## PRP Records

### Probable Primes Top 10000

#### (295503 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 ? 4501 2^436300+1866871 131340 Enzo Doria 03/2016 4502 14^114592-3 131338 Paul Bourdelais 12/2020 4503 36197^4236+4236^36197 131285 Hans Havermann 04/2021 4504 (37*10^131270+341)/9 131271 Robert Price 08/2018 4505 29863^24790+24790^29863 131227 Hans Havermann 03/2021 4506 (5*10^131223-29)/3 131224 Robert Price 03/2018 4507 29524^27825+27825^29524 131218 Hans Havermann 03/2021 4508 (23*2^435891-1)/699 131215 Lelio R Paula 07/2015 4509 (11*2^435879+1)/3337 131211 Lelio R Paula 06/2015 4510 30639^19136+19136^30639 131192 Hans Havermann 04/2021 4511 (2^435808+1)/641/6700417 131182 Lelio R Paula 02/2012 4512 (2^435808+1)/4294967297 131182 Serge Batalov 12/2016 4513 2^435773+1875557 131181 Enzo Doria 06/2016 4514 (16*10^131180+167)/3 131181 Robert Price 06/2019 4515 (26*10^131180-77)/3 131181 Robert Price 11/2019 4516 (25*10^131144-7)/9 131145 Robert Price 05/2018 4517 29299^29358-29358^29299 131138 Norbert Schneider 03/2022 4518 2^435612-2789939 131133 Enzo Doria 12/2015 4519 33976^7231+7231^33976 131121 Hans Havermann 03/2021 4520 33715^7746+7746^33715 131121 Hans Havermann 03/2021 4521 66^72047-65^72047 131093 Robert Price 09/2013 4522 (5*10^131090+37)/3 131091 Robert Price 03/2018 4523 2^435468+75631 131089 Enzo Doria 04/2016 4524 37^83588-2 131083 Lelio R Paula 08/2015 4525 (4^217720+11)/3 131081 Robert Price 02/2017 4526 30407^20448+20448^30407 131074 Hans Havermann 04/2021 4527 (22*10^131070+179)/3 131071 Robert Price 02/2022 4528 28831^29388-29388^28831 131067 Frank Doornink 05/2024 4529 29487^27836+27836^29487 131059 Hans Havermann 04/2021 4530 29962^23615+23615^29962 131030 Hans Havermann 03/2021 4531 2^435202-113193 131009 Enzo Doria 07/2014 4532 41705^1384+1384^41705 131002 Hans Havermann 04/2021 4533 9*10^130998-19 130999 Robert Price 07/2019 4534 36243^4108+4108^36243 130969 Hans Havermann 04/2021 4535 (445^49433+1)/446 130914 Jinyuan Wang 05/2024 4536 floor((sqrt(5)-1)/2*10^130911) 130911 Serge Batalov 06/2017 4537 2^434835-111937 130899 Enzo Doria 05/2014 4538 (62*10^130895-629)/9 130896 Robert Price 07/2021 4539 2^434685+72257 130854 Enzo Doria 04/2016 4540 (7*10^130825+113)/3 130826 Robert Price 02/2018 4541 2^434539-29317 130810 Enzo Doria 07/2015 4542 (74*10^130791+637)/9 130792 Robert Price 01/2022 4543 2^434469-114259 130789 Enzo Doria 01/2015 4544 (5*10^130763+103)/9 130763 Robert Price 04/2022 4545 2^434246+33 130722 Robert Price 11/2015 4546 30156^21599+21599^30156 130710 Hans Havermann 04/2021 4547 (17*10^130695-161)/9 130696 Robert Price 02/2021 4548 30513^19148+19148^30513 130661 Hans Havermann 03/2021 4549 29736^24761+24761^29736 130654 Hans Havermann 04/2021 4550 9*10^130638+41 130639 Robert Price 08/2020 4551 2^433911-91 130621 Lelio R Paula 06/2017 4552 30786^17449+17449^30786 130588 Hans Havermann 03/2021 4553 2^433744-114419 130570 Enzo Doria 02/2015 4555 2^433708+1869451 130560 Enzo Doria 05/2016 4554 2^433710+93 130560 Lelio R Paula 06/2017 4556 7*10^130535-27 130536 Robert Price 11/2022 4557 (9629^32768+1)/120501441265666 130520 Kellen Shenton 05/2021 4558 804*34^85220+713 130516 Eric Chen 08/2023 4559 (29*2^433547-1)/27 130511 Lelio R Paula 06/2015 4560 3^273521+10 130503 Tyler NeSmith 01/2021 4561 41659^1356+1356^41659 130487 Hans Havermann 03/2021 4562 4*10^130480+9 130481 Robert Price 05/2015 4563 (23*2^433449-1)/75 130481 Lelio R Paula 06/2015 4564 3*2^433422+5 130474 Jon Grantham 07/2023 4565 (23*2^433334-1)/3731 130445 Lelio R Paula 06/2015 4566 (31*10^130414-49)/9 130415 Robert Price 11/2021 4567 26462^29485-29485^26462 130402 Frank Doornink 03/2024 4568 33481^7848+7848^33481 130401 Hans Havermann 03/2021 4569 (17*10^130393+7)/3 130394 Robert Price 06/2023 4570 (22*10^130392+203)/9 130393 Robert Price 10/2021 4571 29773^23950+23950^29773 130386 Hans Havermann 04/2021 4572 2^433023-113497 130353 Enzo Doria 08/2014 4573 31175^15178+15178^31175 130350 Hans Havermann 04/2021 4574 2^433002+1179379 130347 Enzo Doria 06/2016 4575 2^432974+19 130339 Robert Price 08/2015 4576 31903^12168+12168^31903 130331 Hans Havermann 04/2021 4577 2^432917+22217 130322 Enzo Doria 09/2023 4578 29387^27112+27112^29387 130278 Hans Havermann 04/2021 4579 2^432768+213181 130277 Enzo Doria 09/2023 4580 29577^25370+25370^29577 130267 Hans Havermann 04/2021 4581 31738^12685+12685^31738 130231 Hans Havermann 03/2021 4582 44235^878+878^44235 130206 Hans Havermann 04/2021 4583 32160^11171+11171^32160 130187 Hans Havermann 04/2021 4584 29489^25956+25956^29489 130172 Hans Havermann 04/2021 4585 (2^432457-1)/1672739247834685086279697 130159 Tony Prest / Never Odd Or Even 09/2013 4586 33005^8766+8766^33005 130133 Hans Havermann 04/2021 4587 (35*10^130132-611)/9 130133 Robert Price 02/2022 4588 (444^49408+1)/(444^256+1) 130125 Martin Hopf 12/2023 4589 2^432217+41 130111 Lelio R Paula 06/2017 4590 (2^216089*(2^216091-1)-339)/25 130098 Makoto Morimoto 03/2017 4591 ((2^216091+1066)^2+(2^216091+1066)+41)/47/2069 130095 Makoto Morimoto 05/2016 4592 97^65480-2 130094 Lelio R Paula 05/2017 4593 36007^4102+4102^36007 130094 Hans Havermann 04/2021 4594 4*10^130088-89 130089 Robert Price 11/2018 4595 2^432117-113215 130081 Enzo Doria 07/2014 4596 (4*10^130080+41)/9 130080 Serge Batalov 11/2022 4597 2^431804+72511 129986 Enzo Doria 04/2016 4598 27902^29237-29237^27902 129978 Frank Doornink 03/2024 4599 (2313^38809-1)/(2313^197-1) 129898 Ryan Propper 11/2023 4600 (13*10^129896+137)/3 129897 Robert Price 06/2021 4601 (13*10^129890+71)/3 129891 Robert Price 06/2021 4602 29048^29101-29101^29048 129882 Norbert Schneider 03/2022 4603 37832^2709+2709^37832 129871 Hans Havermann 04/2021 4604 31055^15184+15184^31055 129853 Hans Havermann 04/2021 4605 (3^272141-3^136071+1)/7 129844 Serge Batalov 03/2014 4606 31385^13702+13702^31385 129833 Hans Havermann 04/2021 4607 (13*10^129826+41)/9 129827 Tyler Busby 02/2023 4608 28901^29102-29102^28901 129822 Norbert Schneider 03/2022 4609 (47*10^129789-119)/9 129790 Robert Price 05/2019 4610 (9*2^431141+1)/17 129787 Lelio R Paula 06/2015 4611 25999^29384-29384^25999 129730 Frank Doornink 03/2024 4612 25771^29408-29408^25771 129723 Frank Doornink 02/2024 4613 (166*10^129712+17)/3 129714 Robert Price 07/2022 4614 (29*2^430881-1)/21 129709 Lelio R Paula 06/2015 4615 2^430807+1869563 129686 Enzo Doria 05/2016 4616 2^430721-21429 129660 Enzo Doria 07/2013 4617 (4*10^129618+89)/3 129619 Robert Price 08/2021 4618 (142^60223-1)/141 129616 Anonymous 06/2024 4619 (10^129587-7^129587)/3 129587 Jon Grantham 07/2023 4620 2^430415-276271 129568 Enzo Doria 07/2015 4621 32282^10311+10311^32282 129558 Hans Havermann 04/2021 4622 29486^24741+24741^29486 129545 Hans Havermann 04/2021 4623 (29*10^129543+313)/9 129544 Robert Price 04/2021 4624 37095^3104+3104^37095 129533 Hans Havermann 04/2021 