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
See the Top discoverers
See the Latest PRPs
Search by form
| Rank |
Probable prime |
Digits (> 50000) |
Who ? |
When ? |
| 4251 | 2^510448+24991 | 153661 | Enzo Doria | 11/2023 |
| 4252 | 2^510420+81121 | 153652 | Enzo Doria | 07/2016 |
| 4253 | (197*7^181761-1)/2 | 153608 | Karsten Bonath | 05/2017 |
| 4254 | 2^509894-459161 | 153494 | Enzo Doria | 05/2015 |
| 4255 | (74*10^153489+673)/9 | 153490 | Robert Price | 02/2022 |
| 4256 | (49*10^153484-211)/9 | 153485 | Robert Price | 06/2022 |
| 4257 | 2^509841+71657 | 153478 | Enzo Doria | 04/2016 |
| 4258 | 9*10^153446+41 | 153447 | Robert Price | 08/2020 |
| 4259 | 2^509533-1846723 | 153385 | Enzo Doria | 07/2015 |
| 4260 | 2^509468-39989 | 153366 | Enzo Doria | 09/2015 |
| 4261 | 70^83117-69^83117 | 153360 | Robert Price | 01/2014 |
| 4262 | (209246*34^99997-81)/11 | 153148 | Eric Chen | 08/2023 |
| 4263 | (7*10^153116-1)/3 | 153117 | Robert Price | 08/2022 |
| 4264 | (112*10^153025-1)/3 | 153027 | Serge Batalov | 12/2014 |
| 4265 | 31912^33975-33975^31912 | 153022 | Frank Doornink | 01/2024 |
| 4266 | (19*10^153010+131)/3 | 153011 | Robert Price | 06/2020 |
| 4267 | 2^508174-1855151 | 152976 | Enzo Doria | 09/2015 |
| 4268 | 181^67757-2 | 152974 | Lelio R Paula | 12/2017 |
| 4269 | 2^508160-1864829 | 152972 | Enzo Doria | 01/2016 |
| 4270 | 10^152960+412563 | 152961 | Patrick De Geest | 05/2021 |
| 4271 | 10^152960-50000000001 | 152960 | Robert Price | 12/2020 |
| 4272 | 10^152960-423749 | 152960 | Patrick De Geest | 05/2021 |
| 4273 | (71*10^152933-143)/9 | 152934 | Robert Price | 10/2021 |
| 4274 | 32109^33932-33932^32109 | 152919 | Frank Doornink | 02/2024 |
| 4275 | 2^507857-1848199 | 152881 | Enzo Doria | 07/2015 |
| 4276 | 2^507638-115361 | 152815 | Enzo Doria | 07/2015 |
| 4277 | 2^507551-114025 | 152789 | Enzo Doria | 11/2014 |
| 4278 | (6^196337+1)/7 | 152780 | Paul Bourdelais | 02/2010 |
| 4279 | (22*10^152670-13)/9 | 152671 | Robert Price | 06/2018 |
| 4280 | 86*17^124075+13 | 152670 | Eric Chen | 01/2026 |
| 4281 | 2^507085+28517 | 152648 | Enzo Doria | 01/2024 |
| 4282 | 2^506917+28847 | 152598 | Enzo Doria | 02/2024 |
| 4283 | 2^506451-22339 | 152457 | Enzo Doria | 07/2013 |
| 4284 | 26463^34460-34460^26463 | 152405 | Frank Doornink | 03/2024 |
| 4285 | 31898^33837-33837^31898 | 152394 | Frank Doornink | 01/2024 |
| 4286 | 2^505995-113185 | 152320 | Enzo Doria | 07/2014 |
| 4287 | (8*10^152260-17)/9 | 152260 | Serge Batalov | 11/2022 |
| 4288 | (4*10^152253+149)/9 | 152253 | Robert Price | 04/2018 |
| 4289 | 33530^33643-33643^33530 | 152250 | Norbert Schneider | 04/2024 |
| 4290 | 578^55117-577^55117 | 152230 | Jean-Louis Charton | 08/2012 |
| 4291 | 2^505431-505431 | 152150 | Henri Lifchitz | 04/2005 |
