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 ? |
| 5501 | (F(5)^182099-F(4)^182099)/F(3) | 127282 | Wayne Halsdorf | 08/2013 |
| 5502 | (16*10^127259+197)/3 | 127260 | Robert Price | 04/2019 |
| 5503 | (26*10^127240+61)/3 | 127241 | Robert Price | 10/2019 |
| 5504 | (234483*27^88884-145)/26 | 127230 | Curtis Bright | 05/2015 |
| 5505 | 2^422515-114997 | 127190 | Enzo Doria | 06/2015 |
| 5506 | 5*10^127179-3 | 127180 | Robert Price | 07/2015 |
| 5507 | 31678^10343+10343^31678 | 127176 | Hans Havermann | 03/2021 |
| 5508 | (44*10^127169-233)/9 | 127170 | Robert Price | 01/2019 |
| 5509 | 34947^4352+4352^34947 | 127162 | Hans Havermann | 03/2021 |
| 5510 | 6*10^127158+19 | 127159 | Robert Price | 11/2021 |
| 5511 | 30469^14902+14902^30469 | 127155 | Hans Havermann | 03/2021 |
| 5512 | 5*10^127153+77 | 127154 | Robert Price | 12/2018 |
| 5513 | 29941^17620+17620^29941 | 127130 | Hans Havermann | 02/2021 |
| 5514 | 31607^10516+10516^31607 | 127119 | Hans Havermann | 03/2021 |
| 5515 | (19*10^127118-97)/3 | 127119 | Robert Price | 10/2021 |
| 5516 | (29*10^127111+691)/9 | 127112 | Robert Price | 08/2021 |
| 5517 | 736^44335+44335^736 | 127104 | Norbert Schneider | 07/2019 |
| 5518 | 33040^7023+7023^33040 | 127090 | Hans Havermann | 03/2021 |
| 5519 | (4*10^127081+167)/9 | 127081 | Robert Price | 03/2022 |
| 5520 | 29748^18661+18661^29748 | 127052 | Hans Havermann | 03/2021 |
| 5521 | 27905^28578-28578^27905 | 127049 | Frank Doornink | 03/2024 |
| 5522 | -516776642557847117490*Bern(37960)/34256837217082767928421792453 | 127042 | Thomas Ritschel | 06/2017 |
| 5523 | (78^67141-1)/77 | 127036 | Paul Bourdelais | 09/2017 |
| 5524 | (14*10^127014-137)/3 | 127015 | Robert Price | 04/2021 |
| 5525 | 31436^10965+10965^31436 | 127002 | Hans Havermann | 03/2021 |
| 5526 | 28905^24758+24758^28905 | 127001 | Hans Havermann | 03/2021 |
| 5527 | 2^421860-113285 | 126993 | Enzo Doria | 07/2014 |
| 5528 | (10^127030+7)/81234833/9230384921/6092460488946445358851 | 126991 | Alfred Reich | 07/2021 |
| 5529 | (2^421827-7)/11 | 126982 | Lelio R Paula | 05/2015 |
| 5530 | 26268^28729-28729^26268 | 126966 | Frank Doornink | 03/2024 |
| 5531 | 11^121910-840 | 126957 | Enzo Doria | 12/2012 |
| 5532 | (56*10^126935+187)/9 | 126936 | Robert Price | 10/2021 |
| 5533 | 28915^24538+24538^28915 | 126933 | Hans Havermann | 03/2021 |
| 5534 | (29*10^126928-77)/3 | 126929 | Robert Price | 02/2020 |
| 5535 | (259*10^126919-1)/3 | 126921 | Robert Price | 12/2020 |
| 5536 | 10^126919+204567 | 126920 | Patrick De Geest | 05/2021 |
| 5537 | (2^421617+100280245065) | 126920 | Paul Bourdelais | 05/2022 |
| 5538 | 10^126919-100001 | 126919 | Robert Price | 07/2020 |
| 5539 | 28340^28503+28503^28340 | 126907 | Norbert Schneider | 02/2021 |
