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 ? |
4501 | (97*10^127858-1)/3 | 127860 | Serge Batalov | 12/2014 |
4502 | 28929^26258+26258^28929 | 127845 | Hans Havermann | 03/2021 |
4503 | 30563^15220+15220^30563 | 127828 | Hans Havermann | 03/2021 |
4504 | 2^424632-2786639 | 127827 | Enzo Doria | 03/2016 |
4505 | 10^127821-700001 | 127821 | Robert Price | 08/2021 |
4506 | 2^424577-113755 | 127811 | Enzo Doria | 09/2014 |
4507 | (7*2^424512-1)/3 | 127792 | Lelio R Paula | 05/2014 |
4508 | (56*10^127752+691)/9 | 127753 | Robert Price | 05/2019 |
4509 | 11^122629-720 | 127705 | Enzo Doria | 11/2012 |
4510 | 22*10^127645+3 | 127647 | Robert Price | 01/2020 |
4511 | 28715^27844+27844^28715 | 127631 | Hans Havermann | 03/2021 |
4512 | (56*10^127612+187)/9 | 127613 | Robert Price | 10/2021 |
4513 | (5*36^81995+821)/7 | 127609 | Eric Chen | 01/2021 |
4514 | 4*10^127562-39 | 127563 | Robert Price | 09/2020 |
4515 | 32595^8186+8186^32595 | 127547 | Hans Havermann | 03/2021 |
4516 | 2^423696-21429 | 127546 | Enzo Doria | 07/2013 |
4517 | 2^423664-1864559 | 127536 | Enzo Doria | 03/2016 |
4518 | 37889^2322+2322^37889 | 127530 | Hans Havermann | 03/2021 |
4519 | 37668^2429+2429^37668 | 127523 | Hans Havermann | 03/2021 |
4520 | 3^267267-4 | 127519 | Henri Lifchitz | 10/2014 |
4521 | fibonacci(610144)-2 | 127513 | Jon Grantham | 08/2023 |
4522 | (103*10^127491+17)/3 | 127493 | Robert Price | 08/2020 |
4523 | 29376^21869+21869^29376 | 127487 | Hans Havermann | 03/2021 |
4524 | 31186^12241+12241^31186 | 127483 | Hans Havermann | 02/2021 |
4525 | (19^99689+5^99689)/24 | 127477 | Robert Price | 09/2013 |
4526 | 27069^28754-28754^27069 | 127452 | Frank Doornink | 01/2024 |
4527 | (21*2^423372+1)/101 | 127447 | Lelio R Paula | 05/2014 |
4528 | 30594^14645+14645^30594 | 127446 | Hans Havermann | 03/2021 |
4529 | 2^423328-21537 | 127435 | Enzo Doria | 07/2013 |
4530 | (67*10^127413-7)/3 | 127415 | Robert Price | 01/2020 |
4531 | (5*34^83193+700233)/11 | 127408 | Eric Chen | 08/2023 |
4532 | (2*10^127407+73)/3 | 127407 | Robert Price | 09/2020 |
4533 | (2^423165-7)/25 | 127384 | Lelio R Paula | 05/2015 |
4534 | (7726^32768+1)/13917994151414876602369 | 127379 | Kellen Shenton | 04/2021 |
4535 | (4*10^127349+17)/3 | 127350 | Tyler Busby | 01/2023 |
4536 | 29512^20647+20647^29512 | 127341 | Hans Havermann | 03/2021 |
4537 | 2^422987-3001935 | 127332 | Paul Bourdelais | 07/2023 |
4538 | (112*10^127324+17)/3 | 127326 | Robert Price | 03/2020 |
4539 | 29565^20252+20252^29565 | 127321 | Hans Havermann | 03/2021 |
4540 | fibonacci(609165)-3 | 127308 | Jon Grantham | 08/2023 |
4542 | (F(5)^182099-F(4)^182099)/F(3) | 127282 | Wayne Halsdorf | 08/2013 |
