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) !!!
Submit your PRPs
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Rank |
Probable prime |
Digits (> 50000) |
Who ? |
When ? |
4251 | 27191^30560-30560^27191 | 135517 | Frank Doornink | 01/2024 |
4252 | 40387^2260+2260^40387 | 135463 | Hans Havermann | 12/2020 |
4253 | 2^449944-113247 | 135447 | Enzo Doria | 07/2014 |
4254 | 2^449770-113247 | 135395 | Enzo Doria | 07/2014 |
4255 | 2^449637-21471 | 135355 | Enzo Doria | 07/2013 |
4256 | 26061^30650-30650^26061 | 135351 | Frank Doornink | 03/2024 |
4257 | 2^449571-75 | 135335 | Lelio R Paula | 08/2017 |
4258 | (14*10^135301-53)/3 | 135302 | Robert Price | 12/2018 |
4259 | (3*2^449494+1)/61340334013 | 135301 | Lelio R Paula | 07/2015 |
4260 | (13*10^135279+437)/9 | 135280 | Robert Price | 04/2018 |
4261 | 2^449330-35 | 135262 | Lelio R Paula | 08/2017 |
4262 | (19*2^449325+1)/9 | 135261 | Lelio R Paula | 07/2015 |
4263 | (2709^39601+1)/(2709^199+1) | 135260 | Martin Hopf | 12/2023 |
4264 | (13*10^135184-43)/3 | 135185 | Robert Price | 11/2018 |
4265 | 2^449049-115309 | 135178 | Enzo Doria | 07/2015 |
4266 | (10^135174+191)/3 | 135174 | Robert Price | 02/2018 |
4267 | 2^449030-15 | 135172 | Lelio R Paula | 08/2017 |
4268 | (157*10^135151-1)/3 | 135153 | Robert Price | 01/2022 |
4269 | (2^448966+100280245065) | 135153 | Paul Bourdelais | 05/2022 |
4270 | (27*2^448936-1)/11 | 135144 | Lelio R Paula | 07/2015 |
4271 | (37*10^135099+251)/9 | 135100 | Robert Price | 09/2021 |
4272 | 32221^15586+15586^32221 | 135095 | Hans Havermann | 12/2020 |
4273 | 2^448762-351401 | 135091 | Enzo Doria | 07/2015 |
4274 | 2*10^135083-43 | 135084 | Robert Price | 04/2018 |
4275 | 31357^20278+20278^31357 | 135056 | Hans Havermann | 12/2020 |
4276 | 32242^15445+15445^32242 | 135055 | Hans Havermann | 12/2020 |
4277 | k(198476) | 135054 | Robert Price | 07/2020 |
4278 | 32461^14470+14470^32461 | 135053 | Hans Havermann | 12/2020 |
4279 | 31353^20288+20288^31353 | 135045 | Hans Havermann | 12/2020 |
4280 | 5*10^135019+77 | 135020 | Robert Price | 12/2018 |
4281 | (10^135011+719)/9 | 135011 | Serge Batalov | 12/2014 |
4282 | (197*10^134978+7)/3 | 134980 | Robert Price | 12/2020 |
4283 | 2^448386-2786261 | 134978 | Enzo Doria | 03/2016 |
4284 | 26480^30517-30517^26480 | 134975 | Frank Doornink | 03/2024 |
4285 | (73*10^134939+143)/9 | 134940 | Robert Price | 07/2019 |
4286 | 33957^9392+9392^33957 | 134903 | Hans Havermann | 12/2020 |
4287 | 2^448122+20809 | 134899 | Enzo Doria | 08/2023 |
4288 | 2^448113-113949 | 134896 | Enzo Doria | 11/2014 |
4289 | 30958^22755+22755^30958 | 134887 | Hans Havermann | 12/2020 |
