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
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| Rank |
Probable prime |
Digits (> 50000) |
Who ? |
When ? |
| 4501 | 2^429194-112685 | 129201 | Enzo Doria | 06/2014 |
| 4502 | 2^429145-2780449 | 129186 | Enzo Doria | 04/2016 |
| 4503 | 32500^9427+9427^32500 | 129168 | Hans Havermann | 04/2021 |
| 4504 | 33577^7014+7014^33577 | 129136 | Hans Havermann | 03/2021 |
| 4505 | 2^428892-113453 | 129110 | Enzo Doria | 07/2014 |
| 4506 | (11*2^428881-7)/15 | 129106 | Renaud Lifchitz | 03/2011 |
| 4507 | 2^428727-113959 | 129060 | Enzo Doria | 10/2014 |
| 4508 | (7*2^428725-1)/13 | 129059 | Lelio R Paula | 05/2014 |
| 4509 | (10^129051-31)/3 | 129051 | Serge Batalov | 12/2014 |
| 4510 | (134*10^129038+7)/3 | 129040 | Robert Price | 02/2020 |
| 4511 | 2^428564+71161 | 129011 | Enzo Doria | 04/2016 |
| 4512 | 28781^28930+28930^28781 | 129002 | Norbert Schneider | 02/2021 |
| 4513 | 29065^27424+27424^29065 | 128995 | Hans Havermann | 04/2021 |
| 4514 | 2^428502-113285 | 128992 | Enzo Doria | 07/2014 |
| 4515 | 2^428421-21373 | 128968 | Enzo Doria | 06/2013 |
| 4516 | L(616787) | 128901 | Henri Lifchitz | 09/2008 |
| 4517 | 20^99055-3 | 128874 | Paul Bourdelais | 12/2020 |
| 4518 | 91^65772-2 | 128851 | Lelio R Paula | 05/2017 |
| 4519 | 2^428022+43 | 128848 | Lelio R Paula | 05/2017 |
| 4520 | 2^427999-459397 | 128841 | Enzo Doria | 05/2015 |
| 4521 | 2^427993+76847 | 128839 | Enzo Doria | 05/2016 |
| 4522 | 31059^14060+14060^31059 | 128833 | Hans Havermann | 03/2021 |
| 4523 | 10^128805+152871 | 128806 | Patrick De Geest | 05/2021 |
| 4524 | 10^128805-10001 | 128805 | Robert Price | 02/2021 |
| 4525 | 2^427824-1851507 | 128788 | Enzo Doria | 08/2015 |
| 4526 | 2^427807-21469 | 128783 | Enzo Doria | 07/2013 |
| 4527 | 29082^26783+26783^29082 | 128772 | Hans Havermann | 04/2021 |
| 4528 | 40055^1638+1638^40055 | 128750 | Hans Havermann | 04/2021 |
| 4529 | 11^123594-240 | 128710 | Enzo Doria | 09/2012 |
| 4530 | 2^427504-21503 | 128692 | Enzo Doria | 07/2013 |
| 4531 | 37727^2574+2574^37727 | 128673 | Hans Havermann | 04/2021 |
| 4532 | 29686^21591+21591^29686 | 128668 | Hans Havermann | 04/2021 |
| 4533 | 10^128668-70000000001 | 128668 | Robert Price | 08/2021 |
| 4534 | 2^427420+91 | 128667 | Lelio R Paula | 05/2017 |
| 4535 | 8*10^128651-37 | 128652 | Robert Price | 03/2022 |
| 4536 | (68*10^128645-257)/9 | 128646 | Robert Price | 07/2019 |
| 4537 | 2^427269-113635 | 128621 | Enzo Doria | 08/2014 |
| 4538 | 2^427130+1877569 | 128579 | Enzo Doria | 08/2016 |
| 4539 | 2^427068+20011 | 128561 | Enzo Doria | 06/2023 |
| 4540 | 2^427016-115349 | 128545 | Enzo Doria | 07/2015 |
| 4541 | (4*10^128510+137)/3 | 128511 | Robert Price | 03/2018 |