4541 | (5^182099-3^182099)/2 | 127282 | Kellen Shenton | 05/2022 |
4543 | (16*10^127259+197)/3 | 127260 | Robert Price | 04/2019 |
4544 | (26*10^127240+61)/3 | 127241 | Robert Price | 10/2019 |
4545 | (234483*27^88884-145)/26 | 127230 | Curtis Bright | 05/2015 |
4546 | 2^422515-114997 | 127190 | Enzo Doria | 06/2015 |
4547 | 5*10^127179-3 | 127180 | Robert Price | 07/2015 |
4548 | 31678^10343+10343^31678 | 127176 | Hans Havermann | 03/2021 |
4549 | (44*10^127169-233)/9 | 127170 | Robert Price | 01/2019 |
4550 | 34947^4352+4352^34947 | 127162 | Hans Havermann | 03/2021 |
4551 | 6*10^127158+19 | 127159 | Robert Price | 11/2021 |
4552 | 30469^14902+14902^30469 | 127155 | Hans Havermann | 03/2021 |
4553 | 5*10^127153+77 | 127154 | Robert Price | 12/2018 |
4554 | 29941^17620+17620^29941 | 127130 | Hans Havermann | 02/2021 |
4555 | 31607^10516+10516^31607 | 127119 | Hans Havermann | 03/2021 |
4556 | (19*10^127118-97)/3 | 127119 | Robert Price | 10/2021 |
4557 | (29*10^127111+691)/9 | 127112 | Robert Price | 08/2021 |
4558 | 736^44335+44335^736 | 127104 | Norbert Schneider | 07/2019 |
4559 | 33040^7023+7023^33040 | 127090 | Hans Havermann | 03/2021 |
4560 | (4*10^127081+167)/9 | 127081 | Robert Price | 03/2022 |
4561 | 29748^18661+18661^29748 | 127052 | Hans Havermann | 03/2021 |
4562 | -516776642557847117490*Bern(37960)/34256837217082767928421792453 | 127042 | Thomas Ritschel | 06/2017 |
4563 | (78^67141-1)/77 | 127036 | Paul Bourdelais | 09/2017 |
4564 | (14*10^127014-137)/3 | 127015 | Robert Price | 04/2021 |
4565 | 31436^10965+10965^31436 | 127002 | Hans Havermann | 03/2021 |
4566 | 28905^24758+24758^28905 | 127001 | Hans Havermann | 03/2021 |
4567 | 2^421860-113285 | 126993 | Enzo Doria | 07/2014 |
4568 | (10^127030+7)/81234833/9230384921/6092460488946445358851 | 126991 | Alfred Reich | 07/2021 |
4569 | (2^421827-7)/11 | 126982 | Lelio R Paula | 05/2015 |
4570 | 11^121910-840 | 126957 | Enzo Doria | 12/2012 |
4571 | (56*10^126935+187)/9 | 126936 | Robert Price | 10/2021 |
4572 | 28915^24538+24538^28915 | 126933 | Hans Havermann | 03/2021 |
4573 | (29*10^126928-77)/3 | 126929 | Robert Price | 02/2020 |
4574 | (259*10^126919-1)/3 | 126921 | Robert Price | 12/2020 |
4575 | 10^126919+204567 | 126920 | Patrick De Geest | 05/2021 |
4576 | (2^421617+100280245065) | 126920 | Paul Bourdelais | 05/2022 |
4577 | 10^126919-100001 | 126919 | Robert Price | 07/2020 |
4578 | 28340^28503+28503^28340 | 126907 | Norbert Schneider | 02/2021 |
4579 | 2^421534-3001935 | 126895 | Paul Bourdelais | 07/2023 |
4580 | (71^68539+1)/72 | 126882 | Paul Bourdelais | 09/2017 |
4581 | (5*10^126871-119)/3 | 126872 | Robert Price | 03/2018 |
