PRP Records

Probable Primes Top 10000

(280932 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 ?
8501(5728^21673-1)/572781444Serge Batalov08/2020
85022^270546-11034581443Enzo Doria05/2014
850313^73105-6081435Lelio R Paula11/2015
8504(2^270502+1518)/281429Stefano Morozzi01/2020
8505(2^270479+2114)/281422Stefano Morozzi01/2020
8506(2^270384+1218)/281394Stefano Morozzi01/2020
850744^49524+4381391Norbert Schneider06/2014
8508(3*2^270368-1)/1381389Lelio R Paula02/2014
850996*10^81387-781389Robert Price03/2021
851019548^14563+14563^1954881384Hans Havermann05/2020
8511(2^270337+1130)/281380Stefano Morozzi01/2020
851227405^932+932^2740581377Hans Havermann05/2020
851319396^15683+15683^1939681375Hans Havermann05/2020
8515(10^81363+719)/981363Serge Batalov12/2014
8514(734^28393-1)/73381363Serge Batalov08/2020
8516(10^81353+449)/981353Serge Batalov12/2014
851714^70978-8981350Lelio R Paula11/2015
851811^78108-204081342Enzo Doria12/2012
85197*10^81327-5781328Robert Price06/2020
8520(7*10^81328-79)/981328Robert Price01/2021
852119102^18065+18065^1910281315Hans Havermann07/2020
85223^170400-5881302Lelio R Paula12/2015
8523(17*10^81300-131)/381301Robert Price12/2017
852410^81297+3699181298Patrick De Geest06/2013
852510^81297-5781297Robert Price05/2011
8526(2^270063+3206)/281297Stefano Morozzi01/2020
852719359^15826+15826^1935981296Hans Havermann06/2020
85282^270055-11304781295Enzo Doria07/2014
852918^64759-5581291Lelio R Paula11/2015
85303*10^81290-1781291Robert Price03/2021
8531(2^269987+1)/381274H.&R. Lifchitz10/2000
8532(31^54493-1)/3081268Alexander Zhirkov10/2010
8533(2^270059-1)/540119/6481417/712497615775672596781265Dario Alpern09/2014
8534(194^35521-1)/19381263Serge Batalov08/2020
853520722^8343+8343^2072281258Hans Havermann07/2020
8536(2^269922+3574)/281255Stefano Morozzi01/2020
853721310^6497+6497^2131081249Hans Havermann07/2020
8538(16392^19273-1)/1639181225Serge Batalov08/2020
85392^269819-459781224Yves Minet03/2019
8540(2^269816+7)/42490181218Lelio R Paula12/2012
854123470^2887+2887^2347081217Hans Havermann05/2020
8542(23*10^81214+1)/381215Serge Batalov06/2009
8543(2^269720+3778)/281194Stefano Morozzi01/2020
8544(17*2^269720+1)/30381193Lelio R Paula07/2012
854556^46441-55^4644181188Robert Price10/2013
85462^269664+17781177Lelio R Paula06/2012
8547(13*2^269665-1)/18581177Lelio R Paula02/2014
854821642^5615+5615^2164281144Hans Havermann07/2020
85492^269539-11224981140Enzo Doria06/2014
8550((2*170026-3)*3^(170026-1)+1)/481128Robert Price01/2015
8552(2^269495-5)/981126Lelio R Paula12/2012
85511239^26228+26228^123981126Norbert Schneider10/2019
85532^269490-362381125Yves Minet10/2009
8554(55459*2^269444+1)/3581114Lelio R Paula06/2014
855519554^14065+14065^1955481113Hans Havermann06/2020
8556(2^269417+78557)/525781099Lelio R Paula12/2012
85574*5^116011-781089Lelio R Paula10/2014
8558(2^269349+2366)/281082Stefano Morozzi01/2020
8559(2^269303+2946)/281068Stefano Morozzi01/2020
85606*10^81060+5381061Robert Price05/2020
85617*10^81058+7981059Robert Price02/2017
