PRP Records

Probable Primes Top 10000

(259919 PRPs in the top)


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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1-250   251-500   501-750   751-1000   1001-1250   1251-1500   1501-1750   1751-2000   
2001-2250   2251-2500   2501-2750   2751-3000   3001-3250   3251-3500   3501-3750   3751-4000   
4001-4250   4251-4500   4501-4750   4751-5000   5001-5250   5251-5500   5501-5750   5751-6000   
6001-6250   6251-6500   6501-6750   6751-7000   7001-7250   7251-7500   7501-7750   7751-8000   
8001-8250   8251-8500   8501-8750   8751-9000   9001-9250   9251-9500   9501-9750   9751-10000   


Rank Probable prime Digits (> 50000) Who ? When ?
65012^272907-11143982154Enzo Doria05/2014
6502(67607*2^272901+1)/5079011582149Lelio R Paula06/2014
65032^272875-6982144Lelio R Paula06/2012
65047^97197+482141Robert Price01/2014
6505(4*6^105554+1)/582137Serge Batalov10/2014
65062^272826-443382129Yves Minet03/2019
65076^105531-10982120Lelio R Paula12/2015
65082^272766-6582111Lelio R Paula06/2012
650919^64205-7882103Lelio R Paula12/2015
65102^272702+186997982092Enzo Doria05/2016
6511(29*2^272687-1)/982088Lelio R Paula02/2014
6512(5*10^82085-119)/382086Robert Price04/2016
6513(2^272665+1334)/282081Stefano Morozzi01/2020
65142^272660-11004982079Enzo Doria04/2014
65156^105474+6782075Lelio R Paula12/2015
65162^272637+8287582072Lelio R Paula07/2013
65172^272587-3182057Lelio R Paula06/2012
6518(41*10^82044-59)/982045Robert Price10/2017
65198*5^117368+982038Lelio R Paula10/2014
6520(101525^16384+1)/13107482023Lelio R Paula11/2011
65214*5^117343-782020Lelio R Paula10/2014
6522(2^272381+506)/281995Stefano Morozzi01/2020
6523(265*10^81990+17)/381992Robert Price05/2016
65243^171843+1081990Robert Price10/2013
6525(2^272361+3762)/281989Stefano Morozzi01/2020
6526(7*10^81985+107)/381986Robert Price02/2017
6527(3*2^272356+1)/17716381983Lelio R Paula12/2012
65282^272296-11114981970Enzo Doria05/2014
6529(2^272293+2810)/281969Stefano Morozzi01/2020
6530(2^272278+2118)/281964Stefano Morozzi01/2020
6531(9*2^272243-1)/781954Lelio R Paula02/2014
65322^272177-11122381934Enzo Doria05/2014
6533(2^272127+3878)/281919Stefano Morozzi01/2020
6535(151009^15817+1)/15101081912Faysal YAtim06/2017
6534(2^272104+1950)/281912Stefano Morozzi01/2020
6536(16*10^81896-19)/381897Robert Price03/2016
6537(2^271922+78557)/6381855Lelio R Paula12/2012
6538(10^81848+77)/381848Robert Price01/2017
6539(24737*2^271883+1)/375781846Lelio R Paula06/2014
6540(2^271885+1670)/281846Stefano Morozzi01/2020
654118813^19144-19144^1881381831Norbert Schneider02/2020
6542(2^271734+3942)/281800Stefano Morozzi01/2020
654310^81778+3981779Robert Price03/2011
654410^81778-17199981778Patrick De Geest07/2013
6545(2^271652+2886)/281776Stefano Morozzi01/2020
6546(14*10^81767-11)/381768Erik Branger09/2014
6547(2^271546+610)/281744Stefano Morozzi01/2020
65482^271541+186841781742Enzo Doria04/2016
6549(2^271549-1)/23874968248781734Jens K. Andersen02/2009
65502^271484-16781725Lelio R Paula06/2012
6551(8*10^81709-611)/981709Robert Price11/2017
6552(2^271431+1790)/281709Stefano Morozzi01/2020