4290 | 2^447888-2786639 | 134828 | Enzo Doria | 03/2016 |
4291 | 2^447870-396765 | 134823 | Enzo Doria | 07/2013 |
4292 | 10^(2*67404+1)-10^67404-1 | 134809 | Robert Price | 07/2023 |
4293 | 2^447766-21791 | 134791 | Enzo Doria | 07/2013 |
4294 | (19*10^134786-49)/3 | 134787 | Robert Price | 05/2019 |
4295 | Phi(202173,10)/10064306514895399941409 | 134758 | Makoto Kamada | 05/2019 |
4296 | (23*2^447647+1)/155 | 134755 | Lelio R Paula | 07/2015 |
4297 | 2^447552-1019 | 134727 | Yves Minet | 02/2014 |
4298 | (2*10^134720-41)/3 | 134720 | Robert Price | 02/2018 |
4299 | (25*10^134695-97)/9 | 134696 | Robert Price | 01/2022 |
4300 | 2^447437-113569 | 134692 | Enzo Doria | 08/2014 |
4301 | 2^447426-65 | 134689 | Lelio R Paula | 08/2017 |
4302 | 2^447357-2797573 | 134668 | Enzo Doria | 04/2016 |
4303 | 2^447278+93 | 134645 | Lelio R Paula | 08/2017 |
4304 | 33193^11370+11370^33193 | 134623 | Hans Havermann | 12/2020 |
4305 | 30736^23979+23979^30736 | 134619 | Hans Havermann | 11/2020 |
4306 | 2^447094-113193 | 134589 | Enzo Doria | 07/2014 |
4307 | 3^282041-9934 | 134568 | Enzo Doria | 05/2014 |
4308 | 2^447019-109039 | 134567 | Enzo Doria | 04/2014 |
4309 | 31376^19437+19437^31376 | 134561 | Hans Havermann | 12/2020 |
4310 | 2^446990-22041 | 134558 | Enzo Doria | 07/2013 |
4311 | 123^64370+122 | 134528 | Karsten Bonath | 04/2018 |
4312 | 30100^29461+29461^30100 | 134525 | Hans Havermann | 11/2020 |
4313 | 31251^20158+20158^31251 | 134519 | Hans Havermann | 11/2020 |
4314 | 2^446782-39701 | 134495 | Enzo Doria | 09/2015 |
4315 | 31817^16858+16858^31817 | 134485 | Hans Havermann | 12/2020 |
4316 | 32448^13937+13937^32448 | 134471 | Hans Havermann | 12/2020 |
4317 | 5^192321+3^192321-1 | 134427 | Jon Grantham | 08/2023 |
4318 | 2^446494-16485 | 134409 | Enzo Doria | 04/2013 |
4319 | 30042^29785+29785^30042 | 134408 | Hans Havermann | 12/2020 |
4320 | 29504^30069-30069^29504 | 134405 | Norbert Schneider | 12/2014 |
4321 | 2^446441+65 | 134393 | Lelio R Paula | 08/2017 |
4322 | (10^134385+719)/9 | 134385 | Serge Batalov | 12/2014 |
4323 | 30043^29688+29688^30043 | 134370 | Hans Havermann | 12/2020 |
4324 | (2*10^134364+529)/9 | 134364 | Robert Price | 01/2018 |
4325 | 34657^7512+7512^34657 | 134323 | Hans Havermann | 11/2020 |
4326 | (13*2^446187-1)/661 | 134314 | Lelio R Paula | 07/2015 |
4327 | 5^192103+3^192103+2^192103+1 | 134275 | Matthias Baur | 12/2019 |
4328 | 42035^1564+1564^42035 | 134270 | Hans Havermann | 12/2020 |
4330 | (2^446022-7)/339 | 134264 | Lelio R Paula | 07/2015 |
4329 | 30621^24248+24248^30621 | 134264 | Hans Havermann | 12/2020 |
4331 | 30341^26562+26562^30341 | 134237 | Hans Havermann | 11/2020 |