| 4292 | (203*10^152143+1)/3 | 152145 | Robert Price | 03/2020 |
| 4293 | 31730^33787-33787^31730 | 152092 | Frank Doornink | 01/2024 |
| 4294 | 2^505089+217787 | 152047 | Enzo Doria | 01/2024 |
| 4295 | 33565^33594-33594^33565 | 152043 | Norbert Schneider | 04/2024 |
| 4296 | 2^505053+73097 | 152037 | Enzo Doria | 04/2016 |
| 4297 | 22*10^151998+3 | 152000 | Robert Price | 01/2020 |
| 4298 | (238*10^151979-1)/3 | 151981 | Robert Price | 04/2020 |
| 4299 | (2^504793-7)/46765 | 151954 | Lelio R Paula | 12/2017 |
| 4300 | 3^318465+4 | 151947 | Aurel Gibier | 09/2024 |
| 4301 | 350377#+797581 | 151937 | Nicolas PALAU | 08/2017 |
| 4302 | Phi(97785,1105) | 151925 | Henri Lifchitz | 12/2025 |
| 4303 | (79*10^151906-529)/9 | 151907 | Robert Price | 01/2022 |
| 4304 | 2^504618-343991 | 151906 | Enzo Doria | 07/2015 |
| 4305 | 2^504259+211193 | 151798 | Enzo Doria | 08/2023 |
| 4306 | 2^504212-461939 | 151783 | Enzo Doria | 07/2015 |
| 4307 | 7*10^151772-41 | 151773 | Robert Price | 08/2021 |
| 4308 | (47^90749-4^90749)/43 | 151740 | Robert Price | 12/2025 |
| 4309 | 2^504054-2231 | 151736 | Yves Minet | 10/2011 |
| 4310 | 25237^34458-34458^25237 | 151686 | Frank Doornink | 11/2023 |
| 4311 | (28*10^151682+191)/3 | 151683 | Robert Price | 02/2020 |
| 4312 | 2^503817+23961 | 151665 | Enzo Doria | 10/2023 |
| 4313 | 2^503475-933075 | 151562 | Paul Bourdelais | 06/2021 |
| 4314 | 2^503371+26289 | 151530 | Enzo Doria | 12/2023 |
| 4315 | 2^503361-39883 | 151527 | Enzo Doria | 09/2015 |
| 4316 | 2^503225+382667 | 151486 | Enzo Doria | 10/2016 |
| 4317 | (206*10^151483-11)/3 | 151485 | Robert Price | 02/2022 |
| 4318 | (844*10^151396-7)/9 | 151398 | Robert Price | 05/2021 |
| 4319 | (26*10^151391-503)/9 | 151392 | Robert Price | 07/2018 |
| 4320 | 2^502769+1877567 | 151349 | Enzo Doria | 08/2016 |
| 4321 | 2^502576-4019 | 151291 | Yves Minet | 10/2011 |
| 4322 | 5*10^151257+41 | 151258 | Robert Price | 03/2019 |
| 4323 | 2^502290-2792501 | 151205 | Enzo Doria | 02/2016 |
| 4324 | 17015^35734+35734^17015 | 151185 | Norbert Schneider | 12/2025 |
| 4325 | 2^502181+1868417 | 151172 | Enzo Doria | 04/2016 |
| 4326 | 2^502055+22583 | 151134 | Enzo Doria | 09/2023 |
| 4327 | (3*23^110967+41)/22 | 151106 | Anonymous | 12/2023 |
| 4328 | 6*10^151063-77 | 151064 | Robert Price | 09/2021 |
| 4329 | 2^501781-1850503 | 151052 | Enzo Doria | 08/2015 |
| 4330 | (2^82589933-1)%(10^151020) | 151020 | Anonymous | 05/2025 |
| 4331 | (5*10^151007+37)/3 | 151008 | Robert Price | 03/2018 |
| 4332 | 3^316494+5*2^316494 | 151007 | Jon Grantham | 08/2023 |
| 4333 | 2^501627-991 | 151005 | Yves Minet | 02/2014 |
| 4334 | 2^501577-115333 | 150990 | Enzo Doria | 07/2015 |
