PRP Records

Probable Primes Top 10000

(295756 PRPs in the top)

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) !!!

See the Top discoverers
See the Latest PRPs
Search by form

 1-250 251-500 501-750 751-1000 1001-1250 1251-1500 1501-1750 1751-2000 2001-2250 2251-2500 2501-2750 2751-3000 3001-3250 3251-3500 3501-3750 3751-4000 4001-4250 4251-4500 4501-4750 4751-5000 5001-5250 5251-5500 5501-5750 5751-6000 6001-6250 6251-6500 6501-6750 6751-7000 7001-7250 7251-7500 7501-7750 7751-8000 8001-8250 8251-8500 8501-8750 8751-9000 9001-9250 9251-9500 9501-9750 9751-10000

 Rank Probable prime Digits (> 50000) Who ? When ? 5251 28119^22268+22268^28119 122253 Hans Havermann 03/2021 5252 32167^6312+6312^32167 122240 Hans Havermann 03/2021 5253 3^256199-2^256199 122238 Mike Oakes 06/2005 5254 27678^26053+26053^27678 122223 Hans Havermann 03/2021 5255 2^405992-78557 122216 Jorge Menendez 03/2018 5256 (8*10^122203+43)/3 122204 Robert Price 06/2018 5257 (58*10^122170+329)/9 122171 Robert Price 05/2019 5258 2^405774+179149 122151 Enzo Doria 06/2016 5259 2^405693+20417 122126 Enzo Doria 07/2023 5260 (218*10^122109+7)/9 122111 Robert Price 06/2022 5261 29189^15246+15246^29189 122103 Hans Havermann 03/2021 5263 34*10^122082-9 122084 Robert Price 06/2020 5262 33442^4473+4473^33442 122084 Hans Havermann 03/2021 5264 5*10^122082+41 122083 Robert Price 03/2019 5265 31849^6808+6808^31849 122078 Hans Havermann 03/2021 5267 2^405514-3311 122072 Yves Minet 12/2014 5268 2^405514-115511 122072 Enzo Doria 07/2015 5266 23*10^122070-7 122072 Robert Price 02/2020 5269 2^405422-113261 122045 Enzo Doria 07/2014 5270 2^405173+71237 121970 Enzo Doria 04/2016 5271 fibonacci(583574)+2 121960 Jon Grantham 08/2023 5272 (154*10^121953+17)/9 121955 Robert Price 06/2022 5273 (34*10^121924+191)/9 121925 Robert Price 08/2021 5274 (2^405016+1)/257 121920 Lelio R Paula 04/2014 5275 28557^18590+18590^28557 121918 Hans Havermann 03/2021 5276 28641^18002+18002^28641 121877 Hans Havermann 03/2021 5277 2^404858+71329 121875 Enzo Doria 04/2016 5278 2^404813-114703 121861 Enzo Doria 04/2015 5279 2^404764+77791 121847 Enzo Doria 05/2016 5280 28830^16841+16841^28830 121847 Hans Havermann 03/2021 5281 (4*10^121825+89)/3 121826 Robert Price 08/2021 5282 317^48694+48694^317 121787 Norbert Schneider 08/2015 5283 2^404536-115259 121778 Enzo Doria 06/2015 5284 2^404501-631 121767 Yves Minet 07/2012 5285 5*10^121764-69 121765 Robert Price 02/2021 5286 28236^20485+20485^28236 121738 Hans Havermann 02/2021 5287 (382*10^121694-31)/9 121696 Robert Price 06/2022 5288 63^67620+2 121672 Lelio R Paula 08/2015 5289 (25*34^79445-28062367)/33 121669 Eric Chen 08/2023 5290 (13*33^80110-121453)/32 121648 Eric Chen 12/2023 5291 (16*10^121633+167)/3 121634 Robert Price 06/2019 5292 29955^11494+11494^29955 