| 4542 | 2^426889-112879 | 128507 | Enzo Doria | 06/2014 |
| 4543 | 2^426804+1869931 | 128481 | Enzo Doria | 05/2016 |
| 4544 | 2^426750+77635 | 128465 | Enzo Doria | 05/2016 |
| 4545 | 27708^28913-28913^27708 | 128450 | Frank Doornink | 03/2024 |
| 4546 | 36988^2969+2969^36988 | 128445 | Hans Havermann | 03/2021 |
| 4547 | 36664^3185+3185^36664 | 128439 | Hans Havermann | 03/2021 |
| 4548 | 32618^8649+8649^32618 | 128416 | Hans Havermann | 04/2021 |
| 4549 | 28883^27874+27874^28883 | 128391 | Hans Havermann | 04/2021 |
| 4550 | 2^426425-91 | 128367 | Lelio R Paula | 05/2017 |
| 4551 | (15*2^426398-1)/11 | 128359 | Lelio R Paula | 05/2014 |
| 4552 | 2^426352+74971 | 128345 | Enzo Doria | 04/2016 |
| 4553 | (199*10^128343-7)/3 | 128345 | Robert Price | 05/2020 |
| 4554 | 4*10^128343-21 | 128344 | Robert Price | 09/2018 |
| 4555 | (65*10^128338+493)/9 | 128339 | Robert Price | 08/2021 |
| 4556 | 35632^3997+3997^35632 | 128337 | Hans Havermann | 04/2021 |
| 4557 | 2^426300-1863689 | 128330 | Enzo Doria | 03/2016 |
| 4558 | 2^426293+1881017 | 128327 | Enzo Doria | 11/2016 |
| 4559 | (88*10^128324-637)/9 | 128325 | Robert Price | 11/2020 |
| 4560 | (491*10^128285+31)/9 | 128287 | Robert Price | 04/2022 |
| 4561 | 39103^1908+1908^39103 | 128281 | Hans Havermann | 04/2021 |
| 4562 | 2^426043+35 | 128252 | Robert Price | 11/2015 |
| 4563 | (4*10^128244-19)/3 | 128245 | Robert Price | 03/2018 |
| 4564 | 26220^29021-29021^26220 | 128234 | Frank Doornink | 03/2024 |
| 4565 | 35489^4102+4102^35489 | 128222 | Hans Havermann | 04/2021 |
| 4566 | 34721^4926+4926^34721 | 128208 | Hans Havermann | 04/2021 |
| 4567 | (305*10^128198+1)/9 | 128200 | Robert Price | 02/2020 |
| 4568 | 2^425808-459959 | 128181 | Enzo Doria | 06/2015 |
| 4569 | 30632^15291+15291^30632 | 128178 | Hans Havermann | 04/2021 |
| 4570 | 35981^3648+3648^35981 | 128167 | Hans Havermann | 04/2021 |
| 4571 | 2^425627-113605 | 128127 | Enzo Doria | 08/2014 |
| 4572 | (4*10^128109+119)/3 | 128110 | Robert Price | 12/2021 |
| 4573 | (22*10^128094+53)/3 | 128095 | Robert Price | 07/2019 |
| 4574 | (86*10^128086-221)/9 | 128087 | Robert Price | 09/2019 |
| 4575 | 18565^30002-30002^18565 | 128070 | Norbert Schneider | 01/2015 |
| 4576 | (2^425287-9)/2737 | 128021 | Lelio R Paula | 05/2015 |
| 4577 | (3*2^425233-1)/25 | 128007 | Lelio R Paula | 05/2014 |
| 4578 | Phi(149401,10)/30037901719561 | 128003 | Makoto Kamada | 07/2022 |
| 4579 | 2^425205+4911 | 128000 | Marek Hubal | 02/2017 |
| 4580 | 29241^23836+23836^29241 | 127995 | Hans Havermann | 04/2021 |
| 4581 | 2^425118-113663 | 127974 | Enzo Doria | 08/2014 |
| 4582 | (86*10^127967-329)/9 | 127968 | Robert Price | 01/2020 |
| 4583 | 2^425061+1869761 | 127957 | Enzo Doria | 05/2016 |