65532^271382+1290981695Lelio R Paula07/2013
655449^48334+4881694Norbert Schneider07/2014
65557^96668+4881694Lelio R Paula10/2015
655611^78435-141081682Enzo Doria12/2012
65575*10^81653+981654Dmitry Domanov11/2010
6558(2^271224+1230)/281647Stefano Morozzi01/2020
6559(2^271211-1)/61396149515981631Jens K. Andersen02/2009
6560(2^271168+1806)/281630Stefano Morozzi01/2020
65613^171068+5281621Lelio R Paula12/2015
65622^271115-11040781614Enzo Doria05/2014
65632^271111-11063581613Enzo Doria05/2014
65642^271098-11181609Lelio R Paula06/2012
6565(77*10^81606+13)/981607Robert Price10/2015
65662^271064-279020981599Enzo Doria03/2016
6567(13*2^271053-1)/309581593Lelio R Paula02/2014
65682^271040-5781592Lelio R Paula06/2012
6569(14*10^81585+73)/381586Robert Price04/2016
6570127^38779+12681584Norbert Schneider02/2015
657118^64966-4381551Lelio R Paula11/2015
6572(2^270843+1074)/281532Stefano Morozzi01/2020
6573(2^270840+47)/59181529Lelio R Paula12/2012
657420^62654+8781515Lelio R Paula01/2016
6575(19*10^81488+191)/381489Robert Price01/2017
65768*10^81487+2181488Robert Price02/2017
6577(73*10^81485+107)/981486Robert Price08/2016
6578536^29847+29847^53681458Norbert Schneider03/2017
65798*7^96378+981450Lelio R Paula10/2014
6580(2^270560+3862)/281447Stefano Morozzi01/2020
65812^270546-11034581443Enzo Doria05/2014
658213^73105-6081435Lelio R Paula11/2015
6583(2^270502+1518)/281429Stefano Morozzi01/2020
6584(2^270479+2114)/281422Stefano Morozzi01/2020
6585(2^270384+1218)/281394Stefano Morozzi01/2020
658644^49524+4381391Norbert Schneider06/2014
6587(3*2^270368-1)/1381389Lelio R Paula02/2014
6588(2^270337+1130)/281380Stefano Morozzi01/2020
6589(10^81363+719)/981363Serge Batalov12/2014
6590(10^81353+449)/981353Serge Batalov12/2014
659114^70978-8981350Lelio R Paula11/2015
659211^78108-204081342Enzo Doria12/2012
65933^170400-5881302Lelio R Paula12/2015
6594(17*10^81300-131)/381301Robert Price12/2017
659510^81297+3699181298Patrick De Geest06/2013
659610^81297-5781297Robert Price05/2011
6597(2^270063+3206)/281297Stefano Morozzi01/2020
65982^270055-11304781295Enzo Doria07/2014
659918^64759-5581291Lelio R Paula11/2015
6600(2^269987+1)/381274H.&R. Lifchitz10/2000
6601(31^54493-1)/3081268Alexander Zhirkov10/2010
6602(2^270059-1)/540119/6481417/712497615775672596781265Dario Alpern09/2014
6603(2^269922+3574)/281255Stefano Morozzi01/2020
66042^269819-459781224Yves Minet03/2019
6605(2^269816+7)/42490181218Lelio R Paula12/2012
6606(23*10^81214+1)/381215Serge Batalov06/2009
6607(2^269720+3778)/281194Stefano Morozzi01/2020
6608(17*2^269720+1)/30381193Lelio R Paula07/2012
660956^46441-55^4644181188Robert Price10/2013
66102^269664+17781177Lelio R Paula06/2012
6611(13*2^269665-1)/18581177Lelio R Paula02/2014
66122^269539-11224981140Enzo Doria06/2014
6613((2*170026-3)*3^(170026-1)+1)/481128Robert Price01/2015
6615(2^269495-5)/981126Lelio R Paula12/2012
66141239^26228+26228^123981126Norbert Schneider10/2019
66162^269490-362381125Yves Minet10/2009
6617(55459*2^269444+1)/3581114Lelio R Paula06/2014
6618(2^269417+78557)/525781099Lelio R Paula12/2012
66194*5^116011-781089Lelio R Paula10/2014