85622^269236-10990781049Enzo Doria04/2014
8563(2^269182+1870)/281032Stefano Morozzi01/2020
8564(2^269179+3006)/281031Stefano Morozzi01/2020
8565(8*10^81029-11)/381030Erik Branger03/2014
856619749^12668+12668^1974981025Hans Havermann05/2020
85673*10^81021+781022Erik Branger11/2013
85686^104115+10381018Lelio R Paula12/2015
85692^269120+186915181014Enzo Doria05/2016
85705^115901+1281012Lelio R Paula10/2015
8571(2^269072+3610)/280999Stefano Morozzi01/2020
8572(2^269083-9)/32036980997Lelio R Paula12/2012
8573(5*10^80992-179)/380993Robert Price10/2020
85742*10^80981-4980982Robert Price09/2020
8575(2^269002+1614)/280978Stefano Morozzi01/2020
857617^65810-2080976Lelio R Paula11/2015
857720^62236-2380971Lelio R Paula01/2016
85782^268974-11218180970Enzo Doria06/2014
8580L(387433)80969Renaud Lifchitz11/2003
8579V(387433)80969Serge Batalov03/2015
858122732^3645+3645^2273280965Hans Havermann06/2020
8582(2^268957+602)/280964Stefano Morozzi01/2020
8583(2^268955-509203)/580963Lelio R Paula12/2012
858419485^14284+14284^1948580958Hans Havermann05/2020
8585(87398^16384+1)/6553780957Lelio R Paula11/2011
8586329^32160+32160^32980954Norbert Schneider11/2014
858719678^12973+12973^1967880937Hans Havermann02/2020
8588(2^268864+3558)/280936Stefano Morozzi01/2020
85892^268859-15980935Lelio R Paula05/2012
8590(2^268841-lucasV(1,2,268841)+1)/280929Mike Oakes11/2016
85922^268827+577580925Lelio R Paula07/2013
85912^268824-11025580925Enzo Doria05/2014
8593(2^268824+1902)/280924Stefano Morozzi01/2020
85942^268798-186832180917Enzo Doria04/2016
859520613^8420+8420^2061380913Hans Havermann03/2020
85962^268753-11462180903Enzo Doria05/2015
85972^268743+160580900Lelio R Paula07/2013
85986^103954-13980892Lelio R Paula12/2015
859910^80883+4980884Robert Price03/2011
860010^80883-8032780883Patrick De Geest07/2013
86016^103937+12180879Lelio R Paula12/2015
8602148^37266+14780877Norbert Schneider12/2018
8603(26*10^80875-119)/380876Robert Price07/2016
8604(22699*2^268657+1)/635180875Lelio R Paula06/2014
8605(2^268612+2530)/280860Stefano Morozzi01/2020
86062^268581-86968810580851Lelio R Paula05/2016
8607(11*2^268521-1)/380834Lelio R Paula02/2014
86082^268516-24980832Yves Minet02/2012
860922259^4278+4278^2225980828Hans Havermann03/2020
86102^268500+1609580827Lelio R Paula07/2013
86113^169402+10080826Lelio R Paula12/2015
8612(2^268495+566)/280825Stefano Morozzi01/2020
86139^84698+8^(84698-1)80823Robert Price03/2016
86142^268472-10973980819Enzo Doria04/2014
8615(9*2^268454+1)/3780813Lelio R Paula12/2012
8616(3*2^268502+1)/37790218843535364780811Lelio R Paula12/2012
8617(2^268441+3962)/280809Stefano Morozzi01/2020
8618134^37987-133^3798780803Jean-Louis Charton12/2005
861915^68702-7680800Lelio R Paula11/2015
86202^268408+780799Lelio R Paula05/2012
8621(16095^19207-1)/1609480794Serge Batalov08/2020
86222^268375+14180789Lelio R Paula05/2012
862312^74856-4780784Lelio R Paula11/2015
86242^268346+52428780781Paul Underwood08/2018
86259*10^80777-4180778Robert Price08/2020