| 4584 | 746^44541+44541^746 | 127955 | Norbert Schneider | 07/2019 |
| 4585 | 30236^17043+17043^30236 | 127946 | Hans Havermann | 03/2021 |
| 4586 | 2^424938+212419 | 127920 | Enzo Doria | 08/2023 |
| 4587 | 2^424918-21141 | 127914 | Enzo Doria | 07/2013 |
| 4588 | (62*10^127903+91)/9 | 127904 | Robert Price | 07/2021 |
| 4589 | 2^424864-29489 | 127897 | Enzo Doria | 08/2015 |
| 4590 | 30438^15893+15893^30438 | 127877 | Hans Havermann | 02/2021 |
| 4591 | (97*10^127858-1)/3 | 127860 | Serge Batalov | 12/2014 |
| 4592 | 28929^26258+26258^28929 | 127845 | Hans Havermann | 03/2021 |
| 4593 | 30563^15220+15220^30563 | 127828 | Hans Havermann | 03/2021 |
| 4594 | 2^424632-2786639 | 127827 | Enzo Doria | 03/2016 |
| 4595 | 10^127821-700001 | 127821 | Robert Price | 08/2021 |
| 4596 | 2^424577-113755 | 127811 | Enzo Doria | 09/2014 |
| 4597 | (7*2^424512-1)/3 | 127792 | Lelio R Paula | 05/2014 |
| 4598 | (56*10^127752+691)/9 | 127753 | Robert Price | 05/2019 |
| 4599 | 11^122629-720 | 127705 | Enzo Doria | 11/2012 |
| 4600 | 22*10^127645+3 | 127647 | Robert Price | 01/2020 |
| 4601 | 28715^27844+27844^28715 | 127631 | Hans Havermann | 03/2021 |
| 4602 | (56*10^127612+187)/9 | 127613 | Robert Price | 10/2021 |
| 4603 | (5*36^81995+821)/7 | 127609 | Eric Chen | 01/2021 |
| 4604 | 4*10^127562-39 | 127563 | Robert Price | 09/2020 |
| 4605 | 32595^8186+8186^32595 | 127547 | Hans Havermann | 03/2021 |
| 4606 | 2^423696-21429 | 127546 | Enzo Doria | 07/2013 |
| 4607 | 2^423664-1864559 | 127536 | Enzo Doria | 03/2016 |
| 4608 | 37889^2322+2322^37889 | 127530 | Hans Havermann | 03/2021 |
| 4609 | 37668^2429+2429^37668 | 127523 | Hans Havermann | 03/2021 |
| 4610 | 3^267267-4 | 127519 | Henri Lifchitz | 10/2014 |
| 4611 | fibonacci(610144)-2 | 127513 | Jon Grantham | 08/2023 |
| 4612 | 26253^28852-28852^26253 | 127503 | Frank Doornink | 03/2024 |
| 4613 | (103*10^127491+17)/3 | 127493 | Robert Price | 08/2020 |
| 4614 | 29376^21869+21869^29376 | 127487 | Hans Havermann | 03/2021 |
| 4615 | 31186^12241+12241^31186 | 127483 | Hans Havermann | 02/2021 |
| 4616 | (19^99689+5^99689)/24 | 127477 | Robert Price | 09/2013 |
| 4617 | 27069^28754-28754^27069 | 127452 | Frank Doornink | 01/2024 |
| 4618 | (21*2^423372+1)/101 | 127447 | Lelio R Paula | 05/2014 |
| 4619 | 30594^14645+14645^30594 | 127446 | Hans Havermann | 03/2021 |
| 4620 | 2^423328-21537 | 127435 | Enzo Doria | 07/2013 |
| 4621 | (67*10^127413-7)/3 | 127415 | Robert Price | 01/2020 |
| 4622 | (5*34^83193+700233)/11 | 127408 | Eric Chen | 08/2023 |
| 4623 | (2*10^127407+73)/3 | 127407 | Robert Price | 09/2020 |
| 4624 | (2^423165-7)/25 | 127384 | Lelio R Paula | 05/2015 |
| 4625 | (7726^32768+1)/13917994151414876602369 | 127379 | Kellen Shenton | 04/2021 |