4332 | (189^58967-1)/188 | 134234 | Anonymous | 06/2024 |
4333 | 10^134209+99867 | 134210 | Patrick De Geest | 05/2021 |
4334 | 10^134209-80000001 | 134209 | Robert Price | 04/2021 |
4335 | 10^134209-323283 | 134209 | Patrick De Geest | 05/2021 |
4336 | 29976^29953+29953^29976 | 134186 | Hans Havermann | 12/2020 |
4337 | 35038^6755+6755^35038 | 134183 | Hans Havermann | 12/2020 |
4338 | 63^74568+2 | 134174 | Lelio R Paula | 06/2017 |
4339 | 2^445671-22071 | 134161 | Enzo Doria | 07/2013 |
4340 | 532^49205+49205^532 | 134129 | Norbert Schneider | 02/2019 |
4341 | 36453^4780+4780^36453 | 134127 | Hans Havermann | 04/2021 |
4342 | (28*10^134122-1)/9 | 134123 | Serge Batalov | 10/2014 |
4343 | 2^445515-113859 | 134114 | Enzo Doria | 10/2014 |
4345 | (22*10^134111-37)/3 | 134112 | Robert Price | 04/2019 |
4344 | 31083^20636+20636^31083 | 134112 | Hans Havermann | 04/2021 |
4346 | 3*2^445478+5 | 134103 | Jon Grantham | 07/2023 |
4347 | 31622^17379+17379^31622 | 134079 | Hans Havermann | 04/2021 |
4348 | 5*2^445380-3 | 134074 | Jon Grantham | 07/2023 |
4349 | (6*32^89076+4241)/31 | 134073 | Eric Chen | 11/2023 |
4350 | (277*10^134059-7)/9 | 134061 | Robert Price | 02/2022 |
4351 | 2^445328-216917 | 134058 | Enzo Doria | 05/2014 |
4352 | 2^445202+1874899 | 134020 | Enzo Doria | 06/2016 |
4353 | 5^191739-3^191739-1 | 134020 | Jon Grantham | 08/2023 |
4354 | (35*10^134003-89)/9 | 134004 | Robert Price | 02/2022 |
4355 | (13*2^445102+1)/17 | 133989 | Lelio R Paula | 07/2015 |
4356 | (35*10^133979-593)/9 | 133980 | Robert Price | 07/2018 |
4357 | 2*10^133955+51 | 133956 | Robert Price | 05/2018 |
4358 | (49*10^133952+437)/9 | 133953 | Robert Price | 09/2021 |
4359 | 2^444964-113639 | 133948 | Enzo Doria | 08/2014 |
4360 | 31811^16240+16240^31811 | 133943 | Hans Havermann | 04/2021 |
4361 | 10^133902+167841 | 133903 | Patrick De Geest | 05/2021 |
4363 | 28118^30097-30097^28118 | 133902 | Norbert Schneider | 01/2015 |
4362 | 10^133902-100001 | 133902 | Robert Price | 07/2020 |
4364 | 2^444784-113859 | 133894 | Enzo Doria | 10/2014 |
4365 | (132^63127-1)/131 | 133864 | Anonymous | 06/2024 |
4366 | 32303^13914+13914^32303 | 133846 | Hans Havermann | 04/2021 |
4367 | (2276213*2^444444+1)/3 | 133797 | Alex_soldier | 11/2022 |
4368 | (1403559*2^444444+1)/5 | 133797 | Alex_soldier | 11/2022 |
4369 | (1209887*2^444444+1)/9 | 133797 | Alex_soldier | 11/2022 |
4370 | (608239*2^444444+1)/25 | 133796 | Alex_soldier | 11/2022 |
4371 | (1824587*2^444444+1)/27 | 133796 | Alex_soldier | 11/2022 |
4372 | (40795*2^444444+1)/7 | 133795 | Alex_soldier | 11/2022 |
4373 | 30739^22458+22458^30739 | 133757 | Hans Havermann | 04/2021 |