121632 Hans Havermann 02/2021 5293 (17*10^121621+1)/9 121622 Serge Batalov 05/2010 5294 31088^8163+8163^31088 121612 Hans Havermann 02/2021 5295 (15*2^403912+1)/271 121589 Lelio R Paula 05/2014 5296 (211^52301-1)/210 121560 Anonymous 04/2024 5297 (10^121543-79)/3 121543 Robert Price 01/2018 5298 2^403676+76831 121519 Enzo Doria 05/2016 5299 (7*10^121487+143)/3 121488 Robert Price 03/2018 5300 27965^22086+22086^27965 121484 Hans Havermann 02/2021 5301 (893*10^121470+7)/9 121472 Robert Price 06/2021 5302 (206*10^121462-11)/3 121464 Robert Price 02/2022 5303 26282^27481-27481^26282 121457 Frank Doornink 03/2024 5304 (77*10^121455+67)/9 121456 Robert Price 12/2021 5305 2^403363-113635 121425 Enzo Doria 08/2014 5306 25531^27552-27552^25531 121424 Frank Doornink 02/2024 5307 (17*10^121418-113)/3 121419 Robert Price 06/2021 5308 2^403336-1861469 121417 Enzo Doria 03/2016 5309 27929^22186+22186^27929 121382 Hans Havermann 02/2021 5310 p(24442)#/2-64 121381 Robert Price 04/2017 5311 11^116555-720 121380 Enzo Doria 11/2012 5312 2^403100-461267 121346 Enzo Doria 07/2015 5313 2^403093-112213 121344 Enzo Doria 06/2014 5314 29404^13385+13385^29404 121340 Hans Havermann 02/2021 5315 28106^20745+20745^28106 121332 Hans Havermann 02/2021 5316 (316^48539+1)/317 121330 Eric Chen 10/2017 5317 (23*10^121320-71)/3 121321 Robert Price 07/2020 5318 2^403004+1866361 121317 Enzo Doria 03/2016 5319 2^402953+89 121301 Lelio R Paula 10/2013 5320 2^402944-2788319 121299 Enzo Doria 03/2016 5321 (44*10^121297-719)/9 121298 Robert Price 12/2018 5322 (27*2^402865+1)/5 121276 Lelio R Paula 04/2014 5323 2^402828-113183 121264 Enzo Doria 07/2014 5324 (17*10^121242+1)/9 121243 Serge Batalov 05/2010 5325 (15*2^402757+1)/101 121242 Lelio R Paula 05/2014 5327 2^402715+1874223 121230 Enzo Doria 06/2016 5326 (35*10^121229-593)/9 121230 Robert Price 07/2018 5328 (91^61879+1)/92 121222 Paul Bourdelais 09/2017 5329 28719^16568+16568^28719 121174 Hans Havermann 02/2021 5330 7*10^121144+9 121145 Robert Price 09/2015 5331 27490^25467+25467^27490 121121 Hans Havermann 02/2021 5332 34575^3182+3182^34575 121106 Hans Havermann 02/2021 5333 5*10^121100-37 121101 Robert Price 11/2021 5334 F(579521)/516247738177 121101 Serge Batalov 07/2024 5335 25592^27467-27467^25592 121078 Frank Doornink 02/2024 5336 29954^10935+10935^29954 120979 Hans Havermann 02/2021 5337 33585^3992+3992^33585 120946 Hans Havermann 02/2021 5338 40296^1003+1003^40296 120941 Hans Havermann 02/2021 5339 2^401725-113251 120932 Enzo Doria 07/2014 5340 (15*2^401677-1)/19 120917 Lelio R Paula 05/2014 5341 2^401652+73711 120910 Enzo Doria 04/2016 5342 (2^401632+3)/79 120902 Lelio R Paula 04/2014 5343 40450^973+973^40450 120870 Hans Havermann 01/2021 5344 (8*10^120851-11)/3 120852 Robert Price 07/2023 5345 10^120841+88417 