| 5540 | 2^421534-3001935 | 126895 | Paul Bourdelais | 07/2023 |
| 5541 | (71^68539+1)/72 | 126882 | Paul Bourdelais | 09/2017 |
| 5542 | (5*10^126871-119)/3 | 126872 | Robert Price | 03/2018 |
| 5543 | 331^50339-10004 | 126846 | Enzo Doria | 07/2012 |
| 5544 | 2^421363-2790757 | 126843 | Enzo Doria | 03/2016 |
| 5545 | (106*10^126839-1)/3 | 126841 | Serge Batalov | 12/2014 |
| 5546 | 37938^2203+2203^37938 | 126828 | Hans Havermann | 03/2021 |
| 5547 | (13*10^126819+77)/9 | 126820 | Robert Price | 07/2022 |
| 5548 | (7*2^421243+1)/39 | 126807 | Lelio R Paula | 05/2014 |
| 5550 | (14*10^126784-83)/3 | 126785 | Robert Price | 12/2018 |
| 5549 | 2^421169-3001935 | 126785 | Paul Bourdelais | 07/2023 |
| 5551 | 2^421161-286183 | 126783 | Enzo Doria | 06/2015 |
| 5552 | 26733^28628-28628^26733 | 126738 | Frank Doornink | 03/2024 |
| 5553 | (106*10^126726+17)/3 | 126728 | Robert Price | 04/2021 |
| 5554 | 30718^13347+13347^30718 | 126724 | Hans Havermann | 03/2021 |
| 5555 | 2^420939-113935 | 126716 | Enzo Doria | 10/2014 |
| 5556 | 11*23^93048+356 | 126708 | Eric Chen | 08/2023 |
| 5557 | 177^56363-2 | 126703 | Lelio R Paula | 10/2017 |
| 5558 | 2^420741-113659 | 126656 | Enzo Doria | 08/2014 |
| 5559 | 2^420694-21 | 126642 | Lelio R Paula | 05/2017 |
| 5560 | (13*10^126638+437)/9 | 126639 | Robert Price | 04/2018 |
| 5561 | (167*10^126637-17)/3 | 126639 | Robert Price | 03/2020 |
| 5562 | 4*10^126625+87 | 126626 | Robert Price | 08/2018 |
| 5563 | (31*2^420556+1)/7 | 126601 | Lelio R Paula | 05/2014 |
| 5564 | 7*10^126600-99 | 126601 | Robert Price | 06/2019 |
| 5565 | U(655247)/250330563881/206066063082749 | 126596 | Serge Batalov | 07/2024 |
| 5566 | 2^420424-59189 | 126561 | Enzo Doria | 10/2015 |
| 5567 | 28717^25534+25534^28717 | 126560 | Hans Havermann | 03/2021 |
| 5568 | (86*10^126542+103)/9 | 126543 | Robert Price | 12/2021 |
| 5569 | (19*10^126517-7)/3 | 126518 | Robert Price | 12/2023 |
| 5570 | 28922^23655+23655^28922 | 126503 | Hans Havermann | 03/2021 |
| 5571 | 2^420126+71893 | 126471 | Enzo Doria | 04/2016 |
| 5572 | 25982^28643-28643^25982 | 126450 | Frank Doornink | 03/2024 |
| 5573 | (43*10^126441+47)/9 | 126442 | Robert Price | 12/2018 |
| 5574 | 8*10^126408+71 | 126409 | Robert Price | 05/2022 |
| 5575 | 2^419866+1877059 | 126393 | Enzo Doria | 07/2016 |
| 5576 | 29315^20484+20484^29315 | 126390 | Hans Havermann | 03/2021 |
| 5577 | 29433^19676+19676^29433 | 126384 | Hans Havermann | 03/2021 |
| 5578 | F(604711) | 126377 | Henri Lifchitz | 02/2005 |
| 5579 | 2^419757+72707 | 126360 | Enzo Doria | 04/2016 |
| 5580 | 2^419720-21569 | 126349 | Enzo Doria | 07/2013 |
| 5581 | 2^419637+29 | 126324 | Henri Lifchitz | 02/2006 |
| 5582 | 31004^11865+11865^31004 | 126319 | Hans Havermann | 03/2021 |
