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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Rank |
Probable prime |
Digits (> 50000) |
Who ? |
When ? |
5501 | 2^356442-114713 | 107300 | Enzo Doria | 04/2015 |
5502 | 2^356425+72257 | 107295 | Enzo Doria | 04/2016 |
5503 | 2^356351-112237 | 107273 | Enzo Doria | 06/2014 |
5505 | (6^137845-11)/5 | 107264 | Paul Bourdelais | 11/2011 |
5504 | 2^356322+74539 | 107264 | Enzo Doria | 04/2016 |
5506 | 2^356274+1874479 | 107250 | Enzo Doria | 06/2016 |
5507 | 24606^22819+22819^24606 | 107241 | Hans Havermann | 10/2020 |
5508 | (2^356243+3686)/2 | 107240 | Stefano Morozzi | 09/2020 |
5509 | 20^82422-93 | 107234 | Lelio R Paula | 02/2017 |
5510 | 2^356157-20365 | 107214 | Enzo Doria | 06/2013 |
5511 | 8*10^107209+99 | 107210 | Robert Price | 03/2021 |
5512 | 2^356129-18949 | 107206 | Enzo Doria | 05/2013 |
5513 | 2^356100-109587 | 107197 | Enzo Doria | 04/2014 |
5514 | 2*10^107173-37 | 107174 | Robert Price | 11/2021 |
5515 | (2^355978+3262)/2 | 107160 | Stefano Morozzi | 02/2021 |
5516 | (31*2^355970+1)/5 | 107159 | Lelio R Paula | 03/2014 |
5517 | 2^355968-64875 | 107158 | Lelio R Paula | 01/2017 |
5518 | 2^355952+1870321 | 107153 | Enzo Doria | 05/2016 |
5519 | 27069^9088+9088^27069 | 107152 | Hans Havermann | 11/2020 |
5520 | 2^355915-117 | 107142 | Lelio R Paula | 11/2011 |
5521 | (16*10^107140+77)/3 | 107141 | Robert Price | 03/2019 |
5522 | 24628^22369+22369^24628 | 107124 | Hans Havermann | 11/2020 |
5523 | (19*2^355838-1)/15 | 107119 | Lelio R Paula | 03/2014 |
5524 | 3^224495-8 | 107112 | Lelio R Paula | 12/2013 |
5525 | 3*10^107096+23 | 107097 | Robert Price | 03/2022 |
5526 | 25077^18632+18632^25077 | 107086 | Hans Havermann | 10/2020 |
5527 | 7^126691-44 | 107067 | Lelio R Paula | 03/2017 |
5528 | 4^177830-8243 | 107065 | Mike Oakes | 02/2011 |
5529 | (509*10^107057+13)/9 | 107059 | Robert Price | 05/2022 |
5530 | (2^355562+1702)/2 | 107035 | Stefano Morozzi | 09/2020 |
5531 | 10^107028+3593037 | 107029 | Paul Bourdelais | 10/2021 |
5532 | 2^355524-21237 | 107024 | Enzo Doria | 06/2013 |
5533 | (10223*2^355515+1)/4855 | 107022 | Lelio R Paula | 07/2014 |
5534 | 24843^20320+20320^24843 | 107022 | Hans Havermann | 10/2020 |
5535 | 2^355494-19901 | 107015 | Enzo Doria | 06/2013 |
5536 | 2^355454-869688105 | 107003 | Lelio R Paula | 01/2017 |
5537 | 4*10^106997+13 | 106998 | Robert Price | 02/2021 |
5538 | (8*10^106985-629)/9 | 106985 | Robert Price | 01/2022 |
5539 | 2^355366+54615 | 106976 | Lelio R Paula | 01/2017 |
5540 | (31*2^355346-1)/1563 | 106969 | Lelio R Paula | 03/2014 |
