What is a PRP ?
A PRP is a probable prime number, a number that nobody knows how to prove
or disprove its primality.
Here are some criterions that can be used to recognize these numbers
:
- N does not have any prime factor up to 2^32.
- N cannot be trivially written into a product.
- Take 3 square-free consecutive bases such that (b1/N)=(b2/N)=(b3/N)= -1. N
should be such that b1^((N-1)/2)=b2^((N-1)/2)=b3^((N-1)/2)= -1 (mod N).
- Take a prime base such that (b/N)= -1 and b<>b1<>b2<>b3.
N should pass the strong test in base b.
- or more (if someone has got an idea) !!!
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Rank |
Probable prime |
Digits (> 50000) |
Who ? |
When ? |
6251 | p(23879)#/2+64 | 118317 | Robert Price | 03/2017 |
6252 | 2^393033+20147 | 118315 | Enzo Doria | 08/2023 |
6253 | 8*10^118308+59 | 118309 | Robert Price | 11/2021 |
6254 | 9*10^118282+29 | 118283 | Robert Price | 03/2022 |
6255 | (9*35^76602+12877)/34 | 118279 | Eric Chen | 05/2025 |
6256 | (238*10^118265-1)/3 | 118267 | Robert Price | 04/2020 |
6258 | (53*10^118216+1)/9 | 118217 | Serge Batalov | 11/2010 |
6257 | (2^392707+1710)/2 | 118217 | Stefano Morozzi | 09/2020 |
6259 | (7*2^392697+1)/15 | 118214 | Renaud Lifchitz | 03/2011 |
6260 | (157^53819-1)/156 | 118179 | Alexander Zhirkov | 06/2016 |
6261 | (2^392567+2750)/2 | 118175 | Stefano Morozzi | 01/2021 |
6262 | 55*10^118172+3 | 118174 | Robert Price | 07/2022 |
6263 | (19*2^392551+1)/3 | 118171 | Lelio R Paula | 04/2014 |
6264 | 27185^22222+22222^27185 | 118168 | Hans Havermann | 01/2021 |
6265 | 2^392516-29219 | 118160 | Enzo Doria | 07/2015 |
6266 | 66*10^118155+7 | 118157 | Robert Price | 07/2020 |
6267 | Phi(177231,10) | 118152 | Maksym Voznyy | 09/2015 |
6268 | 2^392413-112123 | 118129 | Enzo Doria | 06/2014 |
6269 | 27491^19798+19798^27491 | 118119 | Hans Havermann | 02/2021 |
6270 | (49*10^118109-319)/9 | 118110 | Robert Price | 10/2021 |
6271 | (2^392342+5)/27 | 118106 | Lelio R Paula | 04/2014 |
6272 | (2^392333+1782)/2 | 118104 | Stefano Morozzi | 01/2021 |
6273 | 2^392300-1841429 | 118095 | Enzo Doria | 06/2015 |
6274 | 3*2^392260-5 | 118083 | Jon Grantham | 07/2023 |
6275 | 2^392220+75241 | 118070 | Enzo Doria | 04/2016 |
6276 | 27836^17409+17409^27836 | 118047 | Hans Havermann | 02/2021 |
6277 | (13^118026)%(10^118026) | 118026 | Henri Lifchitz | 05/2025 |
6278 | 10^118009+664447 | 118010 | Patrick De Geest | 07/2018 |
6279 | 10^118009-20001 | 118009 | Robert Price | 01/2018 |
6280 | (14*10^117991+61)/3 | 117992 | Robert Price | 12/2018 |
6281 | 2^391933+5897 | 117984 | Yves Minet | 02/2011 |
6282 | 2^391912-1849259 | 117978 | Enzo Doria | 08/2015 |
6283 | (2*34^77029+1043)/11 | 117968 | Eric Chen | 08/2023 |