| 5583 | 2^419612+1876741 | 126316 | Enzo Doria | 07/2016 |
| 5584 | 2^419520+2793271 | 126289 | Enzo Doria | 03/2016 |
| 5585 | (2^419447-5)/369 | 126264 | Lelio R Paula | 05/2014 |
| 5586 | 2^419328-1859939 | 126231 | Enzo Doria | 03/2016 |
| 5587 | 2^419282-1851507 | 126217 | Enzo Doria | 08/2015 |
| 5588 | (133*10^126212+17)/3 | 126214 | Robert Price | 11/2021 |
| 5589 | 2^419251+1866143 | 126208 | Enzo Doria | 03/2016 |
| 5590 | 11^121185+2 | 126202 | Robert Price | 05/2014 |
| 5591 | 28203^28352+28352^28203 | 126175 | Norbert Schneider | 01/2021 |
| 5592 | (23*2^419036-1)/1393 | 126141 | Lelio R Paula | 05/2014 |
| 5593 | 2^418851+23 | 126087 | Robert Price | 09/2015 |
| 5594 | (2^418849-9)/2681 | 126083 | Lelio R Paula | 05/2014 |
| 5595 | 2^418829+167 | 126081 | Lelio R Paula | 01/2012 |
| 5596 | 31037^11530+11530^31037 | 126067 | Hans Havermann | 03/2021 |
| 5597 | 4*10^126064-69 | 126065 | Robert Price | 01/2022 |
| 5598 | (31*2^418782-1)/75891 | 126063 | Lelio R Paula | 05/2014 |
| 5599 | (19*2^418754-1)/15 | 126058 | Lelio R Paula | 05/2014 |
| 5600 | (35*10^126048-323)/9 | 126049 | Robert Price | 10/2021 |
| 5601 | 33016^6551+6551^33016 | 126000 | Hans Havermann | 03/2021 |
| 5602 | 2^418548-111546435 | 125996 | Paul Bourdelais | 10/2021 |
| 5603 | 25134^28625-28625^25134 | 125958 | Frank Doornink | 12/2023 |
| 5604 | 34736^4227+4227^34736 | 125954 | Hans Havermann | 03/2021 |
| 5605 | (23*35^81566-144013)/34 | 125944 | Eric Chen | 05/2025 |
| 5606 | 26197^28502-28502^26197 | 125930 | Frank Doornink | 03/2024 |
| 5607 | 2^418319-109501 | 125927 | Enzo Doria | 04/2014 |
| 5608 | 2^418316-112373 | 125926 | Enzo Doria | 06/2014 |
| 5609 | 40398^1309+1309^40398 | 125919 | Hans Havermann | 03/2021 |
| 5610 | (8*10^125894-29)/3 | 125895 | Robert Price | 07/2018 |
| 5611 | (26*10^125886-413)/9 | 125887 | Robert Price | 05/2018 |
| 5612 | 10^(2*62938+1)-7*10^62938-1 | 125877 | Robert Price | 07/2023 |
| 5613 | 55*10^125847+9 | 125849 | Robert Price | 03/2022 |
| 5614 | 4*10^125832+57 | 125833 | Robert Price | 05/2022 |
| 5615 | 2^417968+1869811 | 125821 | Enzo Doria | 06/2016 |
| 5616 | 2^417902+63 | 125802 | Lelio R Paula | 09/2015 |
| 5617 | (10^125792-91)/9 | 125792 | Serge Batalov | 12/2014 |
| 5618 | 30438^13573+13573^30438 | 125791 | Hans Havermann | 03/2021 |
| 5619 | 32867^6714+6714^32867 | 125782 | Hans Havermann | 03/2021 |
| 5620 | 31155^10892+10892^31155 | 125777 | Hans Havermann | 03/2021 |
| 5621 | (35*10^125754-593)/9 | 125755 | Robert Price | 07/2018 |
| 5622 | 30455^13464+13464^30455 | 125754 | Hans Havermann | 03/2021 |
| 5623 | (32*10^125751-77)/9 | 125752 | Robert Price | 06/2018 |
| 5624 | 2^417704+77011 | 125742 | Enzo Doria | 05/2016 |