4582 | 331^50339-10004 | 126846 | Enzo Doria | 07/2012 |
4583 | 2^421363-2790757 | 126843 | Enzo Doria | 03/2016 |
4584 | (106*10^126839-1)/3 | 126841 | Serge Batalov | 12/2014 |
4585 | 37938^2203+2203^37938 | 126828 | Hans Havermann | 03/2021 |
4586 | (13*10^126819+77)/9 | 126820 | Robert Price | 07/2022 |
4587 | (7*2^421243+1)/39 | 126807 | Lelio R Paula | 05/2014 |
4589 | (14*10^126784-83)/3 | 126785 | Robert Price | 12/2018 |
4588 | 2^421169-3001935 | 126785 | Paul Bourdelais | 07/2023 |
4590 | 2^421161-286183 | 126783 | Enzo Doria | 06/2015 |
4591 | (106*10^126726+17)/3 | 126728 | Robert Price | 04/2021 |
4592 | 30718^13347+13347^30718 | 126724 | Hans Havermann | 03/2021 |
4593 | 2^420939-113935 | 126716 | Enzo Doria | 10/2014 |
4594 | 11*23^93048+356 | 126708 | Eric Chen | 08/2023 |
4595 | 177^56363-2 | 126703 | Lelio R Paula | 10/2017 |
4596 | 2^420741-113659 | 126656 | Enzo Doria | 08/2014 |
4597 | 2^420694-21 | 126642 | Lelio R Paula | 05/2017 |
4598 | (13*10^126638+437)/9 | 126639 | Robert Price | 04/2018 |
4599 | (167*10^126637-17)/3 | 126639 | Robert Price | 03/2020 |
4600 | 4*10^126625+87 | 126626 | Robert Price | 08/2018 |
4601 | (31*2^420556+1)/7 | 126601 | Lelio R Paula | 05/2014 |
4602 | 7*10^126600-99 | 126601 | Robert Price | 06/2019 |
4603 | 2^420424-59189 | 126561 | Enzo Doria | 10/2015 |
4604 | 28717^25534+25534^28717 | 126560 | Hans Havermann | 03/2021 |
4605 | (86*10^126542+103)/9 | 126543 | Robert Price | 12/2021 |
4606 | (19*10^126517-7)/3 | 126518 | Robert Price | 12/2023 |
4607 | 28922^23655+23655^28922 | 126503 | Hans Havermann | 03/2021 |
4608 | 2^420126+71893 | 126471 | Enzo Doria | 04/2016 |
4609 | (43*10^126441+47)/9 | 126442 | Robert Price | 12/2018 |
4610 | 8*10^126408+71 | 126409 | Robert Price | 05/2022 |
4611 | 2^419866+1877059 | 126393 | Enzo Doria | 07/2016 |
4612 | 29315^20484+20484^29315 | 126390 | Hans Havermann | 03/2021 |
4613 | 29433^19676+19676^29433 | 126384 | Hans Havermann | 03/2021 |
4614 | F(604711) | 126377 | Henri Lifchitz | 02/2005 |
4615 | 2^419757+72707 | 126360 | Enzo Doria | 04/2016 |
4616 | 2^419720-21569 | 126349 | Enzo Doria | 07/2013 |
4617 | 2^419637+29 | 126324 | Henri Lifchitz | 02/2006 |
4618 | 31004^11865+11865^31004 | 126319 | Hans Havermann | 03/2021 |
4619 | 2^419612+1876741 | 126316 | Enzo Doria | 07/2016 |
4620 | 2^419520+2793271 | 126289 | Enzo Doria | 03/2016 |
4621 | (2^419447-5)/369 | 126264 | Lelio R Paula | 05/2014 |
4622 | 2^419328-1859939 | 126231 | Enzo Doria | 03/2016 |
4623 | 2^419282-1851507 | 126217 | Enzo Doria | 08/2015 |
4624 | (133*10^126212+17)/3 | 126214 | Robert Price | 11/2021 |