6284 | 5*2^391836-3 | 117956 | Jon Grantham | 07/2023 |
6285 | 28357^14440+14440^28357 | 117953 | Hans Havermann | 02/2021 |
6286 | (2^391812+5)/14181 | 117944 | Lelio R Paula | 04/2014 |
6287 | 85^61124-61124^85 | 117934 | Norman Luhn | 09/2024 |
6288 | (7*10^117930-79)/9 | 117930 | Robert Price | 01/2021 |
6289 | 27531^19168+19168^27531 | 117904 | Hans Havermann | 02/2021 |
6290 | (46*10^117902+683)/9 | 117903 | Robert Price | 03/2019 |
6291 | 26349^26668-26668^26349 | 117893 | Frank Doornink | 03/2024 |
6292 | 27670^18189+18189^27670 | 117869 | Hans Havermann | 02/2021 |
6293 | (7*2^391521+1)/285 | 117858 | Lelio R Paula | 04/2014 |
6294 | (56*10^117856+583)/9 | 117857 | Robert Price | 08/2021 |
6295 | 32169^4606+4606^32169 | 117846 | Hans Havermann | 02/2021 |
6296 | (71*10^117803-143)/9 | 117804 | Robert Price | 10/2021 |
6297 | 2^391324+90901 | 117801 | Yves Minet | 02/2011 |
6298 | 2^391301-1859923 | 117794 | Enzo Doria | 03/2016 |
6299 | 2^391261-4131 | 117782 | Yves Minet | 02/2018 |
6300 | (2^391211+554)/2 | 117766 | Stefano Morozzi | 09/2020 |
6301 | 816^40445-40445^816 | 117764 | Norman Luhn | 09/2024 |
6302 | 38434^1157+1157^38434 | 117737 | Hans Havermann | 01/2021 |
6303 | (2^391115-7)/11791 | 117734 | Lelio R Paula | 04/2014 |
6304 | (85*10^117719+473)/9 | 117720 | Robert Price | 01/2020 |
6305 | (2^391049+582)/2 | 117718 | Stefano Morozzi | 09/2020 |
6306 | (21*23^86445-197)/22 | 117715 | Eric Chen | 08/2023 |
6307 | 31083^6122+6122^31083 | 117709 | Hans Havermann | 02/2021 |
6308 | 2^390960+1880881 | 117691 | Enzo Doria | 11/2016 |
6309 | (71*10^117685+91)/9 | 117686 | Robert Price | 04/2022 |
6311 | 2^390897-1860553 | 117672 | Enzo Doria | 11/2015 |
6310 | (61*10^117671+47)/9 | 117672 | Robert Price | 07/2022 |
6312 | 2^390889-115003 | 117670 | Enzo Doria | 06/2015 |
6313 | 12^109010+35 | 117642 | Riley Fisher | 08/2023 |
6314 | 2^390779-30337 | 117637 | Paul Bourdelais | 02/2012 |
6315 | (2^390735+378)/2 | 117623 | Stefano Morozzi | 02/2021 |
6316 | 11^112916-780 | 117590 | Enzo Doria | 12/2012 |
6317 | 27641^17916+17916^27641 | 117564 | Hans Havermann | 02/2021 |
6318 | 27906^16321+16321^27906 | 117561 | Hans Havermann | 02/2021 |
6319 | 27294^20275+20275^27294 | 117555 | Hans Havermann | 02/2021 |
6320 | (2^390473+1002)/2 | 117544 | Stefano Morozzi | 09/2020 |
6321 | 35912^1875+1875^35912 | 117541 | Hans Havermann | 02/2021 |
6322 | (16^97613-5^97613)/11 | 117537 | Robert Price | 07/2013 |
6323 | (2^390438+1774)/2 | 117534 | Stefano Morozzi | 01/2021 |
6324 | (2^390418+1722)/2 | 117528 | Stefano Morozzi | 09/2020 |
6325 | (2^390403+654)/2 | 117523 | Stefano Morozzi | 09/2020 |
6326 | (2^390343+2246)/2 | 117505 | Stefano Morozzi | 01/2021 |