| 4626 | (4*10^127349+17)/3 | 127350 | Tyler Busby | 01/2023 |
| 4627 | 29512^20647+20647^29512 | 127341 | Hans Havermann | 03/2021 |
| 4628 | 2^422987-3001935 | 127332 | Paul Bourdelais | 07/2023 |
| 4629 | (112*10^127324+17)/3 | 127326 | Robert Price | 03/2020 |
| 4630 | 29565^20252+20252^29565 | 127321 | Hans Havermann | 03/2021 |
| 4631 | fibonacci(609165)-3 | 127308 | Jon Grantham | 08/2023 |
| 4633 | (F(5)^182099-F(4)^182099)/F(3) | 127282 | Wayne Halsdorf | 08/2013 |
| 4632 | (5^182099-3^182099)/2 | 127282 | Kellen Shenton | 05/2022 |
| 4634 | (16*10^127259+197)/3 | 127260 | Robert Price | 04/2019 |
| 4635 | (26*10^127240+61)/3 | 127241 | Robert Price | 10/2019 |
| 4636 | (234483*27^88884-145)/26 | 127230 | Curtis Bright | 05/2015 |
| 4637 | 2^422515-114997 | 127190 | Enzo Doria | 06/2015 |
| 4638 | 5*10^127179-3 | 127180 | Robert Price | 07/2015 |
| 4639 | 31678^10343+10343^31678 | 127176 | Hans Havermann | 03/2021 |
| 4640 | (44*10^127169-233)/9 | 127170 | Robert Price | 01/2019 |
| 4641 | 34947^4352+4352^34947 | 127162 | Hans Havermann | 03/2021 |
| 4642 | 6*10^127158+19 | 127159 | Robert Price | 11/2021 |
| 4643 | 30469^14902+14902^30469 | 127155 | Hans Havermann | 03/2021 |
| 4644 | 5*10^127153+77 | 127154 | Robert Price | 12/2018 |
| 4645 | 29941^17620+17620^29941 | 127130 | Hans Havermann | 02/2021 |
| 4646 | 31607^10516+10516^31607 | 127119 | Hans Havermann | 03/2021 |
| 4647 | (19*10^127118-97)/3 | 127119 | Robert Price | 10/2021 |
| 4648 | (29*10^127111+691)/9 | 127112 | Robert Price | 08/2021 |
| 4649 | 736^44335+44335^736 | 127104 | Norbert Schneider | 07/2019 |
| 4650 | 33040^7023+7023^33040 | 127090 | Hans Havermann | 03/2021 |
| 4651 | (4*10^127081+167)/9 | 127081 | Robert Price | 03/2022 |
| 4652 | 29748^18661+18661^29748 | 127052 | Hans Havermann | 03/2021 |
| 4653 | 27905^28578-28578^27905 | 127049 | Frank Doornink | 03/2024 |
| 4654 | -516776642557847117490*Bern(37960)/34256837217082767928421792453 | 127042 | Thomas Ritschel | 06/2017 |
| 4655 | (78^67141-1)/77 | 127036 | Paul Bourdelais | 09/2017 |
| 4656 | (14*10^127014-137)/3 | 127015 | Robert Price | 04/2021 |
| 4657 | 31436^10965+10965^31436 | 127002 | Hans Havermann | 03/2021 |
| 4658 | 28905^24758+24758^28905 | 127001 | Hans Havermann | 03/2021 |
| 4659 | 2^421860-113285 | 126993 | Enzo Doria | 07/2014 |
| 4660 | (10^127030+7)/81234833/9230384921/6092460488946445358851 | 126991 | Alfred Reich | 07/2021 |
| 4661 | (2^421827-7)/11 | 126982 | Lelio R Paula | 05/2015 |
| 4662 | 26268^28729-28729^26268 | 126966 | Frank Doornink | 03/2024 |
| 4663 | 11^121910-840 | 126957 | Enzo Doria | 12/2012 |
| 4664 | (56*10^126935+187)/9 | 126936 | Robert Price | 10/2021 |
| 4665 | 28915^24538+24538^28915 | 126933 | Hans Havermann | 03/2021 |
