PRP Records

Probable Primes Top 10000

(271000 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 ?
7502(8*10^81709-611)/981709Robert Price11/2017
7501(2^271431+1790)/281709Stefano Morozzi01/2020
750319648^14399+14399^1964881703Hans Havermann05/2020
75042^271382+1290981695Lelio R Paula07/2013
750549^48334+4881694Norbert Schneider07/2014
75067^96668+4881694Lelio R Paula10/2015
750711^78435-141081682Enzo Doria12/2012
750819575^14882+14882^1957581680Hans Havermann04/2020
75095*10^81653+981654Dmitry Domanov11/2010
7510(2^271224+1230)/281647Stefano Morozzi01/2020
7511(2^271211-1)/61396149515981631Jens K. Andersen02/2009
7512(2^271168+1806)/281630Stefano Morozzi01/2020
75133^171068+5281621Lelio R Paula12/2015
75142^271115-11040781614Enzo Doria05/2014
75152^271111-11063581613Enzo Doria05/2014
75162^271098-11181609Lelio R Paula06/2012
7517(77*10^81606+13)/981607Robert Price10/2015
75182^271064-279020981599Enzo Doria03/2016
7519(13*2^271053-1)/309581593Lelio R Paula02/2014
75202^271040-5781592Lelio R Paula06/2012
7521(14*10^81585+73)/381586Robert Price04/2016
7522127^38779+12681584Norbert Schneider02/2015
752318^64966-4381551Lelio R Paula11/2015
752419406^15909+15909^1940681538Hans Havermann06/2020
7525(2^270843+1074)/281532Stefano Morozzi01/2020
7526(2^270840+47)/59181529Lelio R Paula12/2012
752720^62654+8781515Lelio R Paula01/2016
752820120^11241+11241^2012081503Hans Havermann05/2020
7529(19*10^81488+191)/381489Robert Price01/2017
75308*10^81487+2181488Robert Price02/2017
7531(73*10^81485+107)/981486Robert Price08/2016
7532536^29847+29847^53681458Norbert Schneider03/2017
75338*7^96378+981450Lelio R Paula10/2014
7534(2^270560+3862)/281447Stefano Morozzi01/2020
7535(5728^21673-1)/572781444Serge Batalov08/2020
75362^270546-11034581443Enzo Doria05/2014
753713^73105-6081435Lelio R Paula11/2015
7538(2^270502+1518)/281429Stefano Morozzi01/2020
7539(2^270479+2114)/281422Stefano Morozzi01/2020
7540(2^270384+1218)/281394Stefano Morozzi01/2020
754144^49524+4381391Norbert Schneider06/2014
7542(3*2^270368-1)/1381389Lelio R Paula02/2014
754319548^14563+14563^1954881384Hans Havermann05/2020
7544(2^270337+1130)/281380Stefano Morozzi01/2020
754527405^932+932^2740581377Hans Havermann05/2020
754619396^15683+15683^1939681375Hans Havermann05/2020
7548(10^81363+719)/981363Serge Batalov12/2014
7547(734^28393-1)/73381363Serge Batalov08/2020
7549(10^81353+449)/981353Serge Batalov12/2014
755014^70978-8981350Lelio R Paula11/2015
755111^78108-204081342Enzo Doria12/2012
75527*10^81327-5781328Robert Price06/2020
755319102^18065+18065^1910281315Hans Havermann07/2020
75543^170400-5881302Lelio R Paula12/2015
7555(17*10^81300-131)/381301Robert Price12/2017
755610^81297+3699181298Patrick De Geest06/2013
755710^81297-5781297Robert Price05/2011
7558(2^270063+3206)/281297Stefano Morozzi01/2020
755919359^15826+15826^1935981296Hans Havermann06/2020
75602^270055-11304781295Enzo Doria07/2014
756118^64759-5581291Lelio R Paula11/2015
7562(2^269987+1)/381274H.&R. Lifchitz10/2000