4374 | 34942^6721+6721^34942 | 133739 | Hans Havermann | 04/2021 |
4375 | (2^444046+100280245065) | 133672 | Paul Bourdelais | 05/2022 |
4376 | 34792^6935+6935^34792 | 133638 | Hans Havermann | 04/2021 |
4377 | (266*10^133603+1)/3 | 133605 | Robert Price | 04/2020 |
4378 | 32261^13842+13842^32261 | 133600 | Hans Havermann | 04/2021 |
4379 | (89*10^133580+1)/9 | 133581 | Serge Batalov | 05/2010 |
4380 | (134*10^133573-11)/3 | 133575 | Robert Price | 01/2022 |
4381 | 26726^30173-30173^26726 | 133574 | Frank Doornink | 03/2024 |
4382 | 62^74521-61^74521 | 133571 | Robert Price | 05/2013 |
4383 | (182*10^133543+1)/3 | 133545 | Robert Price | 02/2020 |
4384 | (103*10^133535+11)/3 | 133537 | Robert Price | 01/2021 |
4385 | 32589^12520+12520^32589 | 133537 | Hans Havermann | 03/2021 |
4386 | L(638839)/274700771 | 133502 | Serge Batalov | 07/2024 |
4387 | 34516^7373+7373^34516 | 133496 | Hans Havermann | 04/2021 |
4388 | 8*10^133487-37 | 133488 | Robert Price | 03/2022 |
4389 | 30135^26882+26882^30135 | 133482 | Hans Havermann | 04/2021 |
4390 | 2^443198-1867301 | 133416 | Enzo Doria | 03/2016 |
4391 | (19*10^133390+101)/3 | 133391 | Robert Price | 09/2019 |
4392 | (71^72043-1)/70 | 133369 | Paul Bourdelais | 09/2017 |
4393 | 36117^4910+4910^36117 | 133311 | Hans Havermann | 04/2021 |
4394 | 2^442799+1874633 | 133296 | Enzo Doria | 06/2016 |
4395 | L(637751) | 133283 | Henri Lifchitz | 09/2008 |
4396 | 109^65410-2 | 133269 | Lelio R Paula | 10/2017 |
4397 | 2^442688-113489 | 133263 | Enzo Doria | 08/2014 |
4398 | (7*2^442640-1)/783 | 133246 | Lelio R Paula | 07/2015 |
4399 | (9*2^442463+1)/17441 | 133192 | Lelio R Paula | 07/2015 |
4400 | 2^442437-1849993 | 133187 | Enzo Doria | 08/2015 |
4401 | 2^442430-2791721 | 133185 | Enzo Doria | 03/2016 |
4402 | (13*2^442428-1)/309 | 133183 | Lelio R Paula | 07/2015 |
4403 | 29959^27870+27870^29959 | 133172 | Hans Havermann | 03/2021 |
4404 | (25*2^442379-1)/71 | 133169 | Lelio R Paula | 07/2015 |
4405 | 2^442368+213691 | 133167 | Enzo Doria | 09/2023 |
4406 | 34240^7737+7737^34240 | 133145 | Hans Havermann | 03/2021 |
4407 | 452^50145+50145^452 | 133142 | Norbert Schneider | 09/2020 |
4408 | 30659^21796+21796^30659 | 133011 | Hans Havermann | 04/2021 |
4409 | 33276^9935+9935^33276 | 133010 | Hans Havermann | 04/2021 |
4410 | 30111^26122+26122^30111 | 133001 | Hans Havermann | 04/2021 |
4411 | 30790^20869+20869^30790 | 132998 | Hans Havermann | 04/2021 |
4413 | (2^441799+78557)/5 | 132995 | Lelio R Paula | 07/2015 |
4412 | 8*10^132994-27 | 132995 | Robert Price | 10/2021 |
4414 | (109*10^132992+11)/3 | 132994 | Robert Price | 06/2022 |
4415 | 2^441781-2787883 | 132990 | Enzo Doria | 03/2016 |