| 4666 | (29*10^126928-77)/3 | 126929 | Robert Price | 02/2020 |
| 4667 | (259*10^126919-1)/3 | 126921 | Robert Price | 12/2020 |
| 4668 | 10^126919+204567 | 126920 | Patrick De Geest | 05/2021 |
| 4669 | (2^421617+100280245065) | 126920 | Paul Bourdelais | 05/2022 |
| 4670 | 10^126919-100001 | 126919 | Robert Price | 07/2020 |
| 4671 | 28340^28503+28503^28340 | 126907 | Norbert Schneider | 02/2021 |
| 4672 | 2^421534-3001935 | 126895 | Paul Bourdelais | 07/2023 |
| 4673 | (71^68539+1)/72 | 126882 | Paul Bourdelais | 09/2017 |
| 4674 | (5*10^126871-119)/3 | 126872 | Robert Price | 03/2018 |
| 4675 | 331^50339-10004 | 126846 | Enzo Doria | 07/2012 |
| 4676 | 2^421363-2790757 | 126843 | Enzo Doria | 03/2016 |
| 4677 | (106*10^126839-1)/3 | 126841 | Serge Batalov | 12/2014 |
| 4678 | 37938^2203+2203^37938 | 126828 | Hans Havermann | 03/2021 |
| 4679 | (13*10^126819+77)/9 | 126820 | Robert Price | 07/2022 |
| 4680 | (7*2^421243+1)/39 | 126807 | Lelio R Paula | 05/2014 |
| 4682 | (14*10^126784-83)/3 | 126785 | Robert Price | 12/2018 |
| 4681 | 2^421169-3001935 | 126785 | Paul Bourdelais | 07/2023 |
| 4683 | 2^421161-286183 | 126783 | Enzo Doria | 06/2015 |
| 4684 | 26733^28628-28628^26733 | 126738 | Frank Doornink | 03/2024 |
| 4685 | (106*10^126726+17)/3 | 126728 | Robert Price | 04/2021 |
| 4686 | 30718^13347+13347^30718 | 126724 | Hans Havermann | 03/2021 |
| 4687 | 2^420939-113935 | 126716 | Enzo Doria | 10/2014 |
| 4688 | 11*23^93048+356 | 126708 | Eric Chen | 08/2023 |
| 4689 | 177^56363-2 | 126703 | Lelio R Paula | 10/2017 |
| 4690 | 2^420741-113659 | 126656 | Enzo Doria | 08/2014 |
| 4691 | 2^420694-21 | 126642 | Lelio R Paula | 05/2017 |
| 4692 | (13*10^126638+437)/9 | 126639 | Robert Price | 04/2018 |
| 4693 | (167*10^126637-17)/3 | 126639 | Robert Price | 03/2020 |
| 4694 | 4*10^126625+87 | 126626 | Robert Price | 08/2018 |
| 4695 | (31*2^420556+1)/7 | 126601 | Lelio R Paula | 05/2014 |
| 4696 | 7*10^126600-99 | 126601 | Robert Price | 06/2019 |
| 4697 | 2^420424-59189 | 126561 | Enzo Doria | 10/2015 |
| 4698 | 28717^25534+25534^28717 | 126560 | Hans Havermann | 03/2021 |
| 4699 | (86*10^126542+103)/9 | 126543 | Robert Price | 12/2021 |
| 4700 | (19*10^126517-7)/3 | 126518 | Robert Price | 12/2023 |
| 4701 | 28922^23655+23655^28922 | 126503 | Hans Havermann | 03/2021 |
| 4702 | 2^420126+71893 | 126471 | Enzo Doria | 04/2016 |
| 4703 | 25982^28643-28643^25982 | 126450 | Frank Doornink | 03/2024 |
| 4704 | (43*10^126441+47)/9 | 126442 | Robert Price | 12/2018 |
| 4705 | 8*10^126408+71 | 126409 | Robert Price | 05/2022 |
| 4706 | 2^419866+1877059 | 126393 | Enzo Doria | 07/2016 |
| 4707 | 29315^20484+20484^29315 | 126390 | Hans Havermann | 03/2021 |