6327 | 28043^15478+15478^28043 | 117493 | Hans Havermann | 02/2021 |
6328 | (17*2^390272+1)/1983 | 117482 | Lelio R Paula | 04/2014 |
6329 | 37077^1474+1474^37077 | 117479 | Hans Havermann | 01/2021 |
6330 | 31^78759-30 | 117459 | Theodore Burton | 02/2007 |
6331 | (2^390176+1222)/2 | 117455 | Stefano Morozzi | 09/2020 |
6332 | (2^390133+1242)/2 | 117442 | Stefano Morozzi | 09/2020 |
6333 | (2^390013+2634)/2 | 117406 | Stefano Morozzi | 09/2020 |
6334 | 3*10^117402+61 | 117403 | Robert Price | 09/2020 |
6335 | 2^389998+37 | 117402 | Lelio R Paula | 03/2013 |
6336 | (2^389977+314)/2 | 117395 | Stefano Morozzi | 09/2020 |
6337 | (2^389921+342)/2 | 117378 | Stefano Morozzi | 01/2021 |
6338 | 71830^43+43^71830 | 117333 | Hans Havermann | 01/2021 |
6339 | (2^389768+1582)/2 | 117332 | Stefano Morozzi | 09/2020 |
6340 | 33802^2951+2951^33802 | 117292 | Hans Havermann | 02/2021 |
6341 | (2^561185)%L(561185) | 117281 | Henri Lifchitz | 05/2025 |
6342 | 26789^23866+23866^26789 | 117277 | Hans Havermann | 02/2021 |
6343 | 29^80192-1*80192^29 | 117273 | Dylan Delgado | 12/2019 |
6344 | (101*10^117260+7)/9 | 117262 | Robert Price | 02/2022 |
6345 | (13*10^117249+161)/3 | 117250 | Robert Price | 11/2018 |
6346 | 2^389478+43 | 117245 | Lelio R Paula | 03/2013 |
6347 | (298*10^117229-7)/3 | 117231 | Robert Price | 06/2020 |
6348 | (2^389416+342)/2 | 117226 | Stefano Morozzi | 01/2021 |
6349 | (29*2^389351-1)/9 | 117207 | Lelio R Paula | 04/2014 |
6350 | 5*10^117205+23 | 117206 | Robert Price | 03/2019 |
6351 | (2^389341-7)/3865 | 117200 | Lelio R Paula | 03/2014 |
6352 | 27272^19827+19827^27272 | 117195 | Hans Havermann | 01/2021 |
6353 | (2^389276+2650)/2 | 117184 | Stefano Morozzi | 09/2020 |
6354 | (844*10^117175-7)/9 | 117177 | Robert Price | 05/2021 |
6355 | 10^117142+209223 | 117143 | Patrick De Geest | 04/2018 |
6357 | 10^117142-1000000001 | 117142 | Robert Price | 03/2018 |
6356 | 10^117142-966057 | 117142 | Patrick De Geest | 04/2018 |
6358 | 10^117135+360577 | 117136 | Patrick De Geest | 07/2018 |
6359 | 10^117135-401 | 117135 | Robert Price | 01/2018 |
6360 | 26415^26488-26488^26415 | 117126 | Norbert Schneider | 05/2021 |
6361 | 4*10^117123+79 | 117124 | Robert Price | 08/2018 |
6362 | 2^389033-12797413 | 117111 | Enzo Doria | 04/2016 |
6363 | (2^388987+2634)/2 | 117097 | Stefano Morozzi | 09/2020 |
6364 | 2^388960-109505 | 117089 | Enzo Doria | 04/2014 |
6365 | 7*10^117082-57 | 117083 | Robert Price | 06/2020 |
6366 | 791^40398-40398^791 | 117081 | Norman Luhn | 09/2024 |
6367 | (2^388928-5)/569 | 117077 | Lelio R Paula | 03/2014 |
6368 | 2^388888-1529 | 117067 | Yves Minet | 01/2013 |
6369 | 10^117059+28879 | 117060 | Patrick De Geest | 05/2016 |
6370 | (10^117059-71)/1 | 117059 | Serge Batalov | 12/2014 |