120842 Patrick De Geest 04/2020 5346 10^120841-123456789 120841 Robert Price 02/2020 5347 10^120841-176853 120841 Patrick De Geest 04/2020 5348 2^401406-2791331 120836 Enzo Doria 03/2016 5349 (28^83497+1)/29 120832 Robert Price 07/2013 5350 (22*10^120828+161)/3 120829 Robert Price 05/2019 5351 2^401369+1867367 120825 Enzo Doria 03/2016 5352 (5*10^120821+43)/3 120822 Robert Price 12/2021 5353 26990^27263-27263^26990 120808 Frank Doornink 03/2024 5354 (10^120782+29)/3 120782 Serge Batalov 12/2014 5355 2^401215-1657 120778 Yves Minet 07/2014 5356 2^401159+53 120761 Lelio R Paula 10/2013 5357 27782^22179+22179^27782 120739 Hans Havermann 01/2021 5358 32974^4585+4585^32974 120730 Hans Havermann 02/2021 5359 2^401031-113047 120723 Enzo Doria 07/2014 5360 30598^8813+8813^30598 120713 Hans Havermann 02/2021 5361 (71*10^120703-287)/9 120704 Robert Price 09/2019 5362 25671^27370-27370^25671 120687 Frank Doornink 02/2024 5363 (29*2^400909-1)/303 120685 Lelio R Paula 04/2014 5364 34793^2940+2940^34793 120675 Hans Havermann 02/2021 5365 26028^27329-27329^26028 120670 Frank Doornink 03/2024 5366 (2^400846+538)/2 120667 Stefano Morozzi 09/2020 5367 (166*10^120654+11)/3 120656 Robert Price 03/2021 5368 34066^3481+3481^34066 120652 Hans Havermann 02/2021 5369 8*10^120637-27 120638 Robert Price 10/2021 5370 (2^400709+3546)/2 120626 Stefano Morozzi 09/2020 5371 (2^400700+3126)/2 120623 Stefano Morozzi 09/2020 5372 (2^400693+2634)/2 120621 Stefano Morozzi 09/2020 5373 9*10^120617-61 120618 Robert Price 06/2021 5374 (29*10^120590-71)/3 120591 Robert Price 07/2021 5375 2^400571-15 120584 Lelio R Paula 10/2013 5376 (10^120574+359)/9 120574 Serge Batalov 12/2014 5377 (8*10^120552-17)/9 120552 Serge Batalov 11/2022 5378 27431^24810+24810^27431 120550 Hans Havermann 02/2021 5379 2^400424-216413 120540 Enzo Doria 04/2013 5380 29090^13911+13911^29090 120531 Hans Havermann 02/2021 5381 (2^400346+1722)/2 120516 Stefano Morozzi 09/2020 5382 27899^20868+20868^27899 120510 Hans Havermann 02/2021 5383 33740^3729+3729^33740 120506 Hans Havermann 02/2021 5384 (17*2^400200-1)/587 120471 Lelio R Paula 05/2014 5385 2^400166+1874899 120462 Enzo Doria 06/2016 5386 (2^400165+1602)/2 120462 Stefano Morozzi 09/2020 5387 37078^1771+1771^37078 120438 Hans Havermann 02/2021 5388 (2^400084+1638)/2 120437 Stefano Morozzi 09/2020 5389 (3*2^400045-1)/865 120424 Lelio R Paula 04/2014 5390 2^399999+54173 120412 Norman Luhn 08/2023 5391 (2^399974+2790)/2 120404 Stefano Morozzi 02/2021 5392 2^399966+73759 120402 Enzo Doria 04/2016 5393 (2^399961+2306)/2 120400 Stefano Morozzi 02/2021 5394 (112*10^120395-1)/3 120397 Serge Batalov 12/2014 5396 2^399918-95 120388 Lelio R Paula 04/2013 5395 2^399918+214009 120388 Enzo Doria 10/2023 5397 (28*10^120381-67)/3 120382 Robert Price 10/2020 