| 4708 | 29433^19676+19676^29433 | 126384 | Hans Havermann | 03/2021 |
| 4709 | F(604711) | 126377 | Henri Lifchitz | 02/2005 |
| 4710 | 2^419757+72707 | 126360 | Enzo Doria | 04/2016 |
| 4711 | 2^419720-21569 | 126349 | Enzo Doria | 07/2013 |
| 4712 | 2^419637+29 | 126324 | Henri Lifchitz | 02/2006 |
| 4713 | 31004^11865+11865^31004 | 126319 | Hans Havermann | 03/2021 |
| 4714 | 2^419612+1876741 | 126316 | Enzo Doria | 07/2016 |
| 4715 | 2^419520+2793271 | 126289 | Enzo Doria | 03/2016 |
| 4716 | (2^419447-5)/369 | 126264 | Lelio R Paula | 05/2014 |
| 4717 | 2^419328-1859939 | 126231 | Enzo Doria | 03/2016 |
| 4718 | 2^419282-1851507 | 126217 | Enzo Doria | 08/2015 |
| 4719 | (133*10^126212+17)/3 | 126214 | Robert Price | 11/2021 |
| 4720 | 2^419251+1866143 | 126208 | Enzo Doria | 03/2016 |
| 4721 | 11^121185+2 | 126202 | Robert Price | 05/2014 |
| 4722 | 28203^28352+28352^28203 | 126175 | Norbert Schneider | 01/2021 |
| 4723 | (23*2^419036-1)/1393 | 126141 | Lelio R Paula | 05/2014 |
| 4724 | 2^418851+23 | 126087 | Robert Price | 09/2015 |
| 4725 | (2^418849-9)/2681 | 126083 | Lelio R Paula | 05/2014 |
| 4726 | 2^418829+167 | 126081 | Lelio R Paula | 01/2012 |
| 4727 | 31037^11530+11530^31037 | 126067 | Hans Havermann | 03/2021 |
| 4728 | 4*10^126064-69 | 126065 | Robert Price | 01/2022 |
| 4729 | (31*2^418782-1)/75891 | 126063 | Lelio R Paula | 05/2014 |
| 4730 | (19*2^418754-1)/15 | 126058 | Lelio R Paula | 05/2014 |
| 4731 | (35*10^126048-323)/9 | 126049 | Robert Price | 10/2021 |
| 4732 | 33016^6551+6551^33016 | 126000 | Hans Havermann | 03/2021 |
| 4733 | 2^418548-111546435 | 125996 | Paul Bourdelais | 10/2021 |
| 4734 | 25134^28625-28625^25134 | 125958 | Frank Doornink | 12/2023 |
| 4735 | 34736^4227+4227^34736 | 125954 | Hans Havermann | 03/2021 |
| 4736 | 26197^28502-28502^26197 | 125930 | Frank Doornink | 03/2024 |
| 4737 | 2^418319-109501 | 125927 | Enzo Doria | 04/2014 |
| 4738 | 2^418316-112373 | 125926 | Enzo Doria | 06/2014 |
| 4739 | 40398^1309+1309^40398 | 125919 | Hans Havermann | 03/2021 |
| 4740 | (8*10^125894-29)/3 | 125895 | Robert Price | 07/2018 |
| 4741 | (26*10^125886-413)/9 | 125887 | Robert Price | 05/2018 |
| 4742 | 10^(2*62938+1)-7*10^62938-1 | 125877 | Robert Price | 07/2023 |
| 4743 | 55*10^125847+9 | 125849 | Robert Price | 03/2022 |
| 4744 | 4*10^125832+57 | 125833 | Robert Price | 05/2022 |
| 4745 | 2^417968+1869811 | 125821 | Enzo Doria | 06/2016 |
| 4746 | 2^417902+63 | 125802 | Lelio R Paula | 09/2015 |
| 4747 | (10^125792-91)/9 | 125792 | Serge Batalov | 12/2014 |
| 4748 | 30438^13573+13573^30438 | 125791 | Hans Havermann | 03/2021 |
| 4749 | 32867^6714+6714^32867 | 125782 | Hans Havermann | 03/2021 |
| 4750 | 31155^10892+10892^31155 | 125777 | Hans Havermann | 03/2021 |