8626(10868^20011-1)/1086780764Serge Batalov08/2020
86276^103770-10780749Lelio R Paula12/2015
8628(751^28081-1)/75080748Serge Batalov08/2020
86293^169224-6280741Lelio R Paula12/2015
8630p(16866)#/2+6480741Robert Price03/2017
86315^115502-7280733Lelio R Paula10/2015
8632(2^268154+2262)/280723Stefano Morozzi01/2020
8633(2^268156+1290)/280723Stefano Morozzi01/2020
86352^268079-192780700Yves Minet10/2009
8634(2^268078+2514)/280700Stefano Morozzi01/2020
86362^268028+11780685Lelio R Paula05/2012
8637121^38738+12080683Norbert Schneider01/2015
8638(3^169097-8)/83580677Lelio R Paula12/2012
8639(2^267956+1810)/280663Stefano Morozzi01/2020
864019359^14666+14666^1935980656Hans Havermann12/2019
86412^267918+6780652Lelio R Paula05/2012
8642(89*10^80650-179)/980651Robert Price11/2017
8643(2^267914+2094)/280650Stefano Morozzi01/2020
8644(2^267894+2202)/280644Stefano Morozzi01/2020
8645(302*10^80638+13)/980640Robert Price01/2017
86463^169004+266080636Lelio R Paula12/2015
86472^267860-11285980634Enzo Doria06/2014
864896*10^80624-780626Robert Price03/2021
86492^267828-11070580625Enzo Doria05/2014
8650(2956^23227-1)/295580611Serge Batalov08/2020
8651(2^267752+2602)/280602Stefano Morozzi01/2020
86522^267743+1270580599Lelio R Paula07/2013
8653(22*10^80595+23)/980596Robert Price03/2015
8654(2^267712+2358)/280590Stefano Morozzi01/2020
8655(2^267685+854)/280581Stefano Morozzi01/2020
86562^267674-5180578Lelio R Paula05/2012
8657(86*10^80571-41)/980572Robert Price11/2015
8658(2^267637+2454)/280567Stefano Morozzi01/2020
865920452^8693+8693^2045280564Hans Havermann02/2020
86602^267612-196580560Lelio R Paula07/2013
86612^267553+409780542Lelio R Paula07/2013
86627^95276-880518Robert Price01/2014
8663(15185*2^267457-1)/4782980513Lelio R Paula04/2015
86646^103467+16380513Lelio R Paula12/2015
866520283^9314+9314^2028380506Hans Havermann02/2020
8666(2^267387+2294)/280492Stefano Morozzi01/2020
8667(7*10^80490+143)/380491Robert Price04/2016
866819887^11152+11152^1988780490Hans Havermann01/2020
8669(2^267348+3810)/280480Stefano Morozzi01/2020
867086^41597-85^4159780470Robert Price04/2015
867113^72237+3080468Lelio R Paula11/2015
867217^65389+1480458Lelio R Paula11/2015
8673423^30634+30634^42380456Norbert Schneider05/2017
8674(2^267257+470)/280453Stefano Morozzi01/2020
86752^267232+10580445Lelio R Paula05/2012
8676(298*10^80442+11)/380444Robert Price11/2020
867722101^4360+4360^2210180437Hans Havermann02/2020
867811^77237-307200080435Enzo Doria01/2013
867920696^7689+7689^2069680422Hans Havermann01/2020
8680(2^267149+2562)/280420Stefano Morozzi01/2020
868121321^5908+5908^2132180411Hans Havermann02/2020
8682(13100^19531-1)/1309980411Serge Batalov08/2020
86832^267116-45995980410Enzo Doria06/2015
868438715!2+880406Robert Price01/2015
868519579^12786+12786^1957980406Hans Havermann02/2020
8686(2^267017+1)/380380H.&R. Lifchitz09/2000
8687(2^267006+1134)/280377Stefano Morozzi01/2020
868824273^2048+2048^2427380376Hans Havermann01/2020
8689(2^266989+734)/280372Stefano Morozzi01/2020
