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 | (25*10^124076-67)/3 | 124077 | Robert Price | 06/2019 |
4502 | F(593689) | 124074 | Henri Lifchitz | 01/2005 |
4503 | (11*2^412161+1)/19 | 124073 | Lelio R Paula | 05/2014 |
4504 | 35364^3215+3215^35364 | 124028 | Hans Havermann | 03/2021 |
4506 | (266*10^124022-11)/3 | 124024 | Robert Price | 04/2020 |
4505 | 29987^13674+13674^29987 | 124024 | Hans Havermann | 03/2021 |
4507 | 2^411932-111546435 | 124004 | Paul Bourdelais | 10/2021 |
4508 | 2^411884-113279 | 123990 | Enzo Doria | 07/2014 |
4509 | (2^411832+1)/257 | 123972 | Lelio R Paula | 05/2014 |
4510 | (2^411833+2)/514 | 123972 | Stefano Morozzi | 03/2020 |
4511 | (26*10^123970-89)/9 | 123971 | Robert Price | 06/2018 |
4512 | 2^411790-1853531 | 123962 | Enzo Doria | 08/2015 |
4513 | (5^177337+1)/6 | 123953 | Paul Bourdelais | 11/2008 |
4514 | (101*10^123950+7)/9 | 123952 | Robert Price | 02/2022 |
4515 | 2^411711-113257 | 123938 | Enzo Doria | 07/2014 |
4516 | (23*2^411675-1)/3 | 123928 | Lelio R Paula | 05/2014 |
4517 | 36289^2598+2598^36289 | 123914 | Hans Havermann | 03/2021 |
4518 | (11*10^123899-179)/3 | 123900 | Robert Price | 09/2018 |
4519 | 32276^6879+6879^32276 | 123860 | Hans Havermann | 02/2021 |
4520 | 2^411325-351103 | 123822 | Enzo Doria | 06/2015 |
4521 | (646*10^123817+11)/9 | 123819 | Robert Price | 10/2021 |
4522 | 30738^10643+10643^30738 | 123784 | Hans Havermann | 03/2021 |
4523 | 31074^9607+9607^31074 | 123755 | Hans Havermann | 03/2021 |
4524 | 2^411052+1872481 | 123739 | Enzo Doria | 05/2016 |
4525 | 34365^3986+3986^34365 | 123733 | Hans Havermann | 03/2021 |
4526 | 2^410997+39 | 123723 | Lelio R Paula | 05/2014 |
4527 | (649^43987-1)/648 | 123700 | Michael Stocker | 05/2020 |
4528 | (148*10^123688-1)/3 | 123690 | Robert Price | 03/2020 |
4529 | 36825^2284+2284^36825 | 123684 | Hans Havermann | 03/2021 |
4530 | 29582^15171+15171^29582 | 123683 | Hans Havermann | 03/2021 |
4531 | 10^123671+3593037 | 123672 | Paul Bourdelais | 10/2021 |
4532 | 8*10^123657+87 | 123658 | Robert Price | 10/2019 |
4533 | 30505^11302+11302^30505 | 123642 | Hans Havermann | 03/2021 |
4534 | 29956^13401+13401^29956 | 123633 | Hans Havermann | 03/2021 |
4535 | 155^56438+154 | 123618 | Norbert Schneider | 01/2019 |
4536 | 2^410596-39 | 123602 | Lelio R Paula | 05/2014 |
4537 | (41*10^123600-221)/9 | 123601 | Robert Price | 10/2021 |
4538 | 28995^18302+18302^28995 | 123592 | Hans Havermann | 03/2021 |
4539 | 28302^23269+23269^28302 | 123589 | Hans Havermann | 03/2021 |
4540 | 2^410540-115079 | 123585 | Enzo Doria | 06/2015 |
4541 | (7*10^123563+107)/3 | 123564 | Robert Price | 02/2018 |