5542 | 2^355275-19861 | 106949 | Enzo Doria | 06/2013 |
5541 | 27503^7738+7738^27503 | 106949 | Hans Havermann | 11/2020 |
5543 | (85*10^106943+77)/9 | 106944 | Robert Price | 07/2022 |
5544 | (9179*2^355234-1)/1915 | 106937 | Lelio R Paula | 05/2015 |
5545 | 4*10^106914-93 | 106915 | Robert Price | 07/2020 |
5546 | 4*10^106892-3 | 106893 | Robert Price | 10/2015 |
5547 | (66^58741+1)/67 | 106881 | Paul Bourdelais | 08/2017 |
5548 | 2^354946-3 | 106850 | M. Frind & P. Underwood | 08/2002 |
5549 | (2^354945+3134)/2 | 106849 | Stefano Morozzi | 09/2020 |
5550 | 2^354873-18693 | 106828 | Enzo Doria | 05/2013 |
5551 | (2^354831+3186)/2 | 106815 | Stefano Morozzi | 09/2020 |
5553 | 2^354828+4257 | 106814 | Lelio R Paula | 01/2017 |
5552 | 25216^17217+17217^25216 | 106814 | Hans Havermann | 10/2020 |
5554 | (2^354799+1218)/2 | 106805 | Stefano Morozzi | 09/2020 |
5555 | 436^40459+40459^436 | 106791 | Norbert Schneider | 03/2019 |
5556 | (21^80761+1)/22 | 106783 | Paul Bourdelais | 03/2010 |
5557 | (115*10^106772-7)/9 | 106774 | Robert Price | 02/2020 |
5558 | 2^354640-354640+1 | 106758 | Robert Price | 10/2014 |
5559 | (2^354603+2606)/2 | 106746 | Stefano Morozzi | 09/2020 |
5560 | 2^354585+95 | 106741 | Lelio R Paula | 10/2011 |
5561 | (206*10^106737+1)/9 | 106739 | Robert Price | 04/2022 |
5562 | 2^354553+189 | 106732 | Lelio R Paula | 10/2011 |
5564 | (2^354546+1338)/2 | 106729 | Stefano Morozzi | 02/2021 |
5563 | (8*10^106729-71)/9 | 106729 | Serge Batalov | 11/2022 |
5565 | 2^354514-109031 | 106720 | Enzo Doria | 04/2014 |
5566 | 2^354509-109465 | 106718 | Enzo Doria | 04/2014 |
5567 | (15*2^354478-1)/26983 | 106706 | Lelio R Paula | 03/2014 |
5568 | Phi(217618,10)/899798636917 | 106693 | Makoto Kamada | 06/2019 |
5569 | 15^90710+28 | 106684 | Lelio R Paula | 04/2017 |
5570 | 7^126237+34 | 106683 | Lelio R Paula | 03/2017 |
5571 | 2^354385-115315 | 106681 | Enzo Doria | 06/2015 |
5572 | 2^354327-19305 | 106664 | Enzo Doria | 06/2013 |
5573 | (35*10^106649+1)/9 | 106650 | Serge Batalov | 11/2010 |
5574 | 10^106636+97 | 106637 | Lelio R Paula | 02/2017 |
5575 | 10^106636-22923 | 106636 | Patrick De Geest | 03/2017 |
5576 | 2^354220-57 | 106631 | Lelio R Paula | 10/2011 |
5577 | (68*10^106628-329)/9 | 106629 | Robert Price | 03/2021 |
5578 | (29*10^106620-77)/3 | 106621 | Robert Price | 02/2020 |
5579 | (746*10^106618+1)/9 | 106620 | Robert Price | 03/2020 |
5580 | 2*10^106613+29 | 106614 | Robert Price | 02/2021 |
5581 | 2^354157-17041 | 106612 | Enzo Doria | 05/2013 |
5582 | 12^98778+73 | 106600 | Lelio R Paula | 02/2017 |
