## 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
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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 ? 4501 32950^10591+10591^32950 132622 Hans Havermann 04/2021 4502 33302^9597+9597^33302 132614 Hans Havermann 04/2021 4503 (19*10^132550+191)/3 132551 Robert Price 05/2019 4504 (2^440399-1)/(16210820281161978209*31518475633*880799) 132538 Dario Alpern 01/2015 4505 (38^83891+1)/39 132529 Robert Price 09/2013 4506 2*10^132493-43 132494 Robert Price 04/2018 4507 31352^16809+16809^31352 132480 Hans Havermann 04/2021 4508 (418*10^132441+23)/9 132443 Robert Price 02/2020 4509 2^439931-21 132433 Lelio R Paula 08/2017 4510 47^79201-46^79201 132432 Robert Price 10/2012 4511 2^439897-113653 132423 Enzo Doria 08/2014 4512 35505^5362+5362^35505 132410 Hans Havermann 03/2021 4513 30079^25222+25222^30079 132402 Hans Havermann 04/2021 4514 (5*2^439822+1)/9 132400 Lelio R Paula 06/2015 4515 (695*10^132356+7)/9 132358 Robert Price 12/2021 4516 (112*10^132337-1)/3 132339 Serge Batalov 12/2014 4517 2^439576-113247 132326 Enzo Doria 07/2014 4518 30059^25230+25230^30059 132318 Hans Havermann 04/2021 4519 2^439497-29143 132302 Enzo Doria 07/2015 4520 2^439409-114193 132276 Enzo Doria 12/2014 4521 (44*10^132233-233)/9 132234 Robert Price 01/2019 4522 25507^30000-30000^25507 132200 Frank Doornink 02/2024 4523 9*10^132148-7 132149 Robert Price 09/2015 4524 V(790390) 132144 Serge Batalov 07/2024 4525 (47*10^132125-119)/9 132126 Robert Price 05/2019 4526 2^438900+214051 132123 Enzo Doria 10/2023 4527 2^438845+1870217 132106 Enzo Doria 05/2016 4528 2^438789+87855 132089 Lelio R Paula 01/2016 4529 2^438774-2786411 132085 Enzo Doria 03/2016 4530 2^438755-1848205 132079 Enzo Doria 07/2015 4531 30502^21381+21381^30502 132075 Hans Havermann 04/2021 4532 2^438739-112087 132074 Enzo Doria 06/2014 4533 (2^438438+100280245065) 131983 Paul Bourdelais 05/2022 4534 35872^4777+4777^35872 131979 Hans Havermann 04/2021 4535 31198^16945+16945^31198 131938 Hans Havermann 03/2021 4536 13907#+(318259#)/(13907#) 131923 Makoto Morimoto 10/2017 4537 L(631181) 131910 Henri Lifchitz 09/2008 4538 (47*10^131886-119)/9 131887 Robert Price 05/2019 4539 5*2^438096-3 131881 Jon Grantham 07/2023 4540 (3*2^438121+1)/4308193883 131879 Lelio R Paula 06/2015 4541 2^438079-1863877 131875 Enzo Doria 03/2016 4542 (16*10^131872-37)/3 131873 Robert Price 05/2021 4543 (2^438067+5)/329 131869 Lelio R Paula 06/2015 4544 2^437908-113855 131824 Enzo Doria 09/2014 4545 2^437884-286349 131817 Enzo Doria 07/2015 4546 15^112072+14 131807 Alfred Reich 10/2023 4547 5^188558+4 131797 Tyler NeSmith 05/2021 4548 (11*10^131784-17)/3 131785 Robert Price 06/2018 4549 (166^59357-1)/165 131777 Anonymous 06/2024 4551 4*10^131719-93 131720 Robert Price 07/2020 4550 31629^14606+14606^31629 131720 Hans Havermann 04/2021 4552 3^276062-112292 131716 Enzo Doria 07/2014 4553 11*31^88313+322688 131708 Eric Chen 05/2024 4554 (7*10^131682+89)/3 131683 Robert Price 08/2020 4555 29512^28969+28969^29512 131681 Hans Havermann 03/2021 4556 2^437343+75953 131654 Enzo Doria 04/2016 4557 35^85243-34^85243 131621 Robert Price 05/2012 4558 (28*10^131586+59)/3 131587 Robert Price 05/2021 4559 (59*10^131575+391)/9 131576 Robert Price 03/2021 4560 39984^1945+1945^39984 131505 Hans Havermann 03/2021 4561 25842^29801-29801^25842 131492 Frank Doornink 03/2024 4562 28592^29505-29505^28592 131482 Frank