7563(31^54493-1)/3081268Alexander Zhirkov10/2010
7564(2^270059-1)/540119/6481417/712497615775672596781265Dario Alpern09/2014
7565(194^35521-1)/19381263Serge Batalov08/2020
756620722^8343+8343^2072281258Hans Havermann07/2020
7567(2^269922+3574)/281255Stefano Morozzi01/2020
756821310^6497+6497^2131081249Hans Havermann07/2020
7569(16392^19273-1)/1639181225Serge Batalov08/2020
75702^269819-459781224Yves Minet03/2019
7571(2^269816+7)/42490181218Lelio R Paula12/2012
757223470^2887+2887^2347081217Hans Havermann05/2020
7573(23*10^81214+1)/381215Serge Batalov06/2009
7574(2^269720+3778)/281194Stefano Morozzi01/2020
7575(17*2^269720+1)/30381193Lelio R Paula07/2012
757656^46441-55^4644181188Robert Price10/2013
75772^269664+17781177Lelio R Paula06/2012
7578(13*2^269665-1)/18581177Lelio R Paula02/2014
757921642^5615+5615^2164281144Hans Havermann07/2020
75802^269539-11224981140Enzo Doria06/2014
7581((2*170026-3)*3^(170026-1)+1)/481128Robert Price01/2015
7583(2^269495-5)/981126Lelio R Paula12/2012
75821239^26228+26228^123981126Norbert Schneider10/2019
75842^269490-362381125Yves Minet10/2009
7585(55459*2^269444+1)/3581114Lelio R Paula06/2014
758619554^14065+14065^1955481113Hans Havermann06/2020
7587(2^269417+78557)/525781099Lelio R Paula12/2012
75884*5^116011-781089Lelio R Paula10/2014
7589(2^269349+2366)/281082Stefano Morozzi01/2020
7590(2^269303+2946)/281068Stefano Morozzi01/2020
75916*10^81060+5381061Robert Price05/2020
75927*10^81058+7981059Robert Price02/2017
75932^269236-10990781049Enzo Doria04/2014
7594(2^269182+1870)/281032Stefano Morozzi01/2020
7595(2^269179+3006)/281031Stefano Morozzi01/2020
7596(8*10^81029-11)/381030Erik Branger03/2014
759719749^12668+12668^1974981025Hans Havermann05/2020
75983*10^81021+781022Erik Branger11/2013
75996^104115+10381018Lelio R Paula12/2015
76002^269120+186915181014Enzo Doria05/2016
76015^115901+1281012Lelio R Paula10/2015
7602(2^269072+3610)/280999Stefano Morozzi01/2020
7603(2^269083-9)/32036980997Lelio R Paula12/2012
76042*10^80981-4980982Robert Price09/2020
7605(2^269002+1614)/280978Stefano Morozzi01/2020
760617^65810-2080976Lelio R Paula11/2015
760720^62236-2380971Lelio R Paula01/2016
76082^268974-11218180970Enzo Doria06/2014
7610L(387433)80969Renaud Lifchitz11/2003
7609V(387433)80969Serge Batalov03/2015
761122732^3645+3645^2273280965Hans Havermann06/2020
7612(2^268957+602)/280964Stefano Morozzi01/2020
7613(2^268955-509203)/580963Lelio R Paula12/2012
761419485^14284+14284^1948580958Hans Havermann05/2020
7615(87398^16384+1)/6553780957Lelio R Paula11/2011
7616329^32160+32160^32980954Norbert Schneider11/2014
761719678^12973+12973^1967880937Hans Havermann02/2020
7618(2^268864+3558)/280936Stefano Morozzi01/2020
76192^268859-15980935Lelio R Paula05/2012
7620(2^268841-lucasV(1,2,268841)+1)/280929Mike Oakes11/2016
76222^268827+577580925Lelio R Paula07/2013
76212^268824-11025580925Enzo Doria05/2014
7623(2^268824+1902)/280924Stefano Morozzi01/2020
76242^268798-186832180917Enzo Doria04/2016