4542 | 9*10^123549+89 | 123550 | Robert Price | 11/2019 |
4543 | (197*10^123545+7)/3 | 123547 | Robert Price | 12/2020 |
4544 | (3*2^410392-1)/9229 | 123537 | Lelio R Paula | 05/2014 |
4545 | 2^410342+212449 | 123526 | Enzo Doria | 08/2023 |
4546 | (29*10^123510+277)/9 | 123511 | Robert Price | 11/2021 |
4547 | 28118^24687+24687^28118 | 123508 | Hans Havermann | 03/2021 |
4548 | 39994^1225+1225^39994 | 123507 | Hans Havermann | 03/2021 |
4549 | 2^410206-113081 | 123485 | Enzo Doria | 07/2014 |
4550 | (25*2^410192+1)/10397 | 123478 | Lelio R Paula | 04/2014 |
4551 | 28974^18215+18215^28974 | 123442 | Hans Havermann | 03/2021 |
4552 | 28901^18618+18618^28901 | 123406 | Hans Havermann | 03/2021 |
4553 | 2^409909-189 | 123395 | Enzo Doria | 05/2014 |
4554 | 2^409896-109043 | 123391 | Enzo Doria | 04/2014 |
4555 | 2^409890+75409 | 123390 | Enzo Doria | 04/2016 |
4556 | 81254^33+33^81254 | 123386 | Hans Havermann | 03/2021 |
4557 | 33463^4854+4854^33463 | 123348 | Hans Havermann | 03/2021 |
4558 | 34061^4182+4182^34061 | 123348 | Hans Havermann | 03/2021 |
4559 | 133^58076-2 | 123345 | Lelio R Paula | 10/2017 |
4560 | F(590041) | 123311 | Henri Lifchitz | 01/2005 |
4561 | (82*10^123299+377)/9 | 123300 | Robert Price | 03/2022 |
4562 | 2^409566-113501 | 123292 | Enzo Doria | 08/2014 |
4563 | 2^409533+77747 | 123282 | Enzo Doria | 05/2016 |
4564 | 2^409436-112799 | 123253 | Enzo Doria | 06/2014 |
4565 | 28212^23321+23321^28212 | 123223 | Hans Havermann | 03/2021 |
4566 | 2^409225+1873787 | 123189 | Enzo Doria | 06/2016 |
4567 | 2^409174+73009 | 123174 | Enzo Doria | 04/2016 |
4568 | 2^409058-112685 | 123139 | Enzo Doria | 06/2014 |
4569 | (13*10^123137-61)/3 | 123138 | Robert Price | 11/2018 |
4570 | 4*10^123113+21 | 123114 | Robert Price | 12/2018 |
4571 | 2^408778+77689 | 123055 | Enzo Doria | 05/2016 |
4572 | 2^408690-75 | 123028 | Lelio R Paula | 11/2013 |
4573 | 28327^22032+22032^28327 | 123026 | Hans Havermann | 03/2021 |
4574 | (29*10^122996+673)/9 | 122997 | Robert Price | 12/2018 |
4575 | (65*10^122994-101)/9 | 122995 | Robert Price | 01/2022 |
4576 | 2^408574-2787341 | 122994 | Enzo Doria | 03/2016 |
4577 | 3*10^122977+37 | 122978 | Robert Price | 08/2018 |
4578 | (7*10^122976-67)/3 | 122977 | Robert Price | 10/2021 |
4579 | Phi(157825,10) | 122961 | Maksym Voznyy | 06/2015 |
4580 | (68*10^122933-419)/9 | 122934 | Robert Price | 07/2019 |
4581 | 29712^13721+13721^29712 | 122931 | Hans Havermann | 03/2021 |
4582 | (13*2^408283+1)/1665 | 122904 | Lelio R Paula | 05/2014 |
4583 | (266*10^122872-17)/3 | 122874 | Robert Price | 07/2020 |