8690(2^266989+1850)/280372Stefano Morozzi01/2020
8691(13427^19471-1)/1342680372Serge Batalov08/2020
86922^266968-4580366Lelio R Paula05/2012
8693(2^266967+3974)/280365Stefano Morozzi01/2020
869420^61768-6380363Lelio R Paula01/2016
8695(6253^21169-1)/625280356Serge Batalov08/2020
8696(14005^19381-1)/1400480355Serge Batalov08/2020
86972^266920-11296780351Enzo Doria06/2014
8698(2^266910+2394)/280348Stefano Morozzi01/2020
8699(2^266899+1994)/280345Stefano Morozzi01/2020
87008*10^80342+8780343Robert Price10/2017
8701(10^80363+1)/1186613600417422195087690646380335Anonymous10/2020
8702(2^266861+890)/280333Stefano Morozzi01/2020
870312^74428-1380322Lelio R Paula11/2015
8704(2^266810+2718)/280318Stefano Morozzi01/2020
8705(2^266800+2886)/280315Stefano Morozzi01/2020
8706(6163^21187-1)/616280291Serge Batalov08/2020
87072^266680+2780279Lelio R Paula05/2012
8708(232*10^80264+17)/380266Robert Price04/2021
87092^266630-13180264Lelio R Paula05/2012
8710(2^266627+1278)/280263Stefano Morozzi01/2020
87112^266598+7681980254Enzo Doria05/2016
871224463^1908+1908^2446380253Hans Havermann01/2020
87132^266587+188063380251Enzo Doria10/2016
8714(2^266570+3942)/280246Stefano Morozzi01/2020
87152^266541-11004980237Enzo Doria04/2014
871638635!2-880222Robert Price06/2015
8717(2^266465+986)/280214Stefano Morozzi01/2020
87183^168111+168111^3-180210Robert Price04/2014
8719(2^266447+758)/280209Stefano Morozzi01/2020
87202^266443+51380208Lelio R Paula07/2013
8721(26*10^80200+61)/380201Robert Price06/2017
87222^266412-10991380199Enzo Doria04/2014
8723(10223*2^266417+1)/4509180199Lelio R Paula06/2014
87242^266413-469380199Yves Minet05/2019
8725(13737^19381-1)/1373680193Serge Batalov08/2020
872613^71988+6680191Lelio R Paula11/2015
872711^77002-432080190Enzo Doria01/2013
872819839^11012+11012^1983980187Hans Havermann03/2020
873018^63879-1380186Lelio R Paula11/2015
8729(2^266371+1814)/280186Stefano Morozzi01/2020
87312^266368-11229580185Enzo Doria06/2014
873219217^14880+14880^1921780185Hans Havermann03/2020
8733(3^168050+5)/102145480175Lelio R Paula10/2012
8734(2^266324+1386)/280172Stefano Morozzi01/2020
8735(22*10^80167+41)/980168Robert Price02/2015
8736(2^266308+1618)/280167Stefano Morozzi01/2020
8737(34*10^80162-43)/980163Ray Chandler12/2010
8738(2^266276+762)/280157Stefano Morozzi01/2020
8740(38*10^80150-11)/980151Robert Price05/2015
8739(598*10^80149-31)/980151Robert Price02/2017
874119^62678-8080150Lelio R Paula12/2015
8742(559^29173-1)/55880148Serge Batalov08/2020
874310^80139+3234380140Patrick De Geest02/2011
874410^80139-980139Alexander Gramolin01/2011
87453^167955-10680135Lelio R Paula12/2015
874620545^7944+7944^2054580127Hans Havermann04/2020
874718876^17569+17569^1887680124Hans Havermann03/2020
8748(2^266137+3782)/280115Stefano Morozzi01/2020
8749(2^266121+3846)/280111Stefano Morozzi01/2020
875022752^3313+3313^2275280093Hans Havermann03/2020


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: April, 13 2021 12:02 (Time in France)

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