762520613^8420+8420^2061380913Hans Havermann03/2020
76262^268753-11462180903Enzo Doria05/2015
76272^268743+160580900Lelio R Paula07/2013
76286^103954-13980892Lelio R Paula12/2015
762910^80883+4980884Robert Price03/2011
763010^80883-8032780883Patrick De Geest07/2013
76316^103937+12180879Lelio R Paula12/2015
7632148^37266+14780877Norbert Schneider12/2018
7633(26*10^80875-119)/380876Robert Price07/2016
7634(22699*2^268657+1)/635180875Lelio R Paula06/2014
7635(2^268612+2530)/280860Stefano Morozzi01/2020
76362^268581-86968810580851Lelio R Paula05/2016
7637(11*2^268521-1)/380834Lelio R Paula02/2014
76382^268516-24980832Yves Minet02/2012
763922259^4278+4278^2225980828Hans Havermann03/2020
76402^268500+1609580827Lelio R Paula07/2013
76413^169402+10080826Lelio R Paula12/2015
7642(2^268495+566)/280825Stefano Morozzi01/2020
76439^84698+8^(84698-1)80823Robert Price03/2016
76442^268472-10973980819Enzo Doria04/2014
7645(9*2^268454+1)/3780813Lelio R Paula12/2012
7646(3*2^268502+1)/37790218843535364780811Lelio R Paula12/2012
7647(2^268441+3962)/280809Stefano Morozzi01/2020
7648134^37987-133^3798780803Jean-Louis Charton12/2005
764915^68702-7680800Lelio R Paula11/2015
76502^268408+780799Lelio R Paula05/2012
7651(16095^19207-1)/1609480794Serge Batalov08/2020
76522^268375+14180789Lelio R Paula05/2012
765312^74856-4780784Lelio R Paula11/2015
76542^268346+52428780781Paul Underwood08/2018
76559*10^80777-4180778Robert Price08/2020
7656(10868^20011-1)/1086780764Serge Batalov08/2020
76576^103770-10780749Lelio R Paula12/2015
7658(751^28081-1)/75080748Serge Batalov08/2020
76593^169224-6280741Lelio R Paula12/2015
7660p(16866)#/2+6480741Robert Price03/2017
76615^115502-7280733Lelio R Paula10/2015
7662(2^268154+2262)/280723Stefano Morozzi01/2020
7663(2^268156+1290)/280723Stefano Morozzi01/2020
76652^268079-192780700Yves Minet10/2009
7664(2^268078+2514)/280700Stefano Morozzi01/2020
76662^268028+11780685Lelio R Paula05/2012
7667121^38738+12080683Norbert Schneider01/2015
7668(3^169097-8)/83580677Lelio R Paula12/2012
7669(2^267956+1810)/280663Stefano Morozzi01/2020
767019359^14666+14666^1935980656Hans Havermann12/2019
76712^267918+6780652Lelio R Paula05/2012
7672(89*10^80650-179)/980651Robert Price11/2017
7673(2^267914+2094)/280650Stefano Morozzi01/2020
7674(2^267894+2202)/280644Stefano Morozzi01/2020
7675(302*10^80638+13)/980640Robert Price01/2017
76763^169004+266080636Lelio R Paula12/2015
76772^267860-11285980634Enzo Doria06/2014
76782^267828-11070580625Enzo Doria05/2014
7679(2956^23227-1)/295580611Serge Batalov08/2020
7680(2^267752+2602)/280602Stefano Morozzi01/2020
76812^267743+1270580599Lelio R Paula07/2013
7682(22*10^80595+23)/980596Robert Price03/2015
7683(2^267712+2358)/280590Stefano Morozzi01/2020
7684(2^267685+854)/280581Stefano Morozzi01/2020
76852^267674-5180578Lelio R Paula05/2012
7686(86*10^80571-41)/980572Robert Price11/2015
7687(2^267637+2454)/280567Stefano Morozzi01/2020
768820452^8693+8693^2045280564Hans Havermann02/2020
76892^267612-196580560Lelio R Paula07/2013