| 5625 | 29755^16816+16816^29755 | 125737 | Hans Havermann | 03/2021 |
| 5626 | (22*10^125734+203)/9 | 125735 | Robert Price | 10/2021 |
| 5627 | 29918^15915+15915^29918 | 125710 | Hans Havermann | 03/2021 |
| 5628 | (10^125706+149)/3 | 125706 | Serge Batalov | 12/2014 |
| 5629 | 28531^25368+25368^28531 | 125659 | Hans Havermann | 03/2021 |
| 5630 | 2^417419-115309 | 125656 | Enzo Doria | 07/2015 |
| 5631 | (46*10^125642+593)/9 | 125643 | Robert Price | 04/2022 |
| 5632 | 2^417315+213953 | 125625 | Enzo Doria | 10/2023 |
| 5633 | 2^417300+77281 | 125620 | Enzo Doria | 05/2016 |
| 5634 | 30638^12537+12537^30638 | 125561 | Hans Havermann | 03/2021 |
| 5635 | 2^417095-1657 | 125559 | Yves Minet | 07/2014 |
| 5636 | 30162^14525+14525^30162 | 125538 | Hans Havermann | 03/2021 |
| 5637 | (56*10^125535+583)/9 | 125536 | Robert Price | 08/2021 |
| 5638 | (23*10^125517-179)/3 | 125518 | Robert Price | 06/2022 |
| 5639 | 9*10^125516+29 | 125517 | Robert Price | 03/2022 |
| 5640 | 404*35^81280+23 | 125505 | Eric Chen | 05/2025 |
| 5641 | (88*10^125492-637)/9 | 125493 | Robert Price | 11/2020 |
| 5642 | 28958^21525+21525^28958 | 125474 | Hans Havermann | 02/2021 |
| 5645 | 2^416773-25 | 125462 | Lelio R Paula | 09/2015 |
| 5643 | (10^125482+7)/162685667/1639829194459 | 125462 | Alfred Reich | 07/2021 |
| 5644 | 26078^28409-28409^26078 | 125462 | Frank Doornink | 03/2024 |
| 5646 | 33889^5032+5032^33889 | 125449 | Hans Havermann | 03/2021 |
| 5647 | (289511#+292834)/(2^3*146417) | 125444 | Makoto Morimoto | 10/2017 |
| 5648 | (2861^36481+1)/(2861^191+1) | 125438 | Martin Hopf | 12/2023 |
| 5649 | (11*2^416691+1)/43 | 125436 | Lelio R Paula | 05/2014 |
| 5650 | (289511#+1896)/(2*3^3*79*780193*9911849) | 125434 | Makoto Morimoto | 06/2019 |
| 5651 | 2^416641-2*416641+1 | 125422 | Robert Price | 05/2018 |
| 5652 | 33392^5697+5697^33392 | 125409 | Hans Havermann | 03/2021 |
| 5653 | (21*2^416566-1)/17 | 125399 | Lelio R Paula | 05/2014 |
| 5654 | 2^416530+1870429 | 125389 | Enzo Doria | 05/2016 |
| 5655 | (56*10^125385+691)/9 | 125386 | Robert Price | 05/2019 |
| 5656 | 27953^28198+28198^27953 | 125381 | Norbert Schneider | 01/2021 |
| 5657 | 31074^10837+10837^31074 | 125381 | Hans Havermann | 03/2021 |
| 5658 | 33745^5194+5194^33745 | 125380 | Hans Havermann | 03/2021 |
| 5659 | 2^416490+1875109 | 125376 | Enzo Doria | 09/2016 |
| 5660 | 28360^26331+26331^28360 | 125365 | Hans Havermann | 03/2021 |
| 5661 | 2^416416-114929 | 125354 | Enzo Doria | 05/2015 |
| 5662 | 25805^28412-28412^25805 | 125346 | Frank Doornink | 03/2024 |
| 5663 | (77*10^125330-293)/9 | 125331 | Robert Price | 09/2019 |
| 5664 | (172*10^125292-1)/9 | 125294 | Serge Batalov | 12/2014 |
| 5665 | 2^416134+1865899 | 125269 | Enzo Doria | 03/2016 |