5583 | 33333^1576+1576^33333 | 106585 | Hans Havermann | 11/2020 |
5584 | 2^354064+1870651 | 106584 | Enzo Doria | 05/2016 |
5585 | 24568^21779+21779^24568 | 106577 | Hans Havermann | 11/2020 |
5586 | 2^353992-57 | 106563 | Lelio R Paula | 10/2011 |
5587 | 9*10^106559+59 | 106560 | Robert Price | 01/2020 |
5588 | 7*10^106553+27 | 106554 | Robert Price | 11/2020 |
5589 | 28847^4938+4938^28847 | 106548 | Hans Havermann | 10/2020 |
5590 | NSW(139160) | 106535 | Robert Price | 12/2018 |
5591 | (7*10^106516+113)/3 | 106517 | Robert Price | 02/2018 |
5592 | 2^353832-1853849 | 106515 | Enzo Doria | 09/2015 |
5593 | (7^126037-1)/6 | 106513 | Paul Bourdelais | 09/2008 |
5594 | 2^353794-18453 | 106503 | Enzo Doria | 05/2013 |
5595 | (2^353761+2094)/2 | 106493 | Stefano Morozzi | 09/2020 |
5596 | 2^353728+7695 | 106483 | Lelio R Paula | 01/2017 |
5597 | 26476^10509+10509^26476 | 106475 | Hans Havermann | 10/2020 |
5598 | 2^353672-303 | 106466 | Yves Minet | 02/2012 |
5599 | 6^136811+101 | 106460 | Lelio R Paula | 02/2017 |
5600 | 2^353641+1871981 | 106457 | Enzo Doria | 05/2016 |
5601 | (8*10^106454-29)/3 | 106455 | Robert Price | 07/2018 |
5602 | 27845^6654+6654^27845 | 106454 | Hans Havermann | 11/2020 |
5603 | 10^106449-700001 | 106449 | Robert Price | 08/2021 |
5604 | 25316^16017+16017^25316 | 106444 | Hans Havermann | 11/2020 |
5605 | 2^353553+54615 | 106431 | Lelio R Paula | 01/2017 |
5606 | 2^353544-18897 | 106428 | Enzo Doria | 05/2013 |
5607 | 28894^4823+4823^28894 | 106426 | Hans Havermann | 11/2020 |
5608 | (19*10^106422+29)/3 | 106423 | Robert Price | 12/2021 |
5609 | (694*10^106418+53)/9 | 106420 | Robert Price | 02/2022 |
5610 | 6*10^106412-13 | 106413 | Robert Price | 07/2022 |
5611 | 25696^13829+13829^25696 | 106402 | Hans Havermann | 11/2020 |
5612 | 6^136729-133 | 106396 | Lelio R Paula | 02/2017 |
5613 | 2^353418+1605 | 106390 | Lelio R Paula | 01/2017 |
5614 | 2^353387+65 | 106381 | Lelio R Paula | 10/2011 |
5615 | 2^353372+74311 | 106376 | Enzo Doria | 04/2016 |
5616 | 2^353344-3693 | 106368 | Yves Minet | 03/2017 |
5617 | (772*10^106365-7)/9 | 106367 | Robert Price | 06/2022 |
5618 | (56*10^106351+619)/9 | 106352 | Robert Price | 05/2021 |
5620 | 2^353277-20089 | 106347 | Enzo Doria | 06/2013 |
5619 | 2^353275+72173 | 106347 | Enzo Doria | 04/2016 |
5621 | 2^353268-17705 | 106345 | Enzo Doria | 05/2013 |
5622 | 2^353267-19857 | 106344 | Enzo Doria | 06/2013 |
5623 | (46*10^106343+143)/9 | 106344 | Robert Price | 01/2019 |
5625 | (2^353189+3054)/2 | 106321 | Stefano Morozzi | 09/2020 |