Doornink 05/2024 4563 25647^29818-29818^25647 131469 Frank Doornink 02/2024 4564 (203*10^131457+1)/3 131459 Robert Price 03/2020 4565 7*10^131421-41 131422 Robert Price 08/2021 4566 87309^32+32^87309 131414 Hans Havermann 03/2021 4567 (68^71713+1)/69 131413 Paul Bourdelais 09/2017 4568 2^436521+224885 131406 Enzo Doria 07/2024 4569 (650*10^131391+43)/9 131393 Tyler Busby 01/2023 4570 2^436451+1884713 131385 Enzo Doria 03/2017 4571 2^436365+35 131359 Robert Price 11/2015 4573 2^436300+1866871 131340 Enzo Doria 03/2016 4572 (7*10^131339+179)/3 131340 Robert Price 09/2018 4574 14^114592-3 131338 Paul Bourdelais 12/2020 4575 36197^4236+4236^36197 131285 Hans Havermann 04/2021 4576 (37*10^131270+341)/9 131271 Robert Price 08/2018 4577 29863^24790+24790^29863 131227 Hans Havermann 03/2021 4578 (5*10^131223-29)/3 131224 Robert Price 03/2018 4579 29524^27825+27825^29524 131218 Hans Havermann 03/2021 4580 (23*2^435891-1)/699 131215 Lelio R Paula 07/2015 4581 (11*2^435879+1)/3337 131211 Lelio R Paula 06/2015 4582 30639^19136+19136^30639 131192 Hans Havermann 04/2021 4583 (2^435808+1)/641/6700417 131182 Lelio R Paula 02/2012 4584 (2^435808+1)/4294967297 131182 Serge Batalov 12/2016 4585 2^435773+1875557 131181 Enzo Doria 06/2016 4586 (16*10^131180+167)/3 131181 Robert Price 06/2019 4587 (26*10^131180-77)/3 131181 Robert Price 11/2019 4588 (25*10^131144-7)/9 131145 Robert Price 05/2018 4589 29299^29358-29358^29299 131138 Norbert Schneider 03/2022 4590 2^435612-2789939 131133 Enzo Doria 12/2015 4591 33976^7231+7231^33976 131121 Hans Havermann 03/2021 4592 33715^7746+7746^33715 131121 Hans Havermann 03/2021 4593 66^72047-65^72047 131093 Robert Price 09/2013 4594 (5*10^131090+37)/3 131091 Robert Price 03/2018 4595 2^435468+75631 131089 Enzo Doria 04/2016 4596 37^83588-2 131083 Lelio R Paula 08/2015 4597 (4^217720+11)/3 131081 Robert Price 02/2017 4598 30407^20448+20448^30407 131074 Hans Havermann 04/2021 4599 (22*10^131070+179)/3 131071 Robert Price 02/2022 4600 28831^29388-29388^28831 131067 Frank Doornink 05/2024 4601 29487^27836+27836^29487 131059 Hans Havermann 04/2021 4602 29962^23615+23615^29962 131030 Hans Havermann 03/2021 4603 2^435202-113193 131009 Enzo Doria 07/2014 4604 41705^1384+1384^41705 131002 Hans Havermann 04/2021 4605 9*10^130998-19 130999 Robert Price 07/2019 4606 36243^4108+4108^36243 130969 Hans Havermann 04/2021 4607 (445^49433+1)/446 130914 Jinyuan Wang 05/2024 4608 floor((sqrt(5)-1)/2*10^130911) 130911 Serge Batalov 06/2017 4609 2^434835-111937 130899 Enzo Doria 05/2014 4610 (62*10^130895-629)/9 130896 Robert Price 07/2021 4611 2^434685+72257 130854 Enzo Doria 04/2016 4612 (7*10^130825+113)/3 130826 Robert Price 02/2018 4613 2^434539-29317 130810 Enzo Doria 07/2015 4614 (74*10^130791+637)/9 130792 Robert Price 01/2022 4615 2^434469-114259 130789 Enzo Doria 01/2015 4616 (5*10^130763+103)/9 130763 Robert Price 04/2022 4617 2^434246+33 130722 Robert Price 11/2015 4618 30156^21599+21599^30156 130710 Hans Havermann 04/2021 4619 (17*10^130695-161)/9 130696 Robert Price 02/2021 4620 30513^19148+19148^30513 130661 Hans Havermann 03/2021 4621 29736^24761+24761^29736 130654 Hans Havermann 04/2021 4622 9*10^130638+41 130639 Robert Price 08/2020 4623 2^433911-91 130621 Lelio R Paula 06/2017 4624 30786^17449+17449^30786 130588 Hans Havermann 03/2021 4625 2^433744-114419 130570 Enzo Doria 02/2015 4627 2^433708+1869451 130560 Enzo Doria 05/2016 4626 2^433710+93 