4584 | (16*10^122871+77)/3 | 122872 | Robert Price | 03/2019 |
4585 | 30395^11022+11022^30395 | 122865 | Hans Havermann | 03/2021 |
4586 | 4*10^122859-69 | 122860 | Robert Price | 01/2022 |
4587 | (10^122857+167)/3 | 122857 | Robert Price | 05/2021 |
4588 | 33331^4852+4852^33331 | 122856 | Hans Havermann | 03/2021 |
4589 | (11*2^408100-1)/35 | 122850 | Lelio R Paula | 04/2014 |
4590 | (19*10^122836-43)/3 | 122837 | Robert Price | 05/2019 |
4591 | 28420^20969+20969^28420 | 122820 | Hans Havermann | 03/2021 |
4592 | (16*10^122818+179)/3 | 122819 | Robert Price | 11/2021 |
4593 | 29865^12934+12934^29865 | 122797 | Hans Havermann | 03/2021 |
4594 | (2^407821-lucasV(1,2,407821)+1)/2 | 122767 | Mike Oakes | 11/2016 |
4595 | (32*10^122733-77)/9 | 122734 | Robert Price | 06/2018 |
4596 | (21*2^407604-1)/215 | 122701 | Lelio R Paula | 04/2014 |
4598 | (22*10^122681+161)/3 | 122682 | Robert Price | 05/2019 |
4597 | 29513^14350+14350^29513 | 122682 | Hans Havermann | 03/2021 |
4599 | (21*2^407433-1)/13 | 122650 | Lelio R Paula | 04/2014 |
4600 | (26*10^122625-131)/3 | 122626 | Robert Price | 10/2019 |
4601 | 27925^24562+24562^27925 | 122599 | Hans Havermann | 03/2021 |
4602 | (73*10^122592-1)/9 | 122593 | Robert Price | 01/2015 |
4603 | (5*10^122592+91)/3 | 122593 | Robert Price | 04/2018 |
4604 | 36751^2166+2166^36751 | 122589 | Hans Havermann | 03/2021 |
4605 | (85*10^122585-1)/3 | 122587 | Robert Price | 02/2020 |
4606 | 29368^14931+14931^29368 | 122585 | Hans Havermann | 03/2021 |
4607 | 2^407179-112075 | 122574 | Enzo Doria | 06/2014 |
4608 | (21*2^407131+1)/207517523 | 122552 | Lelio R Paula | 04/2014 |
4609 | (66^67349+1)/67 | 122543 | Paul Bourdelais | 09/2017 |
4610 | (646*10^122533+11)/9 | 122535 | Robert Price | 10/2021 |
4611 | 2^407008-1867919 | 122522 | Enzo Doria | 04/2016 |
4612 | 11^117642-300 | 122512 | Enzo Doria | 10/2012 |
4613 | (F(3*97700+1)^2+L(3*97700+1)^2)/2 | 122509 | Henri Lifchitz | 10/2017 |
4614 | 2^406949+72197 | 122504 | Enzo Doria | 04/2016 |
4615 | (19*10^122501+149)/3 | 122502 | Robert Price | 05/2019 |
4616 | 28632^18977+18977^28632 | 122495 | Hans Havermann | 03/2021 |
4617 | 31815^7076+7076^31815 | 122481 | Hans Havermann | 03/2021 |
4618 | 2^406826-65 | 122467 | Lelio R Paula | 11/2013 |
4619 | 2^406821-2797363 | 122466 | Enzo Doria | 04/2016 |
4620 | (7*10^122456-331)/9 | 122456 | Robert Price | 03/2022 |
4621 | 2^406758-17 | 122447 | Lelio R Paula | 11/2013 |
4622 | 29941^12282+12282^29941 | 122437 | Hans Havermann | 03/2021 |
4623 | (30^82883-1)/29 | 122427 | Robert Price | 12/2011 |
4624 | 27496^27577+27577^27496 | 122422 | Norbert Schneider | 12/2020 |