4416 | fibonacci(636232)+4 | 132965 | Jon Grantham | 08/2023 |
4417 | (3*2^441685+1)/749 | 132959 | Lelio R Paula | 07/2015 |
4418 | 2^441618+37 | 132941 | Lelio R Paula | 08/2017 |
4419 | 34857^6514+6514^34857 | 132940 | Hans Havermann | 04/2021 |
4420 | 34065^7988+7988^34065 | 132937 | Hans Havermann | 04/2021 |
4421 | 35571^5452+5452^35571 | 132914 | Hans Havermann | 04/2021 |
4422 | 2^441521-113575 | 132912 | Enzo Doria | 08/2014 |
4423 | 7*10^132884-99 | 132885 | Robert Price | 06/2019 |
4424 | 26987^29988-29988^26987 | 132882 | Frank Doornink | 03/2024 |
4425 | (103*10^132879+17)/3 | 132881 | Robert Price | 08/2020 |
4426 | 2^441396-65 | 132874 | Lelio R Paula | 08/2017 |
4427 | 33350^9633+9633^33350 | 132859 | Hans Havermann | 04/2021 |
4428 | 2^441330+1871959 | 132854 | Enzo Doria | 05/2016 |
4429 | 25772^30111-30111^25772 | 132825 | Frank Doornink | 02/2024 |
4430 | 2^441063+383 | 132774 | Lelio R Paula | 06/2012 |
4431 | (10^132753+7)/17/19 | 132751 | Alfred Reich | 06/2021 |
4432 | (22*10^132746+53)/3 | 132747 | Robert Price | 07/2019 |
4433 | (77*10^132744-149)/9 | 132745 | Robert Price | 03/2022 |
4434 | (22*10^132732+119)/3 | 132733 | Robert Price | 04/2021 |
4435 | 2^440846+1870909 | 132708 | Enzo Doria | 05/2016 |
4436 | (948^44579-1)/947 | 132701 | Jinyuan Wang | 04/2023 |
4437 | 2^440656-113489 | 132651 | Enzo Doria | 08/2014 |
4438 | numbpart(14180123587) | 132646 | Serge Batalov | 04/2017 |
4439 | 32950^10591+10591^32950 | 132622 | Hans Havermann | 04/2021 |
4440 | 33302^9597+9597^33302 | 132614 | Hans Havermann | 04/2021 |
4441 | (19*10^132550+191)/3 | 132551 | Robert Price | 05/2019 |
4442 | (2^440399-1)/(16210820281161978209*31518475633*880799) | 132538 | Dario Alpern | 01/2015 |
4443 | (38^83891+1)/39 | 132529 | Robert Price | 09/2013 |
4444 | 2*10^132493-43 | 132494 | Robert Price | 04/2018 |
4445 | 31352^16809+16809^31352 | 132480 | Hans Havermann | 04/2021 |
4446 | (418*10^132441+23)/9 | 132443 | Robert Price | 02/2020 |
4447 | 2^439931-21 | 132433 | Lelio R Paula | 08/2017 |
4448 | 47^79201-46^79201 | 132432 | Robert Price | 10/2012 |
4449 | 2^439897-113653 | 132423 | Enzo Doria | 08/2014 |
4450 | 35505^5362+5362^35505 | 132410 | Hans Havermann | 03/2021 |
4451 | 30079^25222+25222^30079 | 132402 | Hans Havermann | 04/2021 |
4452 | (5*2^439822+1)/9 | 132400 | Lelio R Paula | 06/2015 |
4453 | (695*10^132356+7)/9 | 132358 | Robert Price | 12/2021 |
4454 | (112*10^132337-1)/3 | 132339 | Serge Batalov | 12/2014 |
4455 | 2^439576-113247 | 132326 | Enzo Doria | 07/2014 |
4456 | 30059^25230+25230^30059 | 132318 | Hans Havermann | 04/2021 |
4457 | 2^439497-29143 | 132302 | Enzo Doria | 07/2015 |