130560 Lelio R Paula 06/2017 4628 7*10^130535-27 130536 Robert Price 11/2022 4629 (9629^32768+1)/120501441265666 130520 Kellen Shenton 05/2021 4630 804*34^85220+713 130516 Eric Chen 08/2023 4631 (29*2^433547-1)/27 130511 Lelio R Paula 06/2015 4632 3^273521+10 130503 Tyler NeSmith 01/2021 4633 41659^1356+1356^41659 130487 Hans Havermann 03/2021 4634 4*10^130480+9 130481 Robert Price 05/2015 4635 (23*2^433449-1)/75 130481 Lelio R Paula 06/2015 4636 3*2^433422+5 130474 Jon Grantham 07/2023 4637 (23*2^433334-1)/3731 130445 Lelio R Paula 06/2015 4638 (31*10^130414-49)/9 130415 Robert Price 11/2021 4639 26462^29485-29485^26462 130402 Frank Doornink 03/2024 4640 33481^7848+7848^33481 130401 Hans Havermann 03/2021 4641 (17*10^130393+7)/3 130394 Robert Price 06/2023 4642 (22*10^130392+203)/9 130393 Robert Price 10/2021 4643 29773^23950+23950^29773 130386 Hans Havermann 04/2021 4644 2^433023-113497 130353 Enzo Doria 08/2014 4645 31175^15178+15178^31175 130350 Hans Havermann 04/2021 4646 2^433002+1179379 130347 Enzo Doria 06/2016 4647 2^432974+19 130339 Robert Price 08/2015 4648 31903^12168+12168^31903 130331 Hans Havermann 04/2021 4649 2^432917+22217 130322 Enzo Doria 09/2023 4650 29387^27112+27112^29387 130278 Hans Havermann 04/2021 4651 2^432768+213181 130277 Enzo Doria 09/2023 4652 29577^25370+25370^29577 130267 Hans Havermann 04/2021 4653 31738^12685+12685^31738 130231 Hans Havermann 03/2021 4654 44235^878+878^44235 130206 Hans Havermann 04/2021 4655 32160^11171+11171^32160 130187 Hans Havermann 04/2021 4656 29489^25956+25956^29489 130172 Hans Havermann 04/2021 4657 (2^432457-1)/1672739247834685086279697 130159 Tony Prest / Never Odd Or Even 09/2013 4658 33005^8766+8766^33005 130133 Hans Havermann 04/2021 4659 (35*10^130132-611)/9 130133 Robert Price 02/2022 4660 (444^49408+1)/(444^256+1) 130125 Martin Hopf 12/2023 4661 2^432217+41 130111 Lelio R Paula 06/2017 4662 (2^216089*(2^216091-1)-339)/25 130098 Makoto Morimoto 03/2017 4663 ((2^216091+1066)^2+(2^216091+1066)+41)/47/2069 130095 Makoto Morimoto 05/2016 4664 97^65480-2 130094 Lelio R Paula 05/2017 4665 36007^4102+4102^36007 130094 Hans Havermann 04/2021 4666 4*10^130088-89 130089 Robert Price 11/2018 4667 2^432117-113215 130081 Enzo Doria 07/2014 4668 (4*10^130080+41)/9 130080 Serge Batalov 11/2022 4669 2^431804+72511 129986 Enzo Doria 04/2016 4670 27902^29237-29237^27902 129978 Frank Doornink 03/2024 4671 (2313^38809-1)/(2313^197-1) 129898 Ryan Propper 11/2023 4672 (13*10^129896+137)/3 129897 Robert Price 06/2021 4673 (13*10^129890+71)/3 129891 Robert Price 06/2021 4674 29048^29101-29101^29048 129882 Norbert Schneider 03/2022 4675 37832^2709+2709^37832 129871 Hans Havermann 04/2021 4676 31055^15184+15184^31055 129853 Hans Havermann 04/2021 4677 (3^272141-3^136071+1)/7 129844 Serge Batalov 03/2014 4678 31385^13702+13702^31385 129833 Hans Havermann 04/2021 4679 (13*10^129826+41)/9 129827 Tyler Busby 02/2023 4680 28901^29102-29102^28901 129822 Norbert Schneider 03/2022 4681 (47*10^129789-119)/9 129790 Robert Price 05/2019 4682 (9*2^431141+1)/17 129787 Lelio R Paula 06/2015 4683 25999^29384-29384^25999 129730 Frank Doornink 03/2024 4684 25771^29408-29408^25771 129723 Frank Doornink 02/2024 4685 (166*10^129712+17)/3 129714 Robert Price 07/2022 4686 (29*2^430881-1)/21 129709 Lelio R Paula 06/2015 4687 2^430807+1869563 129686 Enzo Doria 05/2016 4688 2^430721-21429 129660 Enzo Doria 07/2013 4689 (4*10^129618+89)/3 