5398 (49*10^120380-139)/9 120381 Robert Price 03/2019 5399 (2^399874+2194)/2 120374 Stefano Morozzi 09/2020 5400 2^399792-1849259 120350 Enzo Doria 08/2015 5401 9*10^120342-7 120343 Robert Price 09/2015 5402 (2^399751+786)/2 120337 Stefano Morozzi 09/2020 5403 (331*10^120332-7)/9 120334 Robert Price 04/2022 5404 (13*10^120306-37)/3 120307 Robert Price 01/2019 5405 (23*10^120299+37)/3 120300 Robert Price 02/2022 5406 25935^27254-27254^25935 120297 Frank Doornink 03/2024 5407 (2^399604+3070)/2 120293 Stefano Morozzi 09/2020 5408 (2^399549+1062)/2 120276 Stefano Morozzi 09/2020 5409 2^399526-1861721 120270 Enzo Doria 11/2015 5410 (10^(2*60126+1)+36*10^60126-1)/9 120253 Robert Price 10/2015 5411 32016^5687+5687^32016 120217 Hans Havermann 01/2021 5412 (205*10^120212-1)/3 120214 Robert Price 11/2021 5413 2^399322-2798111 120208 Enzo Doria 04/2016 5414 30438^8867+8867^30438 120163 Hans Havermann 02/2021 5415 3^251841-5*2^251841 120159 Jon Grantham 08/2023 5417 72^64693-71^64693 120157 Robert Price 03/2014 5416 (17*10^120156-161)/9 120157 Robert Price 02/2021 5418 2^399111-28489 120145 Enzo Doria 08/2015 5419 (2^399014+1318)/2 120115 Stefano Morozzi 02/2021 5420 30254^9333+9333^30254 120110 Hans Havermann 02/2021 5421 30882^7745+7745^30882 120101 Hans Havermann 02/2021 5423 2^398877+105 120074 Donovan Johnson 01/2006 5422 (101*10^120072-87)/7 120074 Hans Havermann 02/2015 5424 (88^61751+1)/89 120072 Paul Bourdelais 09/2017 5425 U(686581)/4280145953 120067 Serge Batalov 07/2024 5426 2^398710+57 120024 Lelio R Paula 04/2013 5427 (2^398698+1138)/2 120020 Stefano Morozzi 09/2020 5428 2^398691-115057 120018 Enzo Doria 06/2015 5429 L(574219) 120005 Renaud Lifchitz 03/2004 5430 2^398571+60413 119982 Yves Minet 03/2011 5431 28623^15538+15538^28623 119971 Hans Havermann 02/2021 5432 p(24179)#/2-64 119949 Robert Price 04/2017 5433 2^398448+1872001 119945 Enzo Doria 05/2016 5434 (10^119946*19-91)/6093 119944 Alfred Reich 10/2023 5435 (19*10^119946-91)/9/677 119944 Alfred Reich 11/2023 5436 (191*10^119941-17)/3 119943 Robert Price 11/2021 5437 634^42803+42803^634 119938 Norbert Schneider 07/2019 5438 31083^7220+7220^31083 119935 Hans Havermann 01/2021 5439 (68*10^119931-11)/3 119933 Robert Price 01/2020 5440 8*10^119930-3 119931 Ray Chandler 04/2011 5441 (2^398398+774)/2 119930 Stefano Morozzi 09/2020 5442 (10^119880+179)/9 119880 Serge Batalov 12/2014 5443 (9*2^398145+1)/73 119853 Lelio R Paula 04/2014 5444 (10^119836+77)/3 119836 Robert Price 01/2018 5445 26681^27074-27074^26681 119835 Frank Doornink 03/2024 5446 28179^17870+17870^28179 119821 Hans Havermann 02/2021 5447 2^398029+1872527 119819 Enzo Doria 05/2016 5448 33142^4119+4119^33142 119802 Hans Havermann 01/2021 5449 2^397897-113541 119779 Enzo Doria 08/2014 5450 28636^15171+15171^28636 119728 