4625 | 2^419251+1866143 | 126208 | Enzo Doria | 03/2016 |
4626 | 11^121185+2 | 126202 | Robert Price | 05/2014 |
4627 | 28203^28352+28352^28203 | 126175 | Norbert Schneider | 01/2021 |
4628 | (23*2^419036-1)/1393 | 126141 | Lelio R Paula | 05/2014 |
4629 | 2^418851+23 | 126087 | Robert Price | 09/2015 |
4630 | (2^418849-9)/2681 | 126083 | Lelio R Paula | 05/2014 |
4631 | 2^418829+167 | 126081 | Lelio R Paula | 01/2012 |
4632 | 31037^11530+11530^31037 | 126067 | Hans Havermann | 03/2021 |
4633 | 4*10^126064-69 | 126065 | Robert Price | 01/2022 |
4634 | (31*2^418782-1)/75891 | 126063 | Lelio R Paula | 05/2014 |
4635 | (19*2^418754-1)/15 | 126058 | Lelio R Paula | 05/2014 |
4636 | (35*10^126048-323)/9 | 126049 | Robert Price | 10/2021 |
4637 | 33016^6551+6551^33016 | 126000 | Hans Havermann | 03/2021 |
4638 | 2^418548-111546435 | 125996 | Paul Bourdelais | 10/2021 |
4639 | 25134^28625-28625^25134 | 125958 | Frank Doornink | 12/2023 |
4640 | 34736^4227+4227^34736 | 125954 | Hans Havermann | 03/2021 |
4641 | 2^418319-109501 | 125927 | Enzo Doria | 04/2014 |
4642 | 2^418316-112373 | 125926 | Enzo Doria | 06/2014 |
4643 | 40398^1309+1309^40398 | 125919 | Hans Havermann | 03/2021 |
4644 | (8*10^125894-29)/3 | 125895 | Robert Price | 07/2018 |
4645 | (26*10^125886-413)/9 | 125887 | Robert Price | 05/2018 |
4646 | 10^(2*62938+1)-7*10^62938-1 | 125877 | Robert Price | 07/2023 |
4647 | 55*10^125847+9 | 125849 | Robert Price | 03/2022 |
4648 | 4*10^125832+57 | 125833 | Robert Price | 05/2022 |
4649 | 2^417968+1869811 | 125821 | Enzo Doria | 06/2016 |
4650 | 2^417902+63 | 125802 | Lelio R Paula | 09/2015 |
4651 | (10^125792-91)/9 | 125792 | Serge Batalov | 12/2014 |
4652 | 30438^13573+13573^30438 | 125791 | Hans Havermann | 03/2021 |
4653 | 32867^6714+6714^32867 | 125782 | Hans Havermann | 03/2021 |
4654 | 31155^10892+10892^31155 | 125777 | Hans Havermann | 03/2021 |
4655 | (35*10^125754-593)/9 | 125755 | Robert Price | 07/2018 |
4656 | 30455^13464+13464^30455 | 125754 | Hans Havermann | 03/2021 |
4657 | (32*10^125751-77)/9 | 125752 | Robert Price | 06/2018 |
4658 | 2^417704+77011 | 125742 | Enzo Doria | 05/2016 |
4659 | 29755^16816+16816^29755 | 125737 | Hans Havermann | 03/2021 |
4660 | (22*10^125734+203)/9 | 125735 | Robert Price | 10/2021 |
4661 | 29918^15915+15915^29918 | 125710 | Hans Havermann | 03/2021 |
4662 | (10^125706+149)/3 | 125706 | Serge Batalov | 12/2014 |
4663 | 28531^25368+25368^28531 | 125659 | Hans Havermann | 03/2021 |
4664 | 2^417419-115309 | 125656 | Enzo Doria | 07/2015 |
4665 | (46*10^125642+593)/9 | 125643 | Robert Price | 04/2022 |
4666 | 2^417315+213953 | 125625 | Enzo Doria | 10/2023 |