| 5666 | 153^57337-152 | 125264 | Norbert Schneider | 12/2018 |
| 5667 | (599*10^125224+13)/9 | 125226 | Robert Price | 02/2022 |
| 5668 | (9*2^415992+1)/13560845 | 125220 | Lelio R Paula | 05/2014 |
| 5669 | 30054^14657+14657^30054 | 125207 | Hans Havermann | 03/2021 |
| 5670 | (23^91943-1)/22 | 125201 | Robert Price | 01/2012 |
| 5671 | 2^415884-933075 | 125194 | Paul Bourdelais | 06/2021 |
| 5672 | 43125^27010-106 | 125185 | Enzo Doria | 08/2012 |
| 5673 | (38*10^125166+349)/9 | 125167 | Robert Price | 10/2018 |
| 5674 | 10^125166-5001 | 125166 | Robert Price | 12/2021 |
| 5675 | 2^415765-112603 | 125158 | Enzo Doria | 06/2014 |
| 5676 | 8*10^125088-13 | 125089 | Robert Price | 08/2019 |
| 5677 | (25*10^125076-13)/3 | 125077 | Robert Price | 09/2019 |
| 5678 | (11*10^125054+73)/3 | 125055 | Robert Price | 08/2021 |
| 5679 | (101^62383-1)/17542099700 | 125026 | Paul Vanderveen | 06/2025 |
| 5680 | (29*10^125021-113)/3 | 125022 | Robert Price | 10/2019 |
| 5681 | 2^415290-113591 | 125015 | Enzo Doria | 08/2014 |
| 5682 | 2^415276-460919 | 125011 | Enzo Doria | 06/2015 |
| 5683 | 2^415259+77243 | 125006 | Enzo Doria | 05/2016 |
| 5684 | (67*10^124990+77)/9 | 124991 | Robert Price | 10/2021 |
| 5685 | 2^415144-3683 | 124971 | Yves Minet | 10/2011 |
| 5686 | 2^415092+111546435 | 124956 | Paul Bourdelais | 10/2021 |
| 5687 | 31936^8173+8173^31936 | 124946 | Hans Havermann | 03/2021 |
| 5688 | 27458^28145-28145^27458 | 124927 | Frank Doornink | 03/2024 |
| 5689 | 5^178715-4 | 124917 | Tyler NeSmith | 07/2021 |
| 5690 | 29767^15700+15700^29767 | 124900 | Hans Havermann | 03/2021 |
| 5691 | (310^50131-1)/309 | 124892 | Tom Wu | 07/2024 |
| 5692 | 2^414874+79 | 124890 | Lelio R Paula | 01/2015 |
| 5693 | 25292^28361-28361^25292 | 124874 | Frank Doornink | 01/2024 |
| 5694 | (2^414765+7)/1389 | 124854 | Lelio R Paula | 05/2014 |
| 5695 | 2^414618+79459 | 124813 | Enzo Doria | 06/2016 |
| 5696 | (61*10^124809-1)/3 | 124811 | Robert Price | 01/2020 |
| 5697 | (235*29^85334+129)/28 | 124794 | Eric Chen | 06/2025 |
| 5698 | (29*10^124765-71)/3 | 124766 | Robert Price | 07/2021 |
| 5699 | 2^414432-1846709 | 124757 | Enzo Doria | 07/2015 |
| 5700 | 2*10^124751-51 | 124752 | Robert Price | 04/2018 |
| 5701 | (56*10^124735+367)/9 | 124736 | Robert Price | 06/2019 |
| 5702 | 27362^28111-28111^27362 | 124733 | Frank Doornink | 03/2024 |
| 5703 | (13*2^414274-1)/153 | 124708 | Lelio R Paula | 05/2014 |
| 5704 | (23*10^124690+37)/3 | 124691 | Robert Price | 02/2022 |
| 5705 | p(25046)#-p(25046+1) | 124675 | Henri Lifchitz | 11/2024 |
| 5706 | 56*10^124656-3 | 124658 | Robert Price | 03/2020 |
| 5707 | (7*10^124648+197)/3 | 124649 | Robert Price | 07/2018 |
| 5709 | 2^414032-5 | 124637 | Henri Lifchitz | 07/2006 |
| 5708 | 2^414032+1872331 | 124637 | Enzo Doria | 05/2016 |