5624 | 35087^1072+1072^35087 | 106321 | Hans Havermann | 10/2020 |
5626 | (2^353184+1290)/2 | 106319 | Stefano Morozzi | 01/2021 |
5627 | 26985^8684+8684^26985 | 106287 | Hans Havermann | 10/2020 |
5628 | (2^353051+606)/2 | 106279 | Stefano Morozzi | 09/2020 |
5630 | 222748^3+3^222748 | 106278 | Anatoly F. Selevich | 12/2010 |
5629 | (46*10^106277+107)/9 | 106278 | Robert Price | 06/2022 |
5631 | (9179*2^353019-1)/9 | 106273 | Lelio R Paula | 05/2015 |
5632 | 2^353025+72257 | 106272 | Enzo Doria | 04/2016 |
5635 | 2^352932-20345 | 106244 | Enzo Doria | 06/2013 |
5633 | (2^353011-3)/745325861246794515484535 | 106244 | Lelio R Paula | 12/2013 |
5634 | 25628^13983+13983^25628 | 106244 | Hans Havermann | 10/2020 |
5636 | 2^352883-187 | 106229 | Lelio R Paula | 10/2011 |
5637 | 20^81649-19^81649 | 106228 | Jean-Louis Charton | 03/2011 |
5638 | (55*10^106222+377)/9 | 106223 | Robert Price | 02/2019 |
5639 | 2^352814-131 | 106208 | Lelio R Paula | 10/2011 |
5640 | 2^352752+73951 | 106189 | Enzo Doria | 04/2016 |
5641 | 6^136434+5 | 106167 | Lelio R Paula | 11/2014 |
5642 | 25296^15737+15737^25296 | 106166 | Hans Havermann | 09/2020 |
5643 | 8*10^106157-13 | 106158 | Robert Price | 08/2019 |
5644 | 7*5^151872-8 | 106155 | Lelio R Paula | 11/2014 |
5645 | 105^52520-2 | 106153 | Lelio R Paula | 10/2017 |
5646 | (23*10^106152-29)/3 | 106153 | Robert Price | 03/2022 |
5647 | 2^352601-1604809 | 106144 | Enzo Doria | 05/2015 |
5648 | 12^98353-43 | 106141 | Lelio R Paula | 02/2017 |
5649 | 2^352585-18901 | 106139 | Enzo Doria | 05/2013 |
5650 | 26363^10614+10614^26363 | 106135 | Hans Havermann | 09/2020 |
5651 | (2^352554-3)/193 | 106128 | Lelio R Paula | 12/2013 |
5652 | 2^352540+15015 | 106126 | Lelio R Paula | 01/2017 |
5653 | 25068^17119+17119^25068 | 106125 | Hans Havermann | 09/2020 |
5654 | 2^352524-3149 | 106121 | Yves Minet | 10/2014 |
5655 | (7*10^106119-67)/3 | 106120 | Robert Price | 10/2021 |
5656 | 2^352486-1858781 | 106109 | Enzo Doria | 04/2016 |
5657 | 2^352444+12705 | 106097 | Lelio R Paula | 01/2017 |
5658 | 28561^5182+5182^28561 | 106090 | Hans Havermann | 10/2020 |
5659 | (182*10^106083+43)/9 | 106085 | Robert Price | 02/2020 |
5660 | (266*10^106066+1)/3 | 106068 | Robert Price | 04/2020 |
5661 | (7*10^106066-187)/9 | 106066 | Tyler Busby | 01/2023 |
5662 | 2^352228-18953 | 106032 | Enzo Doria | 05/2013 |
5663 | (2^352223+1118)/2 | 106030 | Stefano Morozzi | 09/2020 |
5664 | (2^352212+2250)/2 | 106027 | Stefano Morozzi | 01/2021 |
5665 | (2^352136+2638)/2 | 106004 | Stefano Morozzi | 09/2020 |