| 4335 | 25239^34298-34298^25239 | 150983 | Frank Doornink | 12/2023 |
| 4336 | (19*10^150977-7)/3 | 150978 | Robert Price | 12/2023 |
| 4337 | 8*10^150975+3 | 150976 | Robert Price | 08/2015 |
| 4338 | 2^501512-113669 | 150971 | Enzo Doria | 09/2014 |
| 4339 | 34180^26101+26101^34180 | 150962 | Norman Luhn | 04/2024 |
| 4340 | U(1083477)/2166953 | 150949 | Serge Batalov | 07/2024 |
| 4341 | (83*10^150908+493)/9 | 150909 | Robert Price | 12/2021 |
| 4342 | 36267^14482+14482^36267 | 150901 | Norman Luhn | 04/2024 |
| 4343 | 2*10^150818+83 | 150819 | Robert Price | 12/2021 |
| 4344 | 48753^1240+1240^48753 | 150814 | Norman Luhn | 04/2024 |
| 4345 | (12^139739+1)/13 | 150803 | Paul Bourdelais | 09/2011 |
| 4346 | (31^101111-1)/30 | 150792 | Alexander Zhirkov | 11/2010 |
| 4347 | 2^500899-500899 | 150786 | Henri Lifchitz | 04/2005 |
| 4348 | 2^500832+1876801 | 150766 | Enzo Doria | 07/2016 |
| 4349 | (23*10^150763-59)/9 | 150764 | Robert Price | 05/2018 |
| 4350 | 46002^1891+1891^46002 | 150735 | Norman Luhn | 04/2024 |
| 4351 | 32001^33458-33458^32001 | 150734 | Frank Doornink | 01/2024 |
| 4352 | 2^500699+1884953 | 150726 | Enzo Doria | 02/2017 |
| 4353 | (13*10^150675-37)/3 | 150676 | Robert Price | 01/2019 |
| 4354 | (2^500527+lucasV(1,2,500527)+1)/4 | 150674 | Mike Oakes | 11/2016 |
| 4355 | 35365^18204+18204^35365 | 150661 | Norman Luhn | 05/2024 |
| 4357 | 2^500337-71101 | 150617 | Enzo Doria | 04/2016 |
| 4356 | (74*10^150616+133)/9 | 150617 | Robert Price | 06/2019 |
| 4358 | (2*10^150612-17)/3 | 150612 | Serge Batalov | 11/2022 |
| 4359 | 4*10^150577+91 | 150578 | Robert Price | 08/2018 |
| 4360 | 5649^40132+40132^5649 | 150575 | Norbert Schneider | 04/2024 |
| 4361 | 2^500160+80071 | 150564 | Enzo Doria | 06/2016 |
| 4362 | (2^500120+5)/9 | 150551 | Lelio R Paula | 12/2017 |
| 4364 | (43*10^150515-421)/9 | 150516 | Robert Price | 01/2019 |
| 4363 | 4695^40994+40994^4695 | 150516 | Norbert Schneider | 11/2023 |
| 4365 | 2^499999+15981 | 150515 | Norman Luhn | 08/2023 |
| 4366 | (10^150551-1)/9/385207015049/57498437921/7808738631274081 | 150512 | Maksym Voznyy | 08/2014 |
| 4367 | (10^150551-1)/1556587827131683185788921941743157225041 | 150512 | Robert Price | 07/2016 |
| 4368 | 26614^34005-34005^26614 | 150476 | Frank Doornink | 03/2024 |
| 4369 | 2^499861-29503 | 150474 | Enzo Doria | 08/2015 |
| 4370 | Phi(64793,-7#) | 150462 | Henri Lifchitz | 12/2025 |
| 4371 | 2^499653-113533 | 150411 | Enzo Doria | 08/2014 |
| 4372 | (14*10^150391-191)/3 | 150392 | Robert Price | 10/2020 |
| 4373 | 29033^33696+33696^29033 | 150382 | Norbert Schneider | 10/2023 |
| 4374 | 2^499534-221 | 150375 | Yves Minet | 06/2012 |
| 4375 | 30110^33567+33567^30110 | 150337 | Norbert Schneider | 10/2023 |
| 4376 | 26212^34023-34023^26212 | 150331 | Frank Doornink | 03/2024 |