6620(2^269349+2366)/281082Stefano Morozzi01/2020
6621(2^269303+2946)/281068Stefano Morozzi01/2020
66227*10^81058+7981059Robert Price02/2017
66232^269236-10990781049Enzo Doria04/2014
6624(2^269182+1870)/281032Stefano Morozzi01/2020
6625(2^269179+3006)/281031Stefano Morozzi01/2020
6626(8*10^81029-11)/381030Erik Branger03/2014
66273*10^81021+781022Erik Branger11/2013
66286^104115+10381018Lelio R Paula12/2015
66292^269120+186915181014Enzo Doria05/2016
66305^115901+1281012Lelio R Paula10/2015
6631(2^269072+3610)/280999Stefano Morozzi01/2020
6632(2^269083-9)/32036980997Lelio R Paula12/2012
6633(2^269002+1614)/280978Stefano Morozzi01/2020
663417^65810-2080976Lelio R Paula11/2015
663520^62236-2380971Lelio R Paula01/2016
66362^268974-11218180970Enzo Doria06/2014
6638L(387433)80969Renaud Lifchitz11/2003
6637V(387433)80969Serge Batalov03/2015
6639(2^268957+602)/280964Stefano Morozzi01/2020
6640(2^268955-509203)/580963Lelio R Paula12/2012
6641(87398^16384+1)/6553780957Lelio R Paula11/2011
6642329^32160+32160^32980954Norbert Schneider11/2014
664319678^12973+12973^1967880937Hans Havermann02/2020
6644(2^268864+3558)/280936Stefano Morozzi01/2020
66452^268859-15980935Lelio R Paula05/2012
6646(2^268841-lucasV(1,2,268841)+1)/280929Mike Oakes11/2016
66482^268827+577580925Lelio R Paula07/2013
66472^268824-11025580925Enzo Doria05/2014
6649(2^268824+1902)/280924Stefano Morozzi01/2020
66502^268798-186832180917Enzo Doria04/2016
665120613^8420+8420^2061380913Hans Havermann03/2020
66522^268753-11462180903Enzo Doria05/2015
66532^268743+160580900Lelio R Paula07/2013
66546^103954-13980892Lelio R Paula12/2015
665510^80883+4980884Robert Price03/2011
665610^80883-8032780883Patrick De Geest07/2013
66576^103937+12180879Lelio R Paula12/2015
6658148^37266+14780877Norbert Schneider12/2018
6659(26*10^80875-119)/380876Robert Price07/2016
6660(22699*2^268657+1)/635180875Lelio R Paula06/2014
6661(2^268612+2530)/280860Stefano Morozzi01/2020
66622^268581-86968810580851Lelio R Paula05/2016
6663(11*2^268521-1)/380834Lelio R Paula02/2014
66642^268516-24980832Yves Minet02/2012
666522259^4278+4278^2225980828Hans Havermann03/2020
66662^268500+1609580827Lelio R Paula07/2013
66673^169402+10080826Lelio R Paula12/2015
6668(2^268495+566)/280825Stefano Morozzi01/2020
66699^84698+8^(84698-1)80823Robert Price03/2016
66702^268472-10973980819Enzo Doria04/2014
6671(9*2^268454+1)/3780813Lelio R Paula12/2012
6672(3*2^268502+1)/37790218843535364780811Lelio R Paula12/2012
6673(2^268441+3962)/280809Stefano Morozzi01/2020
6674134^37987-133^3798780803Jean-Louis Charton12/2005
667515^68702-7680800Lelio R Paula11/2015
66762^268408+780799Lelio R Paula05/2012
66772^268375+14180789Lelio R Paula05/2012
667812^74856-4780784Lelio R Paula11/2015
66792^268346+52428780781Paul Underwood08/2018
66806^103770-10780749Lelio R Paula12/2015
66813^169224-6280741Lelio R Paula12/2015
6682p(16866)#/2+6480741Robert Price03/2017
66835^115502-7280733Lelio R Paula10/2015
6684(2^268154+2262)/280723Stefano Morozzi01/2020
6685(2^268156+1290)/280723Stefano Morozzi01/2020
66872^268079-192780700Yves Minet10/2009
6686(2^268078+2514)/280700Stefano Morozzi01/2020