5666 | 2^352107+1872533 | 105995 | Enzo Doria | 05/2016 |
5667 | (2^352096+2086)/2 | 105992 | Stefano Morozzi | 09/2020 |
5668 | 2^352066-2591 | 105983 | Yves Minet | 07/2014 |
5669 | 2^352030+715 | 105972 | Lelio R Paula | 10/2011 |
5670 | 9*6^136176-5 | 105967 | Lelio R Paula | 11/2014 |
5671 | 17099*2^351991+58329 | 105965 | Paul Vanderveen | 12/2017 |
5672 | 28582^5097+5097^28582 | 105963 | Hans Havermann | 09/2020 |
5673 | 155^48377+2 | 105962 | Lelio R Paula | 08/2013 |
5674 | (23*10^105944-119)/3 | 105945 | Robert Price | 07/2021 |
5675 | 2^351865+1869707 | 105922 | Enzo Doria | 05/2016 |
5676 | 24974^17427+17427^24974 | 105921 | Hans Havermann | 09/2020 |
5677 | 25163^16194+16194^25163 | 105920 | Hans Havermann | 09/2020 |
5678 | 2^351831+23 | 105912 | Lelio R Paula | 10/2011 |
5679 | (2^351818+3798)/2 | 105908 | Stefano Morozzi | 02/2021 |
5680 | 9*2^351784-5 | 105899 | Lelio R Paula | 09/2014 |
5681 | (2^351776+2766)/2 | 105895 | Stefano Morozzi | 01/2021 |
5682 | (85*10^105881+203)/9 | 105882 | Robert Price | 09/2020 |
5683 | 2^351671-112387 | 105864 | Enzo Doria | 06/2014 |
5684 | 2^351669-109501 | 105863 | Enzo Doria | 04/2014 |
5685 | 2^351644+74731 | 105856 | Enzo Doria | 04/2016 |
5686 | 13^95025-42 | 105853 | Lelio R Paula | 12/2016 |
5687 | 2^351599+15015 | 105842 | Lelio R Paula | 01/2017 |
5688 | 19^82763+90 | 105834 | Lelio R Paula | 01/2017 |
5689 | (205*10^105831-1)/3 | 105833 | Robert Price | 11/2021 |
5690 | 26050^11551+11551^26050 | 105832 | Hans Havermann | 09/2020 |
5691 | (9179*2^351540-1)/221 | 105826 | Lelio R Paula | 05/2015 |
5692 | 20^81329-51 | 105812 | Lelio R Paula | 01/2017 |
5693 | (5*10^105811+211)/9 | 105811 | Robert Price | 02/2018 |
5694 | 2^351483+28425 | 105807 | Lelio R Paula | 01/2017 |
5695 | 25231^15610+15610^25231 | 105804 | Hans Havermann | 09/2020 |
5696 | 15^89960+86 | 105802 | Lelio R Paula | 02/2017 |
5697 | 2^351460-17289 | 105801 | Enzo Doria | 05/2013 |
5698 | 19^82735+22 | 105798 | Lelio R Paula | 01/2017 |
5699 | 2^351435-109077 | 105793 | Enzo Doria | 04/2014 |
5700 | 2^351393+1089 | 105780 | Lelio R Paula | 01/2017 |
5701 | 2^351364+72631 | 105772 | Enzo Doria | 04/2016 |
5702 | (2^351333+3626)/2 | 105762 | Stefano Morozzi | 09/2020 |
5703 | 26818^8783+8783^26818 | 105761 | Hans Havermann | 09/2020 |
5706 | 2^351305+1872467 | 105754 | Enzo Doria | 05/2016 |
5705 | 3^221649+16 | 105754 | Lelio R Paula | 11/2016 |
5704 | 32511^1790+1790^32511 | 105754 | Hans Havermann | 09/2020 |
5707 | 8*3^221637-5 | 105749 | Lelio R Paula | 09/2014 |
5708 | 2^351279-2780449 | 105746 | Enzo Doria | 03/2016 |