6371 | (2^388854+3630)/2 | 117057 | Stefano Morozzi | 09/2020 |
6372 | (2^388842+2098)/2 | 117053 | Stefano Morozzi | 09/2020 |
6373 | (2^388789+3150)/2 | 117037 | Stefano Morozzi | 09/2020 |
6374 | (2^388748+378)/2 | 117025 | Stefano Morozzi | 02/2021 |
6375 | (693^41189-1)/692 | 117005 | Michael Stocker | 05/2020 |
6376 | (26*10^116999-503)/9 | 117000 | Robert Price | 07/2018 |
6377 | 20^89917-21 | 116985 | Anonymous | 09/2024 |
6378 | (2^388609+1554)/2 | 116983 | Stefano Morozzi | 09/2020 |
6379 | 38496^1093+1093^38496 | 116975 | Hans Havermann | 02/2021 |
6380 | 3^245154-6256 | 116969 | Enzo Doria | 05/2014 |
6381 | 5*10^116966-43 | 116967 | Robert Price | 01/2019 |
6382 | 2^388536-113495 | 116961 | Enzo Doria | 08/2014 |
6383 | (2^388512+382)/2 | 116954 | Stefano Morozzi | 02/2021 |
6384 | (8*32^77701+271)/31 | 116952 | Eric Chen | 11/2023 |
6385 | 2^388469-43 | 116941 | Lelio R Paula | 03/2013 |
6386 | 27417^18416+18416^27417 | 116939 | Hans Havermann | 02/2021 |
6387 | (2^388438+1842)/2 | 116932 | Stefano Morozzi | 02/2021 |
6388 | (7*2^388372-1)/111 | 116911 | Lelio R Paula | 04/2014 |
6389 | (7*2^388335-1)/25 | 116900 | Lelio R Paula | 04/2014 |
6390 | 2^388180+93 | 116854 | Donovan Johnson | 07/2008 |
6391 | (2^388167+2510)/2 | 116850 | Stefano Morozzi | 09/2020 |
6392 | (85*10^116842+293)/9 | 116843 | Robert Price | 12/2019 |
6393 | 35296^2043+2043^35296 | 116840 | Hans Havermann | 02/2021 |
6394 | (2^388081+7)/1179 | 116821 | Lelio R Paula | 03/2014 |
6395 | 38633^1056+1056^38633 | 116814 | Hans Havermann | 02/2021 |
6396 | 2^387946-113261 | 116784 | Enzo Doria | 07/2014 |
6397 | 28*36^75009+305 | 116739 | Eric Chen | 12/2022 |
6398 | 28363^13056+13056^28363 | 116737 | Hans Havermann | 02/2021 |
6399 | 2^387745+75557 | 116723 | Enzo Doria | 04/2016 |
6400 | (29*10^116719+313)/9 | 116720 | Robert Price | 04/2021 |
6401 | 29622^8699+8699^29622 | 116695 | Hans Havermann | 02/2021 |
6402 | (206*10^116687-17)/9 | 116689 | Robert Price | 01/2020 |
6403 | (7*10^116684+179)/3 | 116685 | Robert Price | 09/2018 |
6404 | 2^387554+71455 | 116666 | Enzo Doria | 04/2016 |
6405 | (602*10^116647-71)/9 | 116649 | Robert Price | 12/2021 |
6406 | 3^244461-10 | 116638 | Tyler NeSmith | 09/2022 |
6407 | (2^387447+78557)/365 | 116631 | Lelio R Paula | 12/2014 |
6408 | (2*10^116620+43)/9 | 116620 | Serge Batalov | 11/2022 |
6409 | (19*10^116617+287)/9/12893 | 116614 | Alfred Reich | 11/2022 |
6410 | (145*10^116610-1)/9 | 116612 | Serge Batalov | 12/2014 |
6411 | (25*10^116601-331)/9 | 116602 | Robert Price | 08/2018 |
6412 | 25791^26428-26428^25791 | 116587 | Frank Doornink | 03/2024 |
6414 | (17*2^387284-1)/59 | 116584 | Lelio R Paula | 04/2014 |