4458 | 2^439409-114193 | 132276 | Enzo Doria | 12/2014 |
4459 | (44*10^132233-233)/9 | 132234 | Robert Price | 01/2019 |
4460 | 25507^30000-30000^25507 | 132200 | Frank Doornink | 02/2024 |
4461 | 9*10^132148-7 | 132149 | Robert Price | 09/2015 |
4462 | (47*10^132125-119)/9 | 132126 | Robert Price | 05/2019 |
4463 | 2^438900+214051 | 132123 | Enzo Doria | 10/2023 |
4464 | 2^438845+1870217 | 132106 | Enzo Doria | 05/2016 |
4465 | 2^438789+87855 | 132089 | Lelio R Paula | 01/2016 |
4466 | 2^438774-2786411 | 132085 | Enzo Doria | 03/2016 |
4467 | 2^438755-1848205 | 132079 | Enzo Doria | 07/2015 |
4468 | 30502^21381+21381^30502 | 132075 | Hans Havermann | 04/2021 |
4469 | 2^438739-112087 | 132074 | Enzo Doria | 06/2014 |
4470 | (2^438438+100280245065) | 131983 | Paul Bourdelais | 05/2022 |
4471 | 35872^4777+4777^35872 | 131979 | Hans Havermann | 04/2021 |
4472 | 31198^16945+16945^31198 | 131938 | Hans Havermann | 03/2021 |
4473 | 13907#+(318259#)/(13907#) | 131923 | Makoto Morimoto | 10/2017 |
4474 | L(631181) | 131910 | Henri Lifchitz | 09/2008 |
4475 | (47*10^131886-119)/9 | 131887 | Robert Price | 05/2019 |
4476 | 5*2^438096-3 | 131881 | Jon Grantham | 07/2023 |
4477 | (3*2^438121+1)/4308193883 | 131879 | Lelio R Paula | 06/2015 |
4478 | 2^438079-1863877 | 131875 | Enzo Doria | 03/2016 |
4479 | (16*10^131872-37)/3 | 131873 | Robert Price | 05/2021 |
4480 | (2^438067+5)/329 | 131869 | Lelio R Paula | 06/2015 |
4481 | 2^437908-113855 | 131824 | Enzo Doria | 09/2014 |
4482 | 2^437884-286349 | 131817 | Enzo Doria | 07/2015 |
4483 | 15^112072+14 | 131807 | Alfred Reich | 10/2023 |
4484 | 5^188558+4 | 131797 | Tyler NeSmith | 05/2021 |
4485 | (11*10^131784-17)/3 | 131785 | Robert Price | 06/2018 |
4486 | (166^59357-1)/165 | 131777 | Anonymous | 06/2024 |
4488 | 4*10^131719-93 | 131720 | Robert Price | 07/2020 |
4487 | 31629^14606+14606^31629 | 131720 | Hans Havermann | 04/2021 |
4489 | 3^276062-112292 | 131716 | Enzo Doria | 07/2014 |
4490 | 11*31^88313+322688 | 131708 | Eric Chen | 05/2024 |
4491 | (7*10^131682+89)/3 | 131683 | Robert Price | 08/2020 |
4492 | 29512^28969+28969^29512 | 131681 | Hans Havermann | 03/2021 |
4493 | 2^437343+75953 | 131654 | Enzo Doria | 04/2016 |
4494 | 35^85243-34^85243 | 131621 | Robert Price | 05/2012 |
4495 | (28*10^131586+59)/3 | 131587 | Robert Price | 05/2021 |
4496 | (59*10^131575+391)/9 | 131576 | Robert Price | 03/2021 |
4497 | 39984^1945+1945^39984 | 131505 | Hans Havermann | 03/2021 |
4498 | 25842^29801-29801^25842 | 131492 | Frank Doornink | 03/2024 |
4499 | 28592^29505-29505^28592 | 131482 | Frank Doornink | 05/2024 |
4500 | 25647^29818-29818^25647 | 131469 | Frank Doornink | 02/2024 |