4667 | 2^417300+77281 | 125620 | Enzo Doria | 05/2016 |
4668 | 30638^12537+12537^30638 | 125561 | Hans Havermann | 03/2021 |
4669 | 2^417095-1657 | 125559 | Yves Minet | 07/2014 |
4670 | 30162^14525+14525^30162 | 125538 | Hans Havermann | 03/2021 |
4671 | (56*10^125535+583)/9 | 125536 | Robert Price | 08/2021 |
4672 | (23*10^125517-179)/3 | 125518 | Robert Price | 06/2022 |
4673 | 9*10^125516+29 | 125517 | Robert Price | 03/2022 |
4674 | (88*10^125492-637)/9 | 125493 | Robert Price | 11/2020 |
4675 | 28958^21525+21525^28958 | 125474 | Hans Havermann | 02/2021 |
4677 | 2^416773-25 | 125462 | Lelio R Paula | 09/2015 |
4676 | (10^125482+7)/162685667/1639829194459 | 125462 | Alfred Reich | 07/2021 |
4678 | 33889^5032+5032^33889 | 125449 | Hans Havermann | 03/2021 |
4679 | (289511#+292834)/(2^3*146417) | 125444 | Makoto Morimoto | 10/2017 |
4680 | (2861^36481+1)/(2861^191+1) | 125438 | Martin Hopf | 12/2023 |
4681 | (11*2^416691+1)/43 | 125436 | Lelio R Paula | 05/2014 |
4682 | (289511#+1896)/(2*3^3*79*780193*9911849) | 125434 | Makoto Morimoto | 06/2019 |
4683 | 2^416641-2*416641+1 | 125422 | Robert Price | 05/2018 |
4684 | 33392^5697+5697^33392 | 125409 | Hans Havermann | 03/2021 |
4685 | (21*2^416566-1)/17 | 125399 | Lelio R Paula | 05/2014 |
4686 | 2^416530+1870429 | 125389 | Enzo Doria | 05/2016 |
4687 | (56*10^125385+691)/9 | 125386 | Robert Price | 05/2019 |
4688 | 27953^28198+28198^27953 | 125381 | Norbert Schneider | 01/2021 |
4689 | 31074^10837+10837^31074 | 125381 | Hans Havermann | 03/2021 |
4690 | 33745^5194+5194^33745 | 125380 | Hans Havermann | 03/2021 |
4691 | 2^416490+1875109 | 125376 | Enzo Doria | 09/2016 |
4692 | 28360^26331+26331^28360 | 125365 | Hans Havermann | 03/2021 |
4693 | 2^416416-114929 | 125354 | Enzo Doria | 05/2015 |
4694 | (77*10^125330-293)/9 | 125331 | Robert Price | 09/2019 |
4695 | (172*10^125292-1)/9 | 125294 | Serge Batalov | 12/2014 |
4696 | 2^416134+1865899 | 125269 | Enzo Doria | 03/2016 |
4697 | 153^57337-152 | 125264 | Norbert Schneider | 12/2018 |
4698 | (599*10^125224+13)/9 | 125226 | Robert Price | 02/2022 |
4699 | (9*2^415992+1)/13560845 | 125220 | Lelio R Paula | 05/2014 |
4700 | 30054^14657+14657^30054 | 125207 | Hans Havermann | 03/2021 |
4701 | (23^91943-1)/22 | 125201 | Robert Price | 01/2012 |
4702 | 2^415884-933075 | 125194 | Paul Bourdelais | 06/2021 |
4703 | 43125^27010-106 | 125185 | Enzo Doria | 08/2012 |
4704 | (38*10^125166+349)/9 | 125167 | Robert Price | 10/2018 |
4705 | 10^125166-5001 | 125166 | Robert Price | 12/2021 |
4706 | 2^415765-112603 | 125158 | Enzo Doria | 06/2014 |
4707 | 8*10^125088-13 | 125089 | Robert Price | 08/2019 |
