182*5^1135262+1 found by Randy Ready on 21 June 2013

329584*5^1122935-1 found by Stephen R Cilliers on 21 June 2013

305716*5^1093095-1 found by Randy Ready on 18 June 2013

130484*5^1080012-1 found by Randy Ready on 17 June 2013

97768*5^987383-1 found by Ulrich Hartel on 17 June 2013

55154*5^1063213+1 found by Senji Yamashita on 16 June 2013

243686*5^1036954-1 found by Katsumi Hirai on 16 June 2013

70082*5^936972-1 found by Scott Brown on 30 May 2013

102976*5^929801-1 found by David Yost on 9 May 2013

110488*5^917100+1 found by Ronny Willig on 25 March 2013

162434*5^856004-1 found by Predrag Kurtovic on 10 January 2013

174344*5^855138-1 found by Ronny Willig on 9 January 2013

57406*5^844253-1 found by David Yost on 7 November 2012

48764*5^831946-1 found by David Yost on 12 October 2012

162668*5^785748-1 found by Lennart Vogel on 3 July 2012

289184*5^770116-1 found by David Yost on 7 June 2012

11812*5^769343-1 found by Göran Schmidt on 2 June 2012

316594*5^766005-1 found by Michael Becker on 30 May 2012

340168*5^753789-1 found by Kimmo Myllyvirta on 18 May 2012

338948*5^743996-1 found by Ricky L Hubbard on 7 May 2012

18656*5^735326-1 found by Lennart Vogel on 3 May 2012

5374*5^723697-1 found by Kelvin Lewis on 13 April 2012

72532*5^708453-1 found by Göran Schmidt on 7 February 2012

2488*5^679769-1 found by Sascha Beat Dinkel on 24 November 2011

331882*5^674961-1 found by Ronny Willig on 11 November 2011

27994*5^645221-1 found by Philipp Bliedung on 18 July 2011

262172*5^643342-1 found by Kimmo Myllyvirta on 13 July 2011

49568*5^640900-1 found by Sascha Beat Dinkel on 1 July 2011

270748*5^614625-1 found by Puzzle Peter on 14 February 2011

266206*5^608649-1 found by Puzzle Peter on 10 February 2011

210092*5^618136-1 found by Puzzle Peter on 31 January 2011

301016*5^586858-1 found by Puzzle Peter on 24 January 2011

 Primes found by SR5 since collaboration 

109988*5^544269+1 found by ltd on 23 April 2011

68492*5^542553+1 found by ltd on 24 April 2011

 Primes found by others 

114986*5^1052966-1 found by Sergey Batalov on 3 June 2013

119878*5^1019645-1 found by Sergey Batalov on 3 June 2013