76902^267553+409780542Lelio R Paula07/2013
76917^95276-880518Robert Price01/2014
7692(15185*2^267457-1)/4782980513Lelio R Paula04/2015
76936^103467+16380513Lelio R Paula12/2015
769420283^9314+9314^2028380506Hans Havermann02/2020
7695(2^267387+2294)/280492Stefano Morozzi01/2020
7696(7*10^80490+143)/380491Robert Price04/2016
769719887^11152+11152^1988780490Hans Havermann01/2020
7698(2^267348+3810)/280480Stefano Morozzi01/2020
769986^41597-85^4159780470Robert Price04/2015
770013^72237+3080468Lelio R Paula11/2015
770117^65389+1480458Lelio R Paula11/2015
7702423^30634+30634^42380456Norbert Schneider05/2017
7703(2^267257+470)/280453Stefano Morozzi01/2020
77042^267232+10580445Lelio R Paula05/2012
770522101^4360+4360^2210180437Hans Havermann02/2020
770611^77237-307200080435Enzo Doria01/2013
770720696^7689+7689^2069680422Hans Havermann01/2020
7708(2^267149+2562)/280420Stefano Morozzi01/2020
770921321^5908+5908^2132180411Hans Havermann02/2020
7710(13100^19531-1)/1309980411Serge Batalov08/2020
77112^267116-45995980410Enzo Doria06/2015
771238715!2+880406Robert Price01/2015
771319579^12786+12786^1957980406Hans Havermann02/2020
7714(2^267017+1)/380380H.&R. Lifchitz09/2000
7715(2^267006+1134)/280377Stefano Morozzi01/2020
771624273^2048+2048^2427380376Hans Havermann01/2020
7717(2^266989+734)/280372Stefano Morozzi01/2020
7718(2^266989+1850)/280372Stefano Morozzi01/2020
7719(13427^19471-1)/1342680372Serge Batalov08/2020
77202^266968-4580366Lelio R Paula05/2012
7721(2^266967+3974)/280365Stefano Morozzi01/2020
772220^61768-6380363Lelio R Paula01/2016
7723(6253^21169-1)/625280356Serge Batalov08/2020
7724(14005^19381-1)/1400480355Serge Batalov08/2020
77252^266920-11296780351Enzo Doria06/2014
7726(2^266910+2394)/280348Stefano Morozzi01/2020
7727(2^266899+1994)/280345Stefano Morozzi01/2020
77288*10^80342+8780343Robert Price10/2017
7729(2^266861+890)/280333Stefano Morozzi01/2020
773012^74428-1380322Lelio R Paula11/2015
7731(2^266810+2718)/280318Stefano Morozzi01/2020
7732(2^266800+2886)/280315Stefano Morozzi01/2020
7733(6163^21187-1)/616280291Serge Batalov08/2020
77342^266680+2780279Lelio R Paula05/2012
77352^266630-13180264Lelio R Paula05/2012
7736(2^266627+1278)/280263Stefano Morozzi01/2020
77372^266598+7681980254Enzo Doria05/2016
773824463^1908+1908^2446380253Hans Havermann01/2020
77392^266587+188063380251Enzo Doria10/2016
7740(2^266570+3942)/280246Stefano Morozzi01/2020
77412^266541-11004980237Enzo Doria04/2014
774238635!2-880222Robert Price06/2015
7743(2^266465+986)/280214Stefano Morozzi01/2020
77443^168111+168111^3-180210Robert Price04/2014
7745(2^266447+758)/280209Stefano Morozzi01/2020
77462^266443+51380208Lelio R Paula07/2013
7747(26*10^80200+61)/380201Robert Price06/2017
77482^266412-10991380199Enzo Doria04/2014
7749(10223*2^266417+1)/4509180199Lelio R Paula06/2014
77502^266413-469380199Yves Minet05/2019


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: September, 29 2020 00:24 (Time in France)

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