4625 31132^14459+14459^31132 129514 Hans Havermann 04/2021 4626 32582^9435+9435^32582 129506 Hans Havermann 03/2021 4627 30442^17953+17953^30442 129505 Hans Havermann 03/2021 4628 (199*10^129487-7)/3 129489 Robert Price 05/2020 4629 2^430142-2791721 129486 Enzo Doria 03/2016 4630 (7*10^129472-13)/3 129473 Robert Price 07/2018 4631 (8*10^129469+79)/3 129470 Robert Price 10/2020 4632 31678^12213+12213^31678 129463 Hans Havermann 04/2021 4633 10620^32143-10619^32143 129412 Norbert Schneider 08/2023 4634 (772*10^129406-7)/9 129408 Robert Price 06/2022 4635 31100^14439+14439^31100 129362 Hans Havermann 04/2021 4636 33009^8288+8288^33009 129345 Hans Havermann 04/2021 4637 25895^29306-29306^25895 129334 Frank Doornink 03/2024 4638 (44^78697+43^78697)/87 129333 Aurel Gibier 11/2023 4639 29675^22804+22804^29675 129324 Hans Havermann 04/2021 4640 29068^28099+28099^29068 129315 Hans Havermann 04/2021 4641 2^429568-21017 129313 Enzo Doria 07/2013 4642 (10^129295+83)/3 129295 Robert Price 08/2021 4643 (853*10^129274-7)/9 129276 Robert Price 07/2021 4644 30958^14961+14961^30958 129249 Hans Havermann 04/2021 4645 (11*10^129239-179)/3 129240 Robert Price 09/2018 4646 28659^28988+28988^28659 129208 Norbert Schneider 02/2021 4647 29423^24616+24616^29423 129203 Hans Havermann 03/2021 4648 2^429194-112685 129201 Enzo Doria 06/2014 4649 2^429145-2780449 129186 Enzo Doria 04/2016 4650 32500^9427+9427^32500 129168 Hans Havermann 04/2021 4651 33577^7014+7014^33577 129136 Hans Havermann 03/2021 4652 2^428892-113453 129110 Enzo Doria 07/2014 4653 (11*2^428881-7)/15 129106 Renaud Lifchitz 03/2011 4654 2^428727-113959 129060 Enzo Doria 10/2014 4655 (7*2^428725-1)/13 129059 Lelio R Paula 05/2014 4656 (10^129051-31)/3 129051 Serge Batalov 12/2014 4657 (134*10^129038+7)/3 129040 Robert Price 02/2020 4658 2^428564+71161 129011 Enzo Doria 04/2016 4659 28781^28930+28930^28781 129002 Norbert Schneider 02/2021 4660 29065^27424+27424^29065 128995 Hans Havermann 04/2021 4661 2^428502-113285 128992 Enzo Doria 07/2014 4662 2^428421-21373 128968 Enzo Doria 06/2013 4663 L(616787) 128901 Henri Lifchitz 09/2008 4664 20^99055-3 128874 Paul Bourdelais 12/2020 4665 91^65772-2 128851 Lelio R Paula 05/2017 4666 2^428022+43 128848 Lelio R Paula 05/2017 4667 2^427999-459397 128841 Enzo Doria 05/2015 4668 2^427993+76847 128839 Enzo Doria 05/2016 4669 31059^14060+14060^31059 128833 Hans Havermann 03/2021 4670 10^128805+152871 128806 Patrick De Geest 05/2021 4671 10^128805-10001 128805 Robert Price 02/2021 4672 2^427824-1851507 128788 Enzo Doria 08/2015 4673 2^427807-21469 128783 Enzo Doria 07/2013 4674 29082^26783+26783^29082 128772 Hans Havermann 04/2021 4675 40055^1638+1638^40055 128750 Hans Havermann 04/2021 4676 11^123594-240 128710 Enzo Doria 09/2012 4677 2^427504-21503 128692 Enzo Doria 07/2013 4678 37727^2574+2574^37727 128673 Hans Havermann 04/2021 4679 29686^21591+21591^29686 128668 Hans Havermann 04/2021 4680 10^128668-70000000001 128668 Robert Price 08/2021 4681 2^427420+91 128667 Lelio R Paula 05/2017 4682 8*10^128651-37 128652 Robert Price 03/2022 4683 (68*10^128645-257)/9 128646 Robert Price 07/2019 4684 2^427269-113635 128621 Enzo Doria 08/2014 4685 2^427130+1877569 128579 Enzo Doria 08/2016 4686 2^427068+20011 128561 Enzo Doria 06/2023 4687 2^427016-115349 128545 Enzo Doria 07/2015 4688 (4*10^128510+137)/3 128511 Robert Price 03/2018 4689 2^426889-112879 128507 Enzo Doria 06/2014 4690 