| 4377 | (28*10^150294+41)/3 | 150295 | Robert Price | 07/2021 |
| 4378 | 2^499225+49727 | 150282 | Enzo Doria | 09/2016 |
| 4379 | (695*10^150274+7)/9 | 150276 | Robert Price | 12/2021 |
| 4380 | 2^499054-29261 | 150231 | Enzo Doria | 07/2015 |
| 4381 | 18580^35187+35187^18580 | 150215 | Norbert Schneider | 10/2023 |
| 4382 | (844*10^150196-7)/9 | 150198 | Robert Price | 05/2021 |
| 4383 | 2^498907-933075 | 150186 | Paul Bourdelais | 06/2021 |
| 4384 | (2^498898-7)/9 | 150183 | Lelio R Paula | 10/2015 |
| 4385 | 3*10^150182+17 | 150183 | Robert Price | 07/2018 |
| 4386 | 5*10^150175+63 | 150176 | Robert Price | 09/2020 |
| 4387 | 29273^33618-33618^29273 | 150154 | Frank Doornink | 06/2024 |
| 4388 | 32363^33292+33292^32363 | 150149 | Norbert Schneider | 07/2022 |
| 4389 | 32^99753-99753^32 | 150144 | Henri Lifchitz | 08/2024 |
| 4390 | (77*10^150128+67)/9 | 150129 | Robert Price | 12/2021 |
| 4391 | (7*10^(2*75062+1)-9*10^75062-7)/9 | 150125 | Robert Price | 12/2023 |
| 4392 | 2^498623+1866983 | 150101 | Enzo Doria | 03/2016 |
| 4393 | 33194^33194-213^213 | 150073 | Serge Batalov | 04/2024 |
| 4394 | 27868^33759-33759^27868 | 150063 | Frank Doornink | 06/2024 |
| 4395 | (25*10^150050-403)/9 | 150051 | Robert Price | 12/2020 |
| 4396 | numbpart(18140942830) | 150033 | Serge Batalov | 04/2017 |
| 4397 | 10^150029+4381 | 150030 | Patrick De Geest | 05/2016 |
| 4398 | 10^150029-41 | 150029 | Serge Batalov | 12/2014 |
| 4399 | 33185^33185+618^618 | 150028 | Serge Batalov | 04/2024 |
| 4400 | 9*34^97952+529 | 150013 | Eric Chen | 08/2023 |
| 4401 | 10^150000+1158603 | 150001 | Patrick De Geest | 09/2018 |
| 4402 | 10^150000-245703 | 150000 | Patrick De Geest | 09/2018 |
| 4403 | (38*10^149999+691)/9 | 150000 | Robert Price | 10/2018 |
| 4404 | 2043563126843649194^8192+2043563126843649185^8192 | 150000 | Youcef Lemsafer | 01/2023 |
| 4405 | (2043563126843649232^8192+2043563126843649201^8192)/147457 | 149994 | Youcef Lemsafer | 01/2023 |
| 4406 | 2^498238-53 | 149985 | Lelio R Paula | 12/2017 |
| 4407 | 45728^1905+1905^45728 | 149984 | Hans Havermann | 10/2020 |
| 4408 | (211^65024+1)/(211^512+1) | 149945 | Martin Hopf | 12/2023 |
| 4409 | 5*10^149907+23 | 149908 | Robert Price | 03/2019 |
| 4410 | 32^99585-829 | 149891 | Eric Chen | 11/2023 |
| 4411 | 39347^6442+6442^39347 | 149874 | Hans Havermann | 09/2020 |
| 4412 | 2^497850+81049 | 149868 | Enzo Doria | 07/2016 |
| 4413 | V(1075416) | 149830 | Serge Batalov | 07/2024 |
| 4414 | 37228^10575+10575^37228 | 149816 | Hans Havermann | 10/2020 |
| 4415 | (5*2^497673+1)/2743 | 149812 | Lelio R Paula | 10/2015 |
| 4416 | (5*2^497671+1)/373703 | 149810 | Lelio R Paula | 10/2015 |
| 4417 | (2*10^149803-143)/3 | 149803 | Robert Price | 03/2018 |