4708 | (25*10^125076-13)/3 | 125077 | Robert Price | 09/2019 |
4709 | (11*10^125054+73)/3 | 125055 | Robert Price | 08/2021 |
4710 | (29*10^125021-113)/3 | 125022 | Robert Price | 10/2019 |
4711 | 2^415290-113591 | 125015 | Enzo Doria | 08/2014 |
4712 | 2^415276-460919 | 125011 | Enzo Doria | 06/2015 |
4713 | 2^415259+77243 | 125006 | Enzo Doria | 05/2016 |
4714 | (67*10^124990+77)/9 | 124991 | Robert Price | 10/2021 |
4715 | 2^415144-3683 | 124971 | Yves Minet | 10/2011 |
4716 | 2^415092+111546435 | 124956 | Paul Bourdelais | 10/2021 |
4717 | 31936^8173+8173^31936 | 124946 | Hans Havermann | 03/2021 |
4718 | 5^178715-4 | 124916 | Tyler NeSmith | 07/2021 |
4719 | 29767^15700+15700^29767 | 124900 | Hans Havermann | 03/2021 |
4720 | 2^414874+79 | 124890 | Lelio R Paula | 01/2015 |
4721 | 25292^28361-28361^25292 | 124874 | Frank Doornink | 01/2024 |
4722 | (2^414765+7)/1389 | 124854 | Lelio R Paula | 05/2014 |
4723 | 2^414618+79459 | 124813 | Enzo Doria | 06/2016 |
4724 | (61*10^124809-1)/3 | 124811 | Robert Price | 01/2020 |
4725 | (29*10^124765-71)/3 | 124766 | Robert Price | 07/2021 |
4726 | 2^414432-1846709 | 124757 | Enzo Doria | 07/2015 |
4727 | 2*10^124751-51 | 124752 | Robert Price | 04/2018 |
4728 | (56*10^124735+367)/9 | 124736 | Robert Price | 06/2019 |
4729 | (13*2^414274-1)/153 | 124708 | Lelio R Paula | 05/2014 |
4730 | (23*10^124690+37)/3 | 124691 | Robert Price | 02/2022 |
4731 | 56*10^124656-3 | 124658 | Robert Price | 03/2020 |
4732 | (7*10^124648+197)/3 | 124649 | Robert Price | 07/2018 |
4734 | 2^414032-5 | 124637 | Henri Lifchitz | 07/2006 |
4733 | 2^414032+1872331 | 124637 | Enzo Doria | 05/2016 |
4735 | 37373^2158+2158^37373 | 124604 | Hans Havermann | 03/2021 |
4736 | 29811^15112+15112^29811 | 124590 | Hans Havermann | 03/2021 |
4737 | 2^413781-2023 | 124561 | Riley Fisher | 09/2023 |
4738 | 14120^30009-30009^14120 | 124533 | Norbert Schneider | 02/2015 |
4739 | 29757^15296+15296^29757 | 124521 | Hans Havermann | 03/2021 |
4740 | 35056^3561+3561^35056 | 124504 | Hans Havermann | 03/2021 |
4741 | 40588^1167+1167^40588 | 124487 | Hans Havermann | 02/2021 |
4742 | (85*10^124485-49)/9 | 124486 | Robert Price | 12/2020 |
4743 | 64^68909-63^68909 | 124463 | Robert Price | 07/2013 |
4744 | 35016^3581+3581^35016 | 124448 | Hans Havermann | 03/2021 |
4745 | 2^413387+76253 | 124442 | Enzo Doria | 04/2016 |
4746 | 28749^21298+21298^28749 | 124436 | Hans Havermann | 03/2021 |
4747 | 2^413352+524287 | 124432 | Paul Underwood | 09/2018 |
4748 | 287117#+391613 | 124424 | Nicolas PALAU | 01/2017 |
4749 | (4*10^124420+83)/3 | 124421 | Robert Price | 02/2018 |
4750 | 34578^3965+3965^34578 | 124421 | Hans Havermann | 03/2021 |