PRP Records

Probable Primes Top 10000

(277054 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(2^261724+60031)/13/31/702487778778Tony Prest / Never Odd Or Even04/2014
8502(2^261724+121879)/5/78943321778778Tony Prest / Never Odd Or Even04/2014
8503(2^261724+290135)/3/3/8467/905978778Tony Prest / Never Odd Or Even04/2014
8504(2^261724+79857)/59/3847/16533178777Tony Prest / Never Odd Or Even04/2014
8505(2^261724+22883)/3/17/23/2351/1007978777Tony Prest / Never Odd Or Even04/2014
8506(2^261724+154799)/3/5/365565371978777Tony Prest / Never Odd Or Even04/2014
8507(2^261724+391001)/3/11/17/41/43/2407178777Tony Prest / Never Odd Or Even04/2014
8508(2^261724+622383)/34843/55071778777Tony Prest / Never Odd Or Even05/2014
8509(2^261724+302829)/5/37/37/3707814778776Tony Prest / Never Odd Or Even04/2014
8510(2^261724+315837)/43/217613624378776Tony Prest / Never Odd Or Even04/2014
8511(2^261724+582373)/53/307/311/3211778776Tony Prest / Never Odd Or Even05/2014
8512(2^261724+295283)/3/3/3/29/43/1781227378775Tony Prest / Never Odd Or Even04/2014
8513(2^261724+27491)/3/22787/10597844978774Tony Prest / Never Odd Or Even04/2014
8514(2^261724+392751)/193813/28782668978774Tony Prest / Never Odd Or Even04/2014
8515(2^261724+328501)/7/1091/3149561051978773Tony Prest / Never Odd Or Even04/2014
8516(2^261724+111267)/19/4637/1514056042778772Tony Prest / Never Odd Or Even04/2014
8517(2^261724+572133)/127/131/7378775233378772Tony Prest / Never Odd Or Even05/2014
8518(2^261724+608733)/59/7079/18451/90915178771Tony Prest / Never Odd Or Even05/2014
8519(2^261724+255449)/3/3/5/7/1759/10177/3315886978770Tony Prest / Never Odd Or Even04/2014
8520(2^261724+99509)/3/5/5/6507271/674965928978769Tony Prest / Never Odd Or Even04/2014
8521(2^261724+52501)/563/53939/2794283139178769Tony Prest / Never Odd Or Even04/2014
8522(2^261724+117089)/3/5/37/149/967/2027/416374178769Tony Prest / Never Odd Or Even04/2014
8523(2^261724+372571)/1487/9209/21559/226324978769Tony Prest / Never Odd Or Even04/2014
8524(2^261724+184549)/5/8699/44053/140932299778769Tony Prest / Never Odd Or Even04/2014
8525(2^261724+363351)/937/159683/5952320022778768Tony Prest / Never Odd Or Even04/2014
8526(2^261724+326501)/3/43/193/263/19403/25350140378768Tony Prest / Never Odd Or Even04/2014
8527(2^261724+629477)/3/17/17/137/263/1993/16187/5734778768Tony Prest / Never Odd Or Even05/2014
8528(2^261724+94871)/3/3/13/6734017/167342524578778766Tony Prest / Never Odd Or Even04/2014
8529(2^261724+25981)/577/1181/3643/51778633474378766Tony Prest / Never Odd Or Even04/2014
8531(23*2^261642+1)/9378762Lelio R Paula10/2012
8530(2^261724+351227)/3/3/3/3/71/13997/9595373/819397800778762Tony Prest / Never Odd Or Even04/2014
8532(2^261724+22571)/3/7243/7321/18046081/4573074121178761Tony Prest / Never Odd Or Even04/2014
8533(2^261724+56495)/3/3/3/7/7/13/9041/512818459/2370858911978760Tony Prest / Never Odd Or Even04/2014
853471293!4-478759Robert Price11/2019
8535(2^261630+3582)/278759Stefano Morozzi01/2020
8536(2^261724+604119)/5/7/7/41/14107/19681/211777/90145981/103602083412778750Tony Prest / Never Odd Or Even05/2014
8537(2^261536+846)/278730Stefano Morozzi01/2020
85382^261507-228778722Yves Minet04/2009
85398*10^78717+3978718Robert Price01/2017
8540(78557*2^261440+1)/378706Lelio R Paula06/2014
8541(290^31963-1)/28978704Serge Batalov08/2020
8542(21323^18181-1)/2132278699Serge Batalov08/2020
85436^101128-1643378693Enzo Doria02/2013
854420^60482+9978689Lelio R Paula03/2015
85452^261348-11063378674Enzo Doria05/2014
8546191^34487+278666Lelio R Paula05/2013