| 4418 | 33845^26604+26604^33845 | 149763 | Hans Havermann | 09/2020 |
| 4419 | 2^497434-2784191 | 149743 | Enzo Doria | 10/2015 |
| 4420 | (865*10^149737-1)/9 | 149739 | Robert Price | 04/2020 |
| 4421 | 10^149695-7000001 | 149695 | Robert Price | 06/2021 |
| 4422 | 38237^8214+8214^38237 | 149681 | Hans Havermann | 09/2020 |
| 4423 | Phi(745791,2)/1491583 | 149664 | Anonymous | 03/2025 |
| 4424 | (497167*2^497167-1)/70975 | 149664 | Anonymous | 04/2025 |
| 4425 | (23*10^149655+19)/3 | 149656 | Robert Price | 07/2019 |
| 4426 | 2^497068-113579 | 149633 | Enzo Doria | 08/2014 |
| 4427 | 2^497037+73727 | 149624 | Enzo Doria | 04/2016 |
| 4428 | 11*10^149618+3 | 149620 | Robert Price | 07/2021 |
| 4429 | 34942^19067+19067^34942 | 149562 | Hans Havermann | 09/2020 |
| 4430 | 33696^27449+27449^33696 | 149561 | Hans Havermann | 09/2020 |
| 4431 | 2^496773+77747 | 149544 | Enzo Doria | 05/2016 |
| 4432 | 29937^33400-33400^29937 | 149506 | Frank Doornink | 06/2024 |
| 4433 | (7*10^149483-493)/9 | 149483 | Robert Price | 04/2021 |
| 4434 | (206*10^149459+7)/3 | 149461 | Robert Price | 07/2020 |
| 4435 | 34589^20940+20940^34589 | 149459 | Hans Havermann | 09/2020 |
| 4436 | 2^496477-113485 | 149455 | Enzo Doria | 08/2014 |
| 4437 | (496423*2^496423-1)/223573 | 149439 | Anonymous | 04/2025 |
| 4438 | 3*2^496411-5 | 149436 | Jon Grantham | 07/2023 |
| 4439 | ((10^74703-1)*10000/9+7481)*10^74703+(10^74703-1)/9 | 149410 | Hans Havermann | 09/2019 |
| 4440 | 2^496270-49451 | 149393 | Enzo Doria | 10/2015 |
| 4441 | 2^496238-1865081 | 149383 | Enzo Doria | 01/2016 |
| 4442 | 33831^26030+26030^33831 | 149380 | Hans Havermann | 09/2020 |
| 4443 | 34131^23780+23780^34131 | 149365 | Hans Havermann | 09/2020 |
| 4444 | (5*10^149335-53)/3 | 149336 | Robert Price | 09/2020 |
| 4445 | 26043^33818-33818^26043 | 149330 | Frank Doornink | 03/2024 |
| 4446 | 2^495968-1853699 | 149302 | Enzo Doria | 09/2015 |
| 4447 | 2^495935-4117 | 149292 | Yves Minet | 02/2018 |
| 4448 | 5*2^495930+3 | 149291 | Jon Grantham | 07/2023 |
| 4449 | 35816^14709+14709^35816 | 149267 | Hans Havermann | 09/2020 |
| 4450 | (10^149264+7)/191/2683/80557 | 149254 | Alfred Reich | 07/2021 |
| 4451 | 3^312800+6560 | 149244 | Alfred Reich | 04/2026 |
| 4452 | 10^149240-40000001 | 149240 | Robert Price | 07/2022 |
| 4453 | 10^149240-10809 | 149240 | Alfred Reich | 08/2024 |
| 4454 | 2^495712-396765 | 149225 | Enzo Doria | 07/2013 |
| 4455 | (21*2^495676-1)/4835 | 149211 | Lelio R Paula | 10/2015 |
| 4456 | 2^495420+1880701 | 149137 | Enzo Doria | 10/2016 |
| 4457 | 25646^33823-33823^25646 | 149127 | Frank Doornink | 02/2024 |
| 4458 | 2^495337-1847293 | 149112 | Enzo Doria | 07/2015 |
| 4459 | (2^495193-7)/5 | 149068 | Lelio R Paula | 10/2015 |
| 4460 | 2^495163+111546435 | 149059 | Paul Bourdelais | 10/2021 |
| 4461 | 33282^30097+30097^33282 | 149055 | Hans Havermann | 09/2020 |
| 4462 | 37384^9705+9705^37384 | 149050 | Hans Havermann | 09/2020 |
| 4463 | 34808^19143+19143^34808 | 149049 | Hans Havermann | 09/2020 |
| 4464 | 413^56963-412^56963 | 149013 | Jean-Louis Charton | 08/2012 |
| 4465 | 30657^33212-33212^30657 | 149007 | Frank Doornink | 06/2024 |
| 4466 | 47^89113-46^89113 | 149006 | Robert Price | 10/2012 |
| 4467 | V(891190) | 148997 | Serge Batalov | 07/2024 |
| 4468 | 2^494916+87855 | 148985 | Lelio R Paula | 01/2016 |
| 4469 | 6*10^148982+73 | 148983 | Robert Price | 04/2019 |
| 4470 | 3^312155-4 | 148936 | Anonymous | 02/2023 |
| 4471 | 10^148934+1530019 | 148935 | Patrick De Geest | 02/2021 |
| 4472 | 10^148934-1000000001 | 148934 | Robert Price | 11/2020 |
| 4473 | 10^148934-512057 | 148934 | Patrick De Geest | 02/2021 |
| 4474 | 39000^6571+6571^39000 | 148888 | Hans Havermann | 10/2020 |
| 4475 | 2^494586-2791991 | 148886 | Enzo Doria | 02/2016 |
| 4476 | Phi(117375,3^5) | 148862 | Henri Lifchitz | 12/2025 |
| 4477 | 8*10^148860-3 | 148861 | Ray Chandler | 04/2011 |
| 4478 | 38262^7769+7769^38262 | 148854 | Hans Havermann | 10/2020 |
| 4479 | 10^148816-500001 | 148816 | Robert Price | 03/2022 |
| 4480 | (53*10^148811-287)/9 | 148812 | Robert Price | 02/2022 |
| 4481 | 2^494333-286183 | 148810 | Enzo Doria | 06/2015 |
| 4482 | 2^494144-264119 | 148753 | Enzo Doria | 05/2014 |
| 4483 | 6*10^148734+47 | 148735 | Robert Price | 06/2022 |
| 4484 | 28724^33353-33353^28724 | 148696 | Frank Doornink | 06/2024 |
| 4485 | 36502^11823+11823^36502 | 148663 | Hans Havermann | 11/2020 |
| 4486 | (5*2^493838-1)/3721 | 148658 | Lelio R Paula | 10/2015 |
| 4487 | 64239^206+206^64239 | 148641 | Hans Havermann | 10/2020 |
| 4488 | (23*2^493761-1)/555 | 148636 | Lelio R Paula | 10/2015 |
| 4489 | (23*10^148627-137)/3 | 148628 | Robert Price | 08/2021 |
| 4490 | (151*10^148601-1)/3 | 148603 | Robert Price | 03/2020 |
| 4491 | 2^493636+82081 | 148600 | Enzo Doria | 09/2016 |
| 4492 | ((((((((((((((34251^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2 | 148593 | Serge Batalov | 07/2016 |
| 4493 | 27134^33509-33509^27134 | 148563 | Frank Doornink | 01/2024 |
| 4494 | 177487#+(519643#)/(177487#) | 148558 | Makoto Morimoto | 11/2017 |
| 4495 | (2*10^148460-23)/3 | 148460 | Robert Price | 04/2018 |
| 4496 | (28*10^148445+101)/3 | 148446 | Robert Price | 09/2020 |
| 4497 | 2^493065+225 | 148428 | Henri Lifchitz | 11/2024 |
| 4498 | 36203^12556+12556^36203 | 148391 | Hans Havermann | 10/2020 |
| 4499 | 33912^23749+23749^33912 | 148387 | Hans Havermann | 10/2020 |
| 4500 | (8*10^148328+1)/9 | 148328 | Serge Batalov | 05/2010 |