6413 | (2^387284+3726)/2 | 116584 | Stefano Morozzi | 09/2020 |
6415 | 2^387211+111546435 | 116563 | Paul Bourdelais | 10/2021 |
6416 | 10^116557+987654321 | 116558 | Robert Price | 12/2019 |
6417 | 10^116557+9141 | 116558 | Patrick De Geest | 02/2020 |
6418 | 10^116557-609431 | 116557 | Patrick De Geest | 02/2020 |
6419 | 209^50234-50234^209 | 116551 | Norman Luhn | 09/2024 |
6420 | (28*10^116546+41)/3 | 116547 | Robert Price | 07/2021 |
6421 | (2^387123+1814)/2 | 116536 | Stefano Morozzi | 02/2021 |
6422 | (2^387076+2046)/2 | 116522 | Stefano Morozzi | 09/2020 |
6423 | (2^387073+2570)/2 | 116521 | Stefano Morozzi | 09/2020 |
6424 | (7*10^116514-1)/3 | 116515 | Robert Price | 08/2022 |
6425 | (26*32^77406-390071011)/31 | 116508 | Eric Chen | 11/2023 |
6426 | 28846^10931+10931^28846 | 116500 | Hans Havermann | 02/2021 |
6427 | 10^116496+3593037 | 116497 | Paul Bourdelais | 10/2021 |
6428 | 272^47851-47851^272 | 116497 | Norman Luhn | 09/2024 |
6429 | (31*2^386968+1)/7 | 116490 | Lelio R Paula | 03/2014 |
6430 | (944^39157+1)/945 | 116489 | Jinyuan Wang | 12/2024 |
6431 | 2^386947+1869143 | 116483 | Enzo Doria | 05/2016 |
6432 | (30^78857-1)/29 | 116480 | Robert Price | 12/2011 |
6433 | (2^386903-3)/5 | 116469 | Lelio R Paula | 03/2014 |
6434 | 28107^13892+13892^28107 | 116441 | Hans Havermann | 02/2021 |
6435 | 29110^9957+9957^29110 | 116386 | Hans Havermann | 02/2021 |
6436 | 26469^24838+24838^26469 | 116335 | Hans Havermann | 01/2021 |
6437 | 2^386389-1864783 | 116315 | Enzo Doria | 03/2016 |
6438 | (8*32^77250-163)/31 | 116273 | Eric Chen | 11/2023 |
6439 | (31*2^386231-1)/1711 | 116266 | Lelio R Paula | 03/2014 |
6440 | 297^47012+47012^297 | 116250 | Norbert Schneider | 07/2018 |
6441 | (35*10^116223-341)/9 | 116224 | Robert Price | 08/2021 |
6442 | (2^386087-5)/40959 | 116220 | Lelio R Paula | 03/2014 |
6443 | (2^386054+714)/2 | 116214 | Stefano Morozzi | 09/2020 |
6444 | (10^116201+7)/39623 | 116197 | Alfred Reich | 06/2021 |
6445 | 2^385969-823 | 116189 | Yves Minet | 05/2012 |
6446 | 57^66162+2 | 116173 | Lelio R Paula | 08/2013 |
6447 | 2^385854+75049 | 116154 | Enzo Doria | 04/2016 |
6448 | (2^385832+2590)/2 | 116147 | Stefano Morozzi | 09/2020 |
6449 | 2^385775-109587 | 116130 | Enzo Doria | 04/2014 |
6450 | (14*10^116112-101)/3 | 116113 | Robert Price | 02/2019 |
6451 | Phi(236354,10)/24817171 | 116109 | Makoto Kamada | 08/2019 |
6452 | 3*10^116107+23 | 116108 | Robert Price | 03/2022 |
6453 | 28729^10990+10990^28729 | 116094 | Hans Havermann | 02/2021 |
6454 | 2^385622+71839 | 116084 | Enzo Doria | 04/2016 |
6455 | 2^385564+781 | 116067 | Lelio R Paula | 01/2012 |
6456 | (2^385565+1562)/2 | 116067 | Stefano Morozzi | 09/2020 |
6457 | (2^385563+378)/2 | 116066 | Stefano Morozzi | 02/2021 |