66882^268028+11780685Lelio R Paula05/2012
6689121^38738+12080683Norbert Schneider01/2015
6690(3^169097-8)/83580677Lelio R Paula12/2012
6691(2^267956+1810)/280663Stefano Morozzi01/2020
669219359^14666+14666^1935980656Hans Havermann12/2019
66932^267918+6780652Lelio R Paula05/2012
6694(89*10^80650-179)/980651Robert Price11/2017
6695(2^267914+2094)/280650Stefano Morozzi01/2020
6696(2^267894+2202)/280644Stefano Morozzi01/2020
6697(302*10^80638+13)/980640Robert Price01/2017
66983^169004+266080636Lelio R Paula12/2015
66992^267860-11285980634Enzo Doria06/2014
67002^267828-11070580625Enzo Doria05/2014
6701(2^267752+2602)/280602Stefano Morozzi01/2020
67022^267743+1270580599Lelio R Paula07/2013
6703(22*10^80595+23)/980596Robert Price03/2015
6704(2^267712+2358)/280590Stefano Morozzi01/2020
6705(2^267685+854)/280581Stefano Morozzi01/2020
67062^267674-5180578Lelio R Paula05/2012
6707(86*10^80571-41)/980572Robert Price11/2015
6708(2^267637+2454)/280567Stefano Morozzi01/2020
670920452^8693+8693^2045280564Hans Havermann02/2020
67102^267612-196580560Lelio R Paula07/2013
67112^267553+409780542Lelio R Paula07/2013
67127^95276-880518Robert Price01/2014
6713(15185*2^267457-1)/4782980513Lelio R Paula04/2015
67146^103467+16380513Lelio R Paula12/2015
671520283^9314+9314^2028380506Hans Havermann02/2020
6716(2^267387+2294)/280492Stefano Morozzi01/2020
6717(7*10^80490+143)/380491Robert Price04/2016
671819887^11152+11152^1988780490Hans Havermann01/2020
6719(2^267348+3810)/280480Stefano Morozzi01/2020
672086^41597-85^4159780470Robert Price04/2015
672113^72237+3080468Lelio R Paula11/2015
672217^65389+1480458Lelio R Paula11/2015
6723423^30634+30634^42380456Norbert Schneider05/2017
6724(2^267257+470)/280453Stefano Morozzi01/2020
67252^267232+10580445Lelio R Paula05/2012
672622101^4360+4360^2210180437Hans Havermann02/2020
672711^77237-307200080435Enzo Doria01/2013
672820696^7689+7689^2069680422Hans Havermann01/2020
6729(2^267149+2562)/280420Stefano Morozzi01/2020
673021321^5908+5908^2132180411Hans Havermann02/2020
67312^267116-45995980410Enzo Doria06/2015
673238715!2+880406Robert Price01/2015
673319579^12786+12786^1957980406Hans Havermann02/2020
6734(2^267017+1)/380380H.&R. Lifchitz09/2000
6735(2^267006+1134)/280377Stefano Morozzi01/2020
673624273^2048+2048^2427380376Hans Havermann01/2020
6737(2^266989+734)/280372Stefano Morozzi01/2020
6738(2^266989+1850)/280372Stefano Morozzi01/2020
67392^266968-4580366Lelio R Paula05/2012
6740(2^266967+3974)/280365Stefano Morozzi01/2020
674120^61768-6380363Lelio R Paula01/2016
67422^266920-11296780351Enzo Doria06/2014
6743(2^266910+2394)/280348Stefano Morozzi01/2020
6744(2^266899+1994)/280345Stefano Morozzi01/2020
67458*10^80342+8780343Robert Price10/2017
6746(2^266861+890)/280333Stefano Morozzi01/2020
674712^74428-1380322Lelio R Paula11/2015
6748(2^266810+2718)/280318Stefano Morozzi01/2020
6749(2^266800+2886)/280315Stefano Morozzi01/2020
67502^266680+2780279Lelio R Paula05/2012


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: March, 29 2020 17:41 (Time in France)

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