| 5710 | 37373^2158+2158^37373 | 124604 | Hans Havermann | 03/2021 |
| 5711 | 29811^15112+15112^29811 | 124590 | Hans Havermann | 03/2021 |
| 5712 | (22^92791-3^92791)/19 | 124564 | Robert Price | 02/2025 |
| 5713 | F(596093)/36870605281541 | 124563 | Serge Batalov | 07/2024 |
| 5714 | 2^413781-2023 | 124561 | Riley Fisher | 09/2023 |
| 5715 | 14120^30009-30009^14120 | 124533 | Norbert Schneider | 02/2015 |
| 5716 | 29757^15296+15296^29757 | 124521 | Hans Havermann | 03/2021 |
| 5717 | 35056^3561+3561^35056 | 124504 | Hans Havermann | 03/2021 |
| 5718 | 40588^1167+1167^40588 | 124487 | Hans Havermann | 02/2021 |
| 5719 | (85*10^124485-49)/9 | 124486 | Robert Price | 12/2020 |
| 5720 | 64^68909-63^68909 | 124463 | Robert Price | 07/2013 |
| 5721 | 35016^3581+3581^35016 | 124448 | Hans Havermann | 03/2021 |
| 5722 | 2^413387+76253 | 124442 | Enzo Doria | 04/2016 |
| 5723 | 28749^21298+21298^28749 | 124436 | Hans Havermann | 03/2021 |
| 5724 | 2^413352+524287 | 124432 | Paul Underwood | 09/2018 |
| 5725 | 287117#+391613 | 124424 | Nicolas PALAU | 01/2017 |
| 5726 | (4*10^124420+83)/3 | 124421 | Robert Price | 02/2018 |
| 5727 | 34578^3965+3965^34578 | 124421 | Hans Havermann | 03/2021 |
| 5728 | (68*10^124392-329)/9 | 124393 | Robert Price | 03/2021 |
| 5729 | (27*2^413207-1)/108335 | 124385 | Lelio R Paula | 05/2014 |
| 5730 | 10^124383+58407 | 124384 | Patrick De Geest | 08/2021 |
| 5732 | 10^124383-8000001 | 124383 | Robert Price | 04/2021 |
| 5731 | 10^124383-5801 | 124383 | Patrick De Geest | 08/2021 |
| 5733 | 26091^28154-28154^26091 | 124342 | Frank Doornink | 03/2024 |
| 5734 | (41*10^124335-383)/9 | 124336 | Robert Price | 11/2018 |
| 5735 | (304*10^124329-43)/9 | 124331 | Robert Price | 02/2020 |
| 5736 | 34716^3811+3811^34716 | 124320 | Hans Havermann | 03/2021 |
| 5737 | 26892^28063-28063^26892 | 124309 | Frank Doornink | 03/2024 |
| 5738 | 2^412868-120599 | 124286 | Paul Bourdelais | 02/2012 |
| 5739 | 10^124248+899089 | 124249 | Patrick De Geest | 05/2021 |
| 5741 | 10^124248-1000001 | 124248 | Robert Price | 08/2020 |
| 5740 | 10^124248-501903 | 124248 | Patrick De Geest | 05/2021 |
| 5742 | 45^75145-2 | 124231 | Lelio R Paula | 08/2015 |
| 5743 | 29901^14272+14272^29901 | 124224 | Hans Havermann | 03/2021 |
| 5744 | 2^412645-112213 | 124219 | Enzo Doria | 06/2014 |
| 5745 | 29837^14500+14500^29837 | 124163 | Hans Havermann | 03/2021 |
| 5746 | 28074^26455+26455^28074 | 124158 | Hans Havermann | 03/2021 |
| 5747 | 954^41669-41669^954 | 124155 | Norman Luhn | 10/2024 |
| 5748 | 432^47093-47093^432 | 124113 | Norman Luhn | 10/2024 |
| 5749 | 2^412285+213317 | 124111 | Enzo Doria | 09/2023 |
| 5750 | (12^115001-1)/2530033 | 124101 | Paul Vanderveen | 06/2025 |