6458 | (2^385557+2214)/2 | 116064 | Stefano Morozzi | 09/2020 |
6459 | 29431^8776+8776^29431 | 116056 | Hans Havermann | 01/2021 |
6460 | (266*10^116024-17)/3 | 116026 | Robert Price | 07/2020 |
6461 | 30263^6820+6820^30263 | 116022 | Hans Havermann | 02/2021 |
6462 | 2^385410+71893 | 116020 | Enzo Doria | 04/2016 |
6463 | 38225^1084+1084^38225 | 116014 | Hans Havermann | 02/2021 |
6464 | 26548^23433+23433^26548 | 116011 | Hans Havermann | 02/2021 |
6465 | 12^107422-11 | 115928 | Riley Fisher | 12/2023 |
6466 | (25*2^385091+1)/27 | 115924 | Lelio R Paula | 04/2014 |
6467 | (11*10^115910-131)/3 | 115911 | Robert Price | 09/2018 |
6468 | 2^384953-111943 | 115883 | Paul Bourdelais | 02/2012 |
6469 | 43^70942-2 | 115882 | Lelio R Paula | 04/2014 |
6470 | (94*10^115879-7)/3 | 115881 | Robert Price | 03/2020 |
6471 | 7*10^115863+3 | 115864 | Robert Price | 08/2015 |
6472 | 2^384834+93 | 115847 | Donovan Johnson | 07/2008 |
6473 | 2^384809+71297 | 115840 | Enzo Doria | 04/2016 |
6474 | (55*10^115829+323)/9 | 115830 | Robert Price | 10/2021 |
6475 | (7*2^384759-1)/5 | 115825 | Lelio R Paula | 04/2014 |
6476 | 31348^4951+4951^31348 | 115822 | Hans Havermann | 02/2021 |
6477 | (793*10^115810+53)/9 | 115812 | Robert Price | 01/2022 |
6478 | (71*10^115810-17)/9 | 115811 | Ray Chandler | 08/2011 |
6479 | (97*10^115794-1)/3 | 115796 | Serge Batalov | 12/2014 |
6480 | 31115^5266+5266^31115 | 115794 | Hans Havermann | 02/2021 |
6481 | 2*10^115784-27 | 115785 | Robert Price | 05/2018 |
6482 | 10^115773+126739 | 115774 | Patrick De Geest | 04/2018 |
6484 | 10^115773-1000000001 | 115773 | Robert Price | 03/2018 |
6483 | 10^115773-396221 | 115773 | Patrick De Geest | 04/2018 |
6485 | (2^384582+778)/2 | 115771 | Stefano Morozzi | 09/2020 |
6486 | 30537^6178+6178^30537 | 115762 | Hans Havermann | 01/2021 |
6487 | 2^384530+1874305 | 115756 | Enzo Doria | 06/2016 |
6488 | (3*2^384524-1)/7631 | 115750 | Lelio R Paula | 03/2014 |
6489 | 28275^12406+12406^28275 | 115748 | Hans Havermann | 01/2021 |
6490 | (44*10^115697-413)/9 | 115698 | Robert Price | 03/2019 |
6491 | 31408^4825+4825^31408 | 115692 | Hans Havermann | 02/2021 |
6492 | (2^384317+1026)/2 | 115691 | Stefano Morozzi | 09/2020 |
6493 | 2^384312+81091 | 115690 | Yves Minet | 02/2010 |
6494 | (2^384265+2150)/2 | 115675 | Stefano Morozzi | 09/2020 |
6495 | (2^384246+2182)/2 | 115670 | Stefano Morozzi | 09/2020 |
6496 | (4*10^115668-79)/3 | 115669 | Robert Price | 02/2018 |
6497 | (2^384193+242)/2 | 115654 | Stefano Morozzi | 09/2020 |
6498 | (266947#+1267)/(7^2*181) | 115647 | Makoto Morimoto | 06/2019 |
6499 | (266947#+273808)/(2*109*157) | 115646 | Makoto Morimoto | 10/2017 |
6500 | 18^92125-92125^18 | 115642 | Dylan Delgado | 08/2019 |