Hans Havermann 02/2021 5451 (10556^29929-1)/(10556^173-1) 119724 Ryan Propper 11/2023 5452 (2^397696+1042)/2 119719 Stefano Morozzi 09/2020 5454 (19*10^119716+101)/3 119717 Robert Price 09/2019 5453 29563^11208+11208^29563 119717 Hans Havermann 02/2021 5455 2^397655-933075 119707 Paul Bourdelais 06/2021 5456 (21*2^397661-1)/27593 119705 Lelio R Paula 04/2014 5457 28243^17308+17308^28243 119701 Hans Havermann 02/2021 5458 77*10^119688+3 119690 Robert Price 06/2020 5459 586*25^85601+3717 119668 Eric Chen 10/2023 5460 (2^397504+1698)/2 119661 Stefano Morozzi 09/2020 5461 (58^67853-1)/57 119653 Paul Bourdelais 09/2017 5462 2^397426+73849 119638 Enzo Doria 04/2016 5463 8*10^119509+29 119510 Robert Price 11/2021 5464 2^396933-112723 119489 Enzo Doria 06/2014 5465 11^114738-150 119488 Enzo Doria 10/2012 5466 (4*10^119474+149)/9 119474 Robert Price 04/2018 5467 26964^26964-13^13 119472 Henri Lifchitz 08/2024 5468 2^396790-21 119446 Lelio R Paula 04/2013 5469 32061^5300+5300^32061 119405 Hans Havermann 01/2021 5470 (2^396633-7)/5 119398 Lelio R Paula 04/2014 5471 27382^22913+22913^27382 119388 Hans Havermann 03/2021 5472 (2^396577+2522)/2 119382 Stefano Morozzi 09/2020 5473 (2^396492+2230)/2 119356 Stefano Morozzi 01/2021 5474 (47*10^119354+259)/9 119355 Robert Price 03/2022 5476 105^59050+104 119352 Norbert Schneider 11/2016 5475 126^56824-125 119352 Norbert Schneider 12/2018 5477 2^396469+111546435 119350 Paul Bourdelais 10/2021 5478 139^55690-138 119345 Norbert Schneider 04/2019 5479 790^41179+41179^790 119322 Norbert Schneider 04/2019 5480 2^396374+73729 119321 Enzo Doria 04/2016 5481 88*10^119295+3 119297 Robert Price 05/2020 5482 2^396258-459491 119286 Enzo Doria 05/2015 5483 (2^396248+3126)/2 119283 Stefano Morozzi 09/2020 5484 2^396128-396128-1 119247 Karsten Bonath 06/2018 5485 (893*10^119228+7)/9 119230 Robert Price 06/2021 5486 (31*10^119229+257)/9 119230 Robert Price 12/2021 5487 (28*10^119206-67)/3 119207 Robert Price 10/2020 5488 (2^395986+5)/76881 119199 Lelio R Paula 04/2014 5489 11^114458+6 119196 Paul Bourdelais 02/2021 5490 (23*2^395942-1)/91 119190 Lelio R Paula 04/2014 5491 (2^395902+202)/2 119179 Stefano Morozzi 09/2020 5492 (2^395825+582)/2 119155 Stefano Morozzi 09/2020 5493 (2^395733+1130)/2 119128 Stefano Morozzi 09/2020 5494 29548^10725+10725^29548 119091 Hans Havermann 02/2021 5495 (11*2^395548+1)/3 119073 Lelio R Paula 04/2014 5496 (30^80599+1)/31 119054 Robert Price 07/2013 5497 (232*10^119047+17)/3 119049 Robert Price 04/2021 5498 (43*10^119024-403)/9 119025 Robert Price 01/2019 5499 (4*10^119021+47)/3 119022 Robert Price 01/2022 5500 fibonacci(569433)+3 119005 Jon Grantham 08/2023

Find by discoverer :

Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: September, 12 2024 08:27 (Time in France)

Go back