5709 | (2^351263+3198)/2 | 105741 | Stefano Morozzi | 09/2020 |
5710 | 15^89903-26 | 105735 | Lelio R Paula | 02/2017 |
5712 | 2^351213-73 | 105726 | Lelio R Paula | 10/2011 |
5711 | (2^351214+1210)/2 | 105726 | Stefano Morozzi | 09/2020 |
5713 | 2^351192-4589 | 105720 | Yves Minet | 07/2011 |
5714 | 20^81250-33 | 105709 | Lelio R Paula | 12/2016 |
5715 | (2^351133+3530)/2 | 105702 | Stefano Morozzi | 09/2020 |
5716 | (2^351103+534)/2 | 105693 | Stefano Morozzi | 09/2020 |
5717 | 2^351076-113159 | 105685 | Enzo Doria | 07/2014 |
5718 | 93^53688-2 | 105684 | Lelio R Paula | 09/2013 |
5719 | 2^351060-4559 | 105680 | Yves Minet | 07/2011 |
5720 | ((10^52836-1)*10000/9+5927)*10^52836+(10^52836-1)/9 | 105676 | Hans Havermann | 08/2019 |
5721 | 11^101473-750 | 105674 | Enzo Doria | 11/2012 |
5722 | 3*5^151181-8 | 105672 | Lelio R Paula | 11/2014 |
5723 | 15^89831-34 | 105650 | Lelio R Paula | 02/2017 |
5725 | 11^101448-360 | 105648 | Enzo Doria | 08/2012 |
5724 | 3*7^125011+4 | 105648 | Lelio R Paula | 11/2014 |
5726 | 2^350943-113269 | 105645 | Enzo Doria | 07/2014 |
5727 | 2*10^105636-91 | 105637 | Robert Price | 04/2020 |
5728 | 24231^22880+22880^24231 | 105634 | Hans Havermann | 09/2020 |
5729 | 35296^983+983^35296 | 105626 | Hans Havermann | 09/2020 |
5730 | 2^350868-19725 | 105622 | Enzo Doria | 06/2013 |
5731 | 2^350858-59291 | 105619 | Enzo Doria | 10/2015 |
5732 | 2^350851+135 | 105617 | Lelio R Paula | 10/2011 |
5733 | 2^350841-741 | 105614 | Lelio R Paula | 01/2017 |
5734 | 3*10^105582+77 | 105583 | Robert Price | 09/2018 |
5735 | 24915^17284+17284^24915 | 105581 | Hans Havermann | 09/2020 |
5736 | (5*10^105576-53)/3 | 105577 | Robert Price | 09/2020 |
5737 | 8*10^105571+3 | 105572 | Robert Price | 08/2015 |
5738 | 2^350674-78557 | 105564 | Jorge Menendez | 03/2018 |
5739 | 2*5^151026-3 | 105563 | Lelio R Paula | 11/2014 |
5740 | (2^350702+5)/34264674063 | 105562 | Lelio R Paula | 12/2013 |
5741 | 6^135647-5^135647 | 105554 | Jean-Louis Charton | 02/2009 |
5742 | 3^221211+236 | 105545 | Lelio R Paula | 11/2016 |
5743 | (32*10^105530-77)/9 | 105531 | Robert Price | 06/2018 |
5744 | 10^105515+33 | 105516 | Lelio R Paula | 11/2016 |
5745 | 24644^19125+19125^24644 | 105516 | Hans Havermann | 10/2020 |
5746 | 10^105515-41033 | 105515 | Patrick De Geest | 12/2016 |
5747 | (29*2^350473-1)/267927 | 105499 | Lelio R Paula | 03/2014 |
5748 | 2^350455-430567 | 105498 | Harrison Mesh | 06/2022 |
5749 | 17^85732-72 | 105489 | Lelio R Paula | 01/2017 |
5750 | (2^350399+3618)/2 | 105481 | Stefano Morozzi | 09/2020 |