2^426804+1869931 128481 Enzo Doria 05/2016 4691 2^426750+77635 128465 Enzo Doria 05/2016 4692 27708^28913-28913^27708 128450 Frank Doornink 03/2024 4693 36988^2969+2969^36988 128445 Hans Havermann 03/2021 4694 36664^3185+3185^36664 128439 Hans Havermann 03/2021 4695 32618^8649+8649^32618 128416 Hans Havermann 04/2021 4696 28883^27874+27874^28883 128391 Hans Havermann 04/2021 4697 2^426425-91 128367 Lelio R Paula 05/2017 4698 (15*2^426398-1)/11 128359 Lelio R Paula 05/2014 4699 2^426352+74971 128345 Enzo Doria 04/2016 4700 (199*10^128343-7)/3 128345 Robert Price 05/2020 4701 4*10^128343-21 128344 Robert Price 09/2018 4702 (65*10^128338+493)/9 128339 Robert Price 08/2021 4703 35632^3997+3997^35632 128337 Hans Havermann 04/2021 4704 2^426300-1863689 128330 Enzo Doria 03/2016 4705 2^426293+1881017 128327 Enzo Doria 11/2016 4706 (88*10^128324-637)/9 128325 Robert Price 11/2020 4707 (491*10^128285+31)/9 128287 Robert Price 04/2022 4708 39103^1908+1908^39103 128281 Hans Havermann 04/2021 4709 2^426043+35 128252 Robert Price 11/2015 4710 (4*10^128244-19)/3 128245 Robert Price 03/2018 4711 26220^29021-29021^26220 128234 Frank Doornink 03/2024 4712 35489^4102+4102^35489 128222 Hans Havermann 04/2021 4713 34721^4926+4926^34721 128208 Hans Havermann 04/2021 4714 (305*10^128198+1)/9 128200 Robert Price 02/2020 4715 2^425808-459959 128181 Enzo Doria 06/2015 4716 30632^15291+15291^30632 128178 Hans Havermann 04/2021 4717 35981^3648+3648^35981 128167 Hans Havermann 04/2021 4718 2^425627-113605 128127 Enzo Doria 08/2014 4719 (4*10^128109+119)/3 128110 Robert Price 12/2021 4720 (22*10^128094+53)/3 128095 Robert Price 07/2019 4721 (86*10^128086-221)/9 128087 Robert Price 09/2019 4722 18565^30002-30002^18565 128070 Norbert Schneider 01/2015 4723 (2^425287-9)/2737 128021 Lelio R Paula 05/2015 4724 (3*2^425233-1)/25 128007 Lelio R Paula 05/2014 4725 Phi(149401,10)/30037901719561 128003 Makoto Kamada 07/2022 4726 2^425205+4911 128000 Marek Hubal 02/2017 4727 29241^23836+23836^29241 127995 Hans Havermann 04/2021 4728 2^425118-113663 127974 Enzo Doria 08/2014 4729 (86*10^127967-329)/9 127968 Robert Price 01/2020 4730 2^425061+1869761 127957 Enzo Doria 05/2016 4731 746^44541+44541^746 127955 Norbert Schneider 07/2019 4732 30236^17043+17043^30236 127946 Hans Havermann 03/2021 4733 2^424938+212419 127920 Enzo Doria 08/2023 4734 2^424918-21141 127914 Enzo Doria 07/2013 4735 (62*10^127903+91)/9 127904 Robert Price 07/2021 4736 2^424864-29489 127897 Enzo Doria 08/2015 4737 30438^15893+15893^30438 127877 Hans Havermann 02/2021 4738 (97*10^127858-1)/3 127860 Serge Batalov 12/2014 4739 28929^26258+26258^28929 127845 Hans Havermann 03/2021 4740 30563^15220+15220^30563 127828 Hans Havermann 03/2021 4741 2^424632-2786639 127827 Enzo Doria 03/2016 4742 10^127821-700001 127821 Robert Price 08/2021 4743 2^424577-113755 127811 Enzo Doria 09/2014 4744 (7*2^424512-1)/3 127792 Lelio R Paula 05/2014 4745 (56*10^127752+691)/9 127753 Robert Price 05/2019 4746 11^122629-720 127705 Enzo Doria 11/2012 4747 22*10^127645+3 127647 Robert Price 01/2020 4748 28715^27844+27844^28715 127631 Hans Havermann 03/2021 4749 (56*10^127612+187)/9 127613 Robert Price 10/2021 4750 (5*36^81995+821)/7 127609 Eric Chen 01/2021

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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: July, 22 2024 13:34 (Time in France)

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