129619 Robert Price 08/2021 4690 (142^60223-1)/141 129616 Anonymous 06/2024 4691 (10^129587-7^129587)/3 129587 Jon Grantham 07/2023 4692 2^430415-276271 129568 Enzo Doria 07/2015 4693 32282^10311+10311^32282 129558 Hans Havermann 04/2021 4694 29486^24741+24741^29486 129545 Hans Havermann 04/2021 4695 (29*10^129543+313)/9 129544 Robert Price 04/2021 4696 37095^3104+3104^37095 129533 Hans Havermann 04/2021 4697 31132^14459+14459^31132 129514 Hans Havermann 04/2021 4698 32582^9435+9435^32582 129506 Hans Havermann 03/2021 4699 30442^17953+17953^30442 129505 Hans Havermann 03/2021 4700 (199*10^129487-7)/3 129489 Robert Price 05/2020 4701 2^430142-2791721 129486 Enzo Doria 03/2016 4702 (7*10^129472-13)/3 129473 Robert Price 07/2018 4703 (8*10^129469+79)/3 129470 Robert Price 10/2020 4704 31678^12213+12213^31678 129463 Hans Havermann 04/2021 4705 10620^32143-10619^32143 129412 Norbert Schneider 08/2023 4706 (772*10^129406-7)/9 129408 Robert Price 06/2022 4707 (535^47431-1)/534 129406 Tom Wu 09/2024 4708 31100^14439+14439^31100 129362 Hans Havermann 04/2021 4709 33009^8288+8288^33009 129345 Hans Havermann 04/2021 4710 25895^29306-29306^25895 129334 Frank Doornink 03/2024 4711 (44^78697+43^78697)/87 129333 Aurel Gibier 11/2023 4712 29675^22804+22804^29675 129324 Hans Havermann 04/2021 4713 29068^28099+28099^29068 129315 Hans Havermann 04/2021 4714 2^429568-21017 129313 Enzo Doria 07/2013 4715 (10^129295+83)/3 129295 Robert Price 08/2021 4716 (853*10^129274-7)/9 129276 Robert Price 07/2021 4717 30958^14961+14961^30958 129249 Hans Havermann 04/2021 4718 (11*10^129239-179)/3 129240 Robert Price 09/2018 4719 28659^28988+28988^28659 129208 Norbert Schneider 02/2021 4720 29423^24616+24616^29423 129203 Hans Havermann 03/2021 4721 2^429194-112685 129201 Enzo Doria 06/2014 4722 2^429145-2780449 129186 Enzo Doria 04/2016 4723 32500^9427+9427^32500 129168 Hans Havermann 04/2021 4724 33577^7014+7014^33577 129136 Hans Havermann 03/2021 4725 2^428892-113453 129110 Enzo Doria 07/2014 4726 (11*2^428881-7)/15 129106 Renaud Lifchitz 03/2011 4727 2^428727-113959 129060 Enzo Doria 10/2014 4728 (7*2^428725-1)/13 129059 Lelio R Paula 05/2014 4729 (10^129051-31)/3 129051 Serge Batalov 12/2014 4730 (134*10^129038+7)/3 129040 Robert Price 02/2020 4731 2^428564+71161 129011 Enzo Doria 04/2016 4732 28781^28930+28930^28781 129002 Norbert Schneider 02/2021 4733 29065^27424+27424^29065 128995 Hans Havermann 04/2021 4734 2^428502-113285 128992 Enzo Doria 07/2014 4735 2^428421-21373 128968 Enzo Doria 06/2013 4736 L(616787) 128901 Henri Lifchitz 09/2008 4737 (765^44701-1)/764 128900 Tom Wu 07/2024 4738 20^99055-3 128874 Paul Bourdelais 12/2020 4739 91^65772-2 128851 Lelio R Paula 05/2017 4740 2^428022+43 128848 Lelio R Paula 05/2017 4741 2^427999-459397 128841 Enzo Doria 05/2015 4742 2^427993+76847 128839 Enzo Doria 05/2016 4743 31059^14060+14060^31059 128833 Hans Havermann 03/2021 4744 10^128805+152871 128806 Patrick De Geest 05/2021 4745 10^128805-10001 128805 Robert Price 02/2021 4746 2^427824-1851507 128788 Enzo Doria 08/2015 4747 2^427807-21469 128783 Enzo Doria 07/2013 4748 29082^26783+26783^29082 128772 Hans Havermann 04/2021 4749 40055^1638+1638^40055 128750 Hans Havermann 04/2021 4750 (923^43411-1)/922 128720 Tom Wu 07/2024

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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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