85472^261305-11013978661Enzo Doria04/2014
8548(82*10^78635-1)/978636Robert Price12/2014
854910^78632+8178633Robert Price03/2011
855010^78632-40269378632Patrick De Geest07/2013
85513*10^78631+1778632Robert Price03/2017
85522^261174-391178622Yves Minet04/2017
85532^261167+7484378620Enzo Doria04/2016
855418810^15119+15119^1881078617Hans Havermann04/2020
8555L(376121)+F(376122)78605Henri Lifchitz01/2007
855614^68580-2978602Lelio R Paula02/2015
8557(4270^21649-1)/426978592Serge Batalov08/2020
855820603^6522+6522^2060378588Hans Havermann03/2020
8559(2^261056+646)/278586Stefano Morozzi01/2020
8560(73*10^78576-1)/978577Robert Price01/2015
8561(2^261020+2158)/278575Stefano Morozzi01/2020
8562(17*2^261026-1)/4045178574Lelio R Paula02/2014
8563(2415^23227-1)/241478572Serge Batalov08/2020
85652^261001-19578570Lelio R Paula05/2012
856418532^17365+17365^1853278570Hans Havermann02/2020
85665*2^260950+978555Lelio R Paula06/2014
85672^260931-760578549Lelio R Paula07/2013
856819863^9002+9002^1986378546Hans Havermann02/2020
856915^66778-3278538Lelio R Paula02/2015
8570(11*2^260896-1)/24578537Lelio R Paula02/2014
857130^53166+2978533Norbert Schneider03/2017
8573lucasU(2403,1,23229)-lucasU(2403,1,23228)78529Mike Oakes05/2009
857218729^15592+15592^1872978529Hans Havermann04/2020
85747*3^164574-278523Lelio R Paula06/2014
857518518^17385+17385^1851878520Hans Havermann03/2020
85762^260830-11213378518Enzo Doria06/2014
857713^70486+4278518Lelio R Paula03/2015
857811^75386-708078507Enzo Doria01/2013
8580(86^40583-1)/8578506Paul Bourdelais08/2017
8579(2^260790+1914)/278506Stefano Morozzi01/2020
85815*10^78504+1178505Robert Price08/2019
85822^260711-5869578482Lelio R Paula07/2013
8583(2^260695+2258)/278477Stefano Morozzi01/2020
85842^260678-11106578472Enzo Doria05/2014
858521560^4359+4359^2156078466Hans Havermann02/2020
858618^62501-9778456Lelio R Paula02/2015
858753^45498-278452Lelio R Paula08/2013
8588(8890^19867-1)/888978449Serge Batalov08/2020
8589(2^260549+642)/278433Stefano Morozzi01/2020
8590(2^260527+3906)/278427Stefano Morozzi01/2020
85912^260513-11112178423Enzo Doria05/2014
859237845!2-6478412Robert Price06/2015
85932^260469-11069578409Enzo Doria05/2014
8594(11*10^78408-113)/378409Robert Price01/2017
85952^260447+841578403Lelio R Paula07/2013
859637837!2-6478394Robert Price06/2015
8597(19*2^260379-1)/5378382Lelio R Paula02/2014
85982^260377-11323378382Enzo Doria07/2014
8599(2^260378+3750)/278382Stefano Morozzi01/2020
86019^82138+6^82138-2^8213878380Mike Oakes08/2010
860069^42624+278380Lelio R Paula05/2013
86022^260369-185971378379Enzo Doria03/2016
860318634^16067+16067^1863478374Hans Havermann02/2020
860414*10^78362+108978364Jens K. Andersen11/2007
8605(2^260317+3542)/278363Stefano Morozzi01/2020
8606(1942^23827-1)/194178346Serge Batalov08/2020
86075^112070-5478334Lelio R Paula02/2015
860820120^7821+7821^2012078333Hans Havermann03/2020
8609(10^(2*39165+1)+54*10^39165-1)/978331Robert Price04/2017
8610(2^260195+3546)/278327Stefano Morozzi01/2020
86112^260182-11345378323Enzo Doria07/2014
8612f(16405)78319Robert Price09/2017
861318547^16678+16678^1854778309Hans Havermann02/2020
8614(78557*2^260084+1)/51978296Lelio R Paula06/2014
861610^78288+9^(78288+1)78289Robert Price08/2016
861510^78288+3910978289Patrick De Geest12/2016
861710^78288-21629978288Patrick De Geest12/2016
8618(2^260059+2430)/278286Stefano Morozzi01/2020
8619(2^260056+1662)/278285Stefano Morozzi01/2020
8620(376*70^42427-1)/378285Eric Chen10/2020
86215^111997+3678283Lelio R Paula02/2015
8622(2^260017+1602)/278273Stefano Morozzi01/2020
8623(2^260017+2162)/278273Stