## 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) !!!

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See the Latest PRPs
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 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 ? 4251 34989^7958+7958^34989 136486 Hans Havermann 12/2020 4252 (2*10^136484+187)/9 136484 Robert Price 06/2022 4253 31007^25158+25158^31007 136452 Hans Havermann 11/2020 4254 2^453267-113827 136447 Enzo Doria 09/2014 4255 32234^17085+17085^32234 136435 Hans Havermann 12/2020 4256 2^453102+1877629 136398 Enzo Doria 08/2016 4257 31016^24981+24981^31016 136397 Hans Havermann 12/2020 4258 (62*10^136384-791)/9 136385 Robert Price 06/2019 4259 34171^9798+9798^34171 136382 Hans Havermann 12/2020 4260 (17*10^136354-113)/3 136355 Robert Price 06/2021 4261 32756^14541+14541^32756 136350 Hans Havermann 11/2020 4262 32205^17086+17086^32205 136313 Hans Havermann 12/2020 4263 (25*10^136303+161)/3 136304 Robert Price 09/2019 4264 35337^7196+7196^35337 136299 Hans Havermann 12/2020 4265 (182*10^136291+1)/3 136293 Robert Price 02/2020 4266 (88*10^136234+83)/9 136235 Robert Price 03/2022 4267 23*10^136225-7 136227 Robert Price 02/2020 4268 L(651821) 136223 Henri Lifchitz 09/2008 4269 25519^30908-30908^25519 136208 Frank Doornink 02/2024 4270 2^452460+77701 136205 Enzo Doria 05/2016 4271 2^452440-114755 136199 Enzo Doria 04/2015 4272 28625^30558-30558^28625 136190 Frank Doornink 05/2024 4273 32286^16489+16489^32286 136157 Hans Havermann 11/2020 4274 (47*10^136141+493)/9 136142 Robert Price 03/2019 4275 27140^30699-30699^27140 136108 Frank Doornink 01/2024 4276 40392^2339+2339^40392 136082 Hans Havermann 12/2020 4277 2*10^136057-43 136058 Robert Price 04/2018 4278 2^451971+21563 136057 Enzo Doria 08/2023 4279 (2^451956-5)/181 136051 Lelio R Paula 07/2015 4280 2^451947-22165 136050 Enzo Doria 07/2013 4281 2^451787-21805 136002 Enzo Doria 07/2013 4282 2^451734-112817 135986 Enzo Doria 06/2014 4283 (11*2^451714+1)/75 135979 Lelio R Paula 07/2015 4284 2^451705-21879 135977 Enzo Doria 07/2013 4285 (4666^37249-1)/(4666^193-1) 135957 Ryan Propper 11/2023 4286 2^451560-112349 135934 Enzo Doria 06/2014 4287 2^451530+45 135925 Lelio R Paula 08/2017 4288 26594^30719-30719^26594 135925 Frank Doornink 03/2024 4289 31622^19875+19875^31622 135922 Hans Havermann 11/2020 4290 (25*10^135906-73)/3 135907 Robert Price 09/2019 4291 2^451450-21743 135900 Enzo Doria 07/2013 4292 (7*10^135879+11)/9 135879 Tyler Busby 01/2023 4293 35218^7199+7199^35218 135846 Hans Havermann 11/2020 4294 35661^6446+6446^35661 135844 Hans Havermann 11/2020 4295 (7*33^89453-4743239)/32 135835 Eric Chen 12/2023 4296 31869^18248+18248^31869 135801 Hans Havermann 12/2020 4297 (77*10^135789+157)/9 135790 Robert Price 05/2022 4298 2^450958+60529 135752 Enzo Doria 08/2023 4299 2^450805+65 135706 Lelio R Paula 08/2017 4300 30761^25728+25728^30761 135669 Hans Havermann 12/2020 4301 2*10^135663+69 135664 Robert Price 06/2020 4302 33962^9867+9867^33962 135651 Hans Havermann 11/2020 4303 34474^8605+8605^34474 135647 Hans Havermann 11/2020 4304 34501^8508+8508^34501 135583 Hans Havermann 12/2020 4305 35487^6614+6614^35487 135577 Hans Havermann 12/2020 4306 (13725^32768+1)/131074 135573 Lelio R Paula 03/2012 4307 (313007#+121876)/(2*30469*424867) 135559 Makoto Morimoto 08/2020 4308 (5^193939+1)/6 135557 Paul Bourdelais 12/2008 4309 (76*10^135553-49)/9 135554 Robert Price 07/2022 4310 5*3^284077+2^284077 135540 Jon Grantham 08/2023 4311 (844*10^135527-7)/9 135529 Robert Price 05/2021 4312 27191^30560-30560^27191 135517 Frank Doornink 01/2024 4313 40387^2260+2260^40387 135463 Hans Havermann 12/2020 4314 2^449944-113247 135447 Enzo Doria 07/2014 4315 2^449770-113247 135395 Enzo Doria 07/2014 4316 2^449637-21471 135355 Enzo Doria 07/2013 4317 26061^30650-30650^26061 135351 Frank Doornink 03/2024 4318 2^449571-75 135335 Lelio R Paula 08/2017 4319 (14*10^135301-53)/3 135302 Robert Price 12/2018 4320 (3*2^449494+1)/61340334013 135301 Lelio R Paula 07/2015 4321 (13*10^135279+437)/9 135280 Robert Price 04/2018 4322 2^449330-35 135262 Lelio R Paula 08/2017 4323 (19*2^449325+1)/9 135261 Lelio R Paula 07/2015 4324 (2709^39601+1)/(2709^199+1) 135260 Martin Hopf 12/2023 4325 (13*10^135184-43)/3 135185 Robert Price 11/2018 4326 2^449049-115309 135178 Enzo Doria 07/2015 4327 (10^135174+191)/3 135174 Robert Price 02/2018 4328 2^449030-15 135172 Lelio R Paula 08/2017 4329 (157*10^135151-1)/3 135153 Robert Price 01/2022 4330 (2^448966+100280245065) 135153 Paul Bourdelais 05/2022 4331 (27*2^448936-1)/11 135144 Lelio R Paula 07/2015 4332 (37*10^135099+251)/9 135100 Robert Price 09/2021 4333 32221^15586+15586^32221 135095 Hans Havermann 12/2020 4334 2^448762-351401 135091 Enzo Doria 07/2015 4335 2*10^135083-43 135084 Robert Price 04/2018 4336 31357^20278+20278^31357 135056 Hans Havermann 12/2020 4337 32242^15445+15445^32242 135055 Hans Havermann 12/2020 4338 k(198476) 135054 Robert Price 07/2020 4339 32461^14470+14470^32461 135053 Hans Havermann 12/2020 4340 31353^20288+20288^31353 135045 Hans Havermann 12/2020 4341 5*10^135019+77 135020 Robert Price 12/2018 4342 (10^135011+719)/9 135011 Serge Batalov 12/2014 4343 (197*10^134978+7)/3 134980 Robert Price 12/2020 4344 2^448386-2786261 134978 Enzo Doria 03/2016 4345 26480^30517-30517^26480 134975 Frank Doornink 03/2024 4346 (73*10^134939+143)/9 134940 Robert Price 07/2019 4347 33957^9392+9392^33957 134903 Hans Havermann 12/2020 4348 2^448122+20809 134899 Enzo Doria 08/2023 4349 2^448113-113949 134896 Enzo Doria 11/2014 4350 30958^22755+22755^30958 134887 Hans Havermann 12/2020 4351 2^447888-2786639 134828 Enzo Doria 03/2016 4352 2^447870-396765 134823 Enzo Doria 07/2013 4353 10^(2*67404+1)-10^67404-1 134809 Robert Price 07/2023 4354 2^447766-21791 134791 Enzo Doria 07/2013 4355 (19*10^134786-49)/3 134787 Robert Price 05/2019 4356 Phi(202173,10)/10064306514895399941409 134758 Makoto Kamada 05/2019 4357 (23*2^447647+1)/155 134755 Lelio R Paula 07/2015 4358 2^447552-1019 134727 Yves Minet 02/2014 4359 (2*10^134720-41)/3 134720 Robert Price 02/2018 4360 (25*10^134695-97)/9 134696 Robert Price 01/2022 4361 2^447437-113569 134692 Enzo Doria 08/2014 4362 2^447426-65 134689 Lelio R Paula 08/2017 4363 2^447357-2797573 134668 Enzo Doria 04/2016 4364 2^447278+93 134645 Lelio R Paula 08/2017 4365 33193^11370+11370^33193 134623 Hans Havermann 12/2020 4366 30736^23979+23979^30736 134619 Hans Havermann 11/2020 4367 2^447094-113193 134589 Enzo Doria 07/2014 4368 3^282041-9934 134568 Enzo Doria 05/2014 4369 2^447019-109039 134567 Enzo Doria 04/2014 4370 31376^19437+19437^31376 134561 Hans Havermann 12/2020 4371 2^446990-22041 134558 Enzo Doria 07/2013 4372 123^64370+122 134528 Karsten Bonath 04/2018 4373 30100^29461+29461^30100 134525 Hans Havermann 11/2020 4374 31251^20158+20158^31251 134519 Hans Havermann 11/2020 4375 2^446782-39701 134495 Enzo Doria 09/2015 4376 31817^16858+16858^31817 134485 Hans Havermann 12/2020 4377 32448^13937+13937^32448 134471 Hans Havermann 12/2020 4378 5^192321+3^192321-1 134427 Jon Grantham 08/2023 4379 2^446494-16485 134409 Enzo Doria 04/2013 4380 30042^29785+29785^30042 134408 Hans Havermann 12/2020 4381 29504^30069-30069^29504 134405 Norbert Schneider 12/2014 4382 2^446441+65 134393 Lelio R Paula 08/2017 4383 (10^134385+719)/9 134385 Serge Batalov 12/2014 4384 30043^29688+29688^30043 134370 Hans Havermann 12/2020 4385 (2*10^134364+529)/9 134364 Robert Price 01/2018 4386 34657^7512+7512^34657 134323 Hans Havermann 11/2020 4387 (13*2^446187-1)/661 134314 Lelio R Paula 07/2015 4388 5^192103+3^192103+2^192103+1 134275 Matthias Baur 12/2019 4389 42035^1564+1564^42035 134270 Hans Havermann 12/2020 4391 (2^446022-7)/339 134264 Lelio R Paula 07/2015 4390 30621^24248+24248^30621 134264 Hans Havermann 12/2020 4392 30341^26562+26562^30341 134237 Hans Havermann 11/2020 4393 (189^58967-1)/188 134234 Anonymous 06/2024 4394 10^134209+99867 134210 Patrick De Geest 05/2021 4395 10^134209-80000001 134209 Robert Price 04/2021 4396 10^134209-323283 134209 Patrick De Geest 05/2021 4397 29976^29953+29953^29976 134186 Hans Havermann 12/2020 4398 35038^6755+6755^35038 134183 Hans Havermann 12/2020 4399 63^74568+2 134174 Lelio R Paula 06/2017 4400 2^445671-22071 134161 Enzo Doria 07/2013 4401 532^49205+49205^532 134129 Norbert Schneider 02/2019 4402 36453^4780+4780^36453 134127 Hans Havermann 04/2021 4403 (28*10^134122-1)/9 134123 Serge Batalov 10/2014 4404 2^445515-113859 134114 Enzo Doria 10/2014 4406 (22*10^134111-37)/3 134112 Robert Price 04/2019 4405 31083^20636+20636^31083 134112 Hans Havermann 04/2021 4407 3*2^445478+5 134103 Jon Grantham 07/2023 4408 31622^17379+17379^31622 134079 Hans Havermann 04/2021 4409 5*2^445380-3 134074 Jon Grantham 07/2023 4410 (6*32^89076+4241)/31 134073 Eric Chen 11/2023 4411 (277*10^134059-7)/9 134061 Robert Price 02/2022 4412 2^445328-216917 134058 Enzo Doria 05/2014 4413 2^445202+1874899 134020 Enzo Doria 06/2016 4414 5^191739-3^191739-1 134020 Jon Grantham 08/2023 4415 (35*10^134003-89)/9 134004 Robert Price 02/2022 4416 (13*2^445102+1)/17 133989 Lelio R Paula 07/2015 4417 (35*10^133979-593)/9 133980 Robert Price 07/2018 4418 2*10^133955+51 133956 Robert Price 05/2018 4419 (49*10^133952+437)/9 133953 Robert Price 09/2021 4420 2^444964-113639 133948 Enzo Doria 08/2014 4421 31811^16240+16240^31811 133943 Hans Havermann 04/2021 4422 10^133902+167841 133903 Patrick De Geest 05/2021 4424 28118^30097-30097^28118 133902 Norbert Schneider 01/2015 4423 10^133902-100001 133902 Robert Price 07/2020 4425 2^444784-113859 133894 Enzo Doria 10/2014 4426 (132^63127-1)/131 133864 Anonymous 06/2024 4427 32303^13914+13914^32303 133846 Hans Havermann 04/2021 4428 (2276213*2^444444+1)/3 133797 Alex_soldier 11/2022 4429 (1403559*2^444444+1)/5 133797 Alex_soldier 11/2022 4430 (1209887*2^444444+1)/9 133797 Alex_soldier 11/2022 4431 (608239*2^444444+1)/25 133796 Alex_soldier 11/2022 4432 (1824587*2^444444+1)/27 133796 Alex_soldier 11/2022 4433 (40795*2^444444+1)/7 133795 Alex_soldier 11/2022 4434 30739^22458+22458^30739 133757 Hans Havermann 04/2021 4435 34942^6721+6721^34942 133739 Hans Havermann 04/2021 4436 (2^444046+100280245065) 133672 Paul Bourdelais 05/2022 4437 34792^6935+6935^34792 133638 Hans Havermann 04/2021 4438 (266*10^133603+1)/3 133605 Robert Price 04/2020 4439 32261^13842+13842^32261 133600 Hans Havermann 04/2021 4440 (89*10^133580+1)/9 133581 Serge Batalov 05/2010 4441 (134*10^133573-11)/3 133575 Robert Price 01/2022 4442 26726^30173-30173^26726 133574 Frank Doornink 03/2024 4443 62^74521-61^74521 133571 Robert Price 05/2013 4444 (182*10^133543+1)/3 133545 Robert Price 02/2020 4445 (103*10^133535+11)/3 133537 Robert Price 01/2021 4446 32589^12520+12520^32589 133537 Hans Havermann 03/2021 4447 L(638839)/274700771 133502 Serge Batalov 07/2024 4448 34516^7373+7373^34516 133496 Hans Havermann 04/2021 4449 8*10^133487-37 133488 Robert Price 03/2022 4450 30135^26882+26882^30135 133482 Hans Havermann 04/2021 4451 2^443198-1867301 133416 Enzo Doria 03/2016 4452 (19*10^133390+101)/3 133391 Robert Price 09/2019 4453 (71^72043-1)/70 133369 Paul Bourdelais 09/2017 4454 36117^4910+4910^36117 133311 Hans Havermann 04/2021 4455 2^442799+1874633 133296 Enzo Doria 06/2016 4456 L(637751) 133283 Henri Lifchitz 09/2008 4457 109^65410-2 133269 Lelio R Paula 10/2017 4458 2^442688-113489 133263 Enzo Doria 08/2014 4459 (7*2^442640-1)/783 133246 Lelio R Paula 07/2015 4460 (9*2^442463+1)/17441 133192 Lelio R Paula 07/2015 4461 2^442437-1849993 133187 Enzo Doria 08/2015 4462 2^442430-2791721 133185 Enzo Doria 03/2016 4463 (13*2^442428-1)/309 133183 Lelio R Paula 07/2015 4464 29959^27870+27870^29959 133172 Hans Havermann 03/2021 4465 (25*2^442379-1)/71 133169 Lelio R Paula 07/2015 4466 2^442368+213691 133167 Enzo Doria 09/2023 4467 34240^7737+7737^34240 133145 Hans Havermann 03/2021 4468 452^50145+50145^452 133142 Norbert Schneider 09/2020 4469 (355^52201-1)/354 133122 Tom Wu 08/2024 4470 30659^21796+21796^30659 133011 Hans Havermann 04/2021 4471 33276^9935+9935^33276 133010 Hans Havermann 04/2021 4472 30111^26122+26122^30111 133001 Hans Havermann 04/2021 4473 30790^20869+20869^30790 132998 Hans Havermann 04/2021 4475 (2^441799+78557)/5 132995 Lelio R Paula 07/2015 4474 8*10^132994-27 132995 Robert Price 10/2021 4476 (109*10^132992+11)/3 132994 Robert Price 06/2022 4477 2^441781-2787883 132990 Enzo Doria 03/2016 4478 fibonacci(636232)+4 132965 Jon Grantham 08/2023 4479 (3*2^441685+1)/749 132959 Lelio R Paula 07/2015 4480 2^441618+37 132941 Lelio R Paula 08/2017 4481 34857^6514+6514^34857 132940 Hans Havermann 04/2021 4482 34065^7988+7988^34065 132937 Hans Havermann 04/2021 4483 35571^5452+5452^35571 132914 Hans Havermann 04/2021 4484 2^441521-113575 132912 Enzo Doria 08/2014 4485 7*10^132884-99 132885 Robert Price 06/2019 4486 26987^29988-29988^26987 132882 Frank Doornink 03/2024 4487 (103*10^132879+17)/3 132881 Robert Price 08/2020 4488 2^441396-65 132874 Lelio R Paula 08/2017 4489 33350^9633+9633^33350 132859 Hans Havermann 04/2021 4490 2^441330+1871959 132854 Enzo Doria 05/2016 4491 25772^30111-30111^25772 132825 Frank Doornink 02/2024 4492 2^441063+383 132774 Lelio R Paula 06/2012 4493 (10^132753+7)/17/19 132751 Alfred Reich 06/2021 4494 (22*10^132746+53)/3 132747 Robert Price 07/2019 4495 (77*10^132744-149)/9 132745 Robert Price 03/2022 4496 (22*10^132732+119)/3 132733 Robert Price 04/2021 4497 2^440846+1870909 132708 Enzo Doria 05/2016 4498 (948^44579-1)/947 132701 Jinyuan Wang 04/2023 4499 2^440656-113489 132651 Enzo Doria 08/2014 4500 numbpart(14180123587) 132646 Serge Batalov 04/2017

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

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