4625 | 28732^18215+18215^28732 | 122411 | Hans Havermann | 03/2021 |
4626 | (2^406583-1)/813167 | 122388 | Jens K. Andersen | 02/2009 |
4627 | 4*10^122377+19 | 122378 | Robert Price | 10/2018 |
4628 | 28227^21634+21634^28227 | 122368 | Hans Havermann | 03/2021 |
4629 | Phi(246362,10) | 122365 | Makoto Kamada | 09/2019 |
4630 | 3*10^122345-97 | 122346 | Robert Price | 07/2018 |
4631 | 97^61575-2 | 122336 | Lelio R Paula | 12/2014 |
4632 | 2*10^122319+47 | 122320 | Robert Price | 12/2021 |
4633 | 208^52765+52765^208 | 122313 | Norbert Schneider | 11/2020 |
4635 | 2^406298+2799109 | 122308 | Enzo Doria | 04/2016 |
4634 | 2^406296+213691 | 122308 | Enzo Doria | 09/2023 |
4636 | 7*10^122294+57 | 122295 | Robert Price | 06/2019 |
4637 | (27*2^406241-1)/10277 | 122289 | Lelio R Paula | 04/2014 |
4638 | 2^406229-1849993 | 122288 | Enzo Doria | 08/2015 |
4639 | 3*10^122274+7 | 122275 | Robert Price | 07/2015 |
4640 | 2^406117+1876577 | 122254 | Enzo Doria | 07/2016 |
4641 | 29308^14835+14835^29308 | 122253 | Hans Havermann | 03/2021 |
4642 | 28119^22268+22268^28119 | 122253 | Hans Havermann | 03/2021 |
4643 | 32167^6312+6312^32167 | 122240 | Hans Havermann | 03/2021 |
4644 | 3^256199-2^256199 | 122238 | Mike Oakes | 06/2005 |
4645 | 27678^26053+26053^27678 | 122223 | Hans Havermann | 03/2021 |
4646 | 2^405992-78557 | 122216 | Jorge Menendez | 03/2018 |
4647 | (8*10^122203+43)/3 | 122204 | Robert Price | 06/2018 |
4648 | (58*10^122170+329)/9 | 122171 | Robert Price | 05/2019 |
4649 | 2^405774+179149 | 122151 | Enzo Doria | 06/2016 |
4650 | 2^405693+20417 | 122126 | Enzo Doria | 07/2023 |
4651 | (218*10^122109+7)/9 | 122111 | Robert Price | 06/2022 |
4652 | 29189^15246+15246^29189 | 122103 | Hans Havermann | 03/2021 |
4654 | 34*10^122082-9 | 122084 | Robert Price | 06/2020 |
4653 | 33442^4473+4473^33442 | 122084 | Hans Havermann | 03/2021 |
4655 | 5*10^122082+41 | 122083 | Robert Price | 03/2019 |
4656 | 31849^6808+6808^31849 | 122078 | Hans Havermann | 03/2021 |
4658 | 2^405514-3311 | 122072 | Yves Minet | 12/2014 |
4659 | 2^405514-115511 | 122072 | Enzo Doria | 07/2015 |
4657 | 23*10^122070-7 | 122072 | Robert Price | 02/2020 |
4660 | 2^405422-113261 | 122045 | Enzo Doria | 07/2014 |
4661 | 2^405173+71237 | 121970 | Enzo Doria | 04/2016 |
4662 | fibonacci(583574)+2 | 121960 | Jon Grantham | 08/2023 |
4663 | (154*10^121953+17)/9 | 121955 | Robert Price | 06/2022 |
4664 | (34*10^121924+191)/9 | 121925 | Robert Price | 08/2021 |
4665 | (2^405016+1)/257 | 121920 | Lelio R Paula | 04/2014 |
4666 | 28557^18590+18590^28557 | 121918 | Hans Havermann | 03/2021 |
4667 | 28641^18002+18002^28641 | 121877 | Hans Havermann | 03/2021 |
4668 | 2^404858+71329 | 121875 | Enzo Doria | 04/2016 |
4669 | 2^404813-114703 | 121861 | Enzo Doria | 04/2015 |
4670 | 2^404764+77791 | 121847 | Enzo Doria | 05/2016 |
4671 | 28830^16841+16841^28830 | 121847 | Hans Havermann | 03/2021 |
4672 | (4*10^121825+89)/3 | 121826 | Robert Price | 08/2021 |
4673 | 317^48694+48694^317 | 121787 | Norbert Schneider | 08/2015 |
4674 | 2^404536-115259 | 121778 | Enzo Doria | 06/2015 |
4675 | 2^404501-631 | 121767 | Yves Minet | 07/2012 |
4676 | 5*10^121764-69 | 121765 | Robert Price | 02/2021 |
4677 | 28236^20485+20485^28236 | 121738 | Hans Havermann | 02/2021 |
4678 | (382*10^121694-31)/9 | 121696 | Robert Price | 06/2022 |
4679 | 63^67620+2 | 121672 | Lelio R Paula | 08/2015 |
4680 | (25*34^79445-28062367)/33 | 121669 | Eric Chen | 08/2023 |
4681 | (16*10^121633+167)/3 | 121634 | Robert Price | 06/2019 |
4682 | 29955^11494+11494^29955 | 121632 | Hans Havermann | 02/2021 |
4683 | (17*10^121621+1)/9 | 121622 | Serge Batalov | 05/2010 |
4684 | 31088^8163+8163^31088 | 121612 | Hans Havermann | 02/2021 |
4685 | (15*2^403912+1)/271 | 121589 | Lelio R Paula | 05/2014 |
4686 | (10^121543-79)/3 | 121543 | Robert Price | 01/2018 |
4687 | 2^403676+76831 | 121519 | Enzo Doria | 05/2016 |
4688 | (7*10^121487+143)/3 | 121488 | Robert Price | 03/2018 |
4689 | 27965^22086+22086^27965 | 121484 | Hans Havermann | 02/2021 |
4690 | (893*10^121470+7)/9 | 121472 | Robert Price | 06/2021 |
4691 | (206*10^121462-11)/3 | 121464 | Robert Price | 02/2022 |
4692 | (77*10^121455+67)/9 | 121456 | Robert Price | 12/2021 |
4693 | 2^403363-113635 | 121425 | Enzo Doria | 08/2014 |
4694 | (17*10^121418-113)/3 | 121419 | Robert Price | 06/2021 |
4695 | 2^403336-1861469 | 121417 | Enzo Doria | 03/2016 |
4696 | 27929^22186+22186^27929 | 121382 | Hans Havermann | 02/2021 |
4697 | p(24442)#/2-64 | 121381 | Robert Price | 04/2017 |
4698 | 11^116555-720 | 121380 | Enzo Doria | 11/2012 |
4699 | 2^403100-461267 | 121346 | Enzo Doria | 07/2015 |
4700 | 2^403093-112213 | 121344 | Enzo Doria | 06/2014 |
4701 | 29404^13385+13385^29404 | 121340 | Hans Havermann | 02/2021 |
4702 | 28106^20745+20745^28106 | 121332 | Hans Havermann | 02/2021 |
4703 | (316^48539+1)/317 | 121330 | Eric Chen | 10/2017 |
4704 | (23*10^121320-71)/3 | 121321 | Robert Price | 07/2020 |
4705 | 2^403004+1866361 | 121317 | Enzo Doria | 03/2016 |
4706 | 2^402953+89 | 121301 | Lelio R Paula | 10/2013 |
4707 | 2^402944-2788319 | 121299 | Enzo Doria | 03/2016 |
4708 | (44*10^121297-719)/9 | 121298 | Robert Price | 12/2018 |
4709 | (27*2^402865+1)/5 | 121276 | Lelio R Paula | 04/2014 |
4710 | 2^402828-113183 | 121264 | Enzo Doria | 07/2014 |
4711 | (17*10^121242+1)/9 | 121243 | Serge Batalov | 05/2010 |
4712 | (15*2^402757+1)/101 | 121242 | Lelio R Paula | 05/2014 |
4714 | 2^402715+1874223 | 121230 | Enzo Doria | 06/2016 |
4713 | (35*10^121229-593)/9 | 121230 | Robert Price | 07/2018 |
4715 | (91^61879+1)/92 | 121222 | Paul Bourdelais | 09/2017 |
4716 | 28719^16568+16568^28719 | 121174 | Hans Havermann | 02/2021 |
4717 | 7*10^121144+9 | 121145 | Robert Price | 09/2015 |
4718 | 27490^25467+25467^27490 | 121121 | Hans Havermann | 02/2021 |
4719 | 34575^3182+3182^34575 | 121106 | Hans Havermann | 02/2021 |
4720 | 5*10^121100-37 | 121101 | Robert Price | 11/2021 |
4721 | 29954^10935+10935^29954 | 120979 | Hans Havermann | 02/2021 |
4722 | 33585^3992+3992^33585 | 120946 | Hans Havermann | 02/2021 |
4723 | 40296^1003+1003^40296 | 120941 | Hans Havermann | 02/2021 |
4724 | 2^401725-113251 | 120932 | Enzo Doria | 07/2014 |
4725 | (15*2^401677-1)/19 | 120917 | Lelio R Paula | 05/2014 |
4726 | 2^401652+73711 | 120910 | Enzo Doria | 04/2016 |
4727 | (2^401632+3)/79 | 120902 | Lelio R Paula | 04/2014 |
4728 | 40450^973+973^40450 | 120870 | Hans Havermann | 01/2021 |
4729 | (8*10^120851-11)/3 | 120852 | Robert Price | 07/2023 |
4730 | 10^120841+88417 | 120842 | Patrick De Geest | 04/2020 |
4731 | 10^120841-123456789 | 120841 | Robert Price | 02/2020 |
4732 | 10^120841-176853 | 120841 | Patrick De Geest | 04/2020 |
4733 | 2^401406-2791331 | 120836 | Enzo Doria | 03/2016 |
4734 | (28^83497+1)/29 | 120832 | Robert Price | 07/2013 |
4735 | (22*10^120828+161)/3 | 120829 | Robert Price | 05/2019 |
4736 | 2^401369+1867367 | 120825 | Enzo Doria | 03/2016 |
4737 | (5*10^120821+43)/3 | 120822 | Robert Price | 12/2021 |
4738 | (10^120782+29)/3 | 120782 | Serge Batalov | 12/2014 |
4739 | 2^401215-1657 | 120778 | Yves Minet | 07/2014 |
4740 | 2^401159+53 | 120761 | Lelio R Paula | 10/2013 |
4741 | 27782^22179+22179^27782 | 120739 | Hans Havermann | 01/2021 |
4742 | 32974^4585+4585^32974 | 120730 | Hans Havermann | 02/2021 |
4743 | 2^401031-113047 | 120723 | Enzo Doria | 07/2014 |
4744 | 30598^8813+8813^30598 | 120713 | Hans Havermann | 02/2021 |
4745 | (71*10^120703-287)/9 | 120704 | Robert Price | 09/2019 |
4746 | (29*2^400909-1)/303 | 120685 | Lelio R Paula | 04/2014 |
4747 | 34793^2940+2940^34793 | 120675 | Hans Havermann | 02/2021 |
4748 | (2^400846+538)/2 | 120667 | Stefano Morozzi | 09/2020 |
4749 | (166*10^120654+11)/3 | 120656 | Robert Price | 03/2021 |
4750 | 34066^3481+3481^34066 | 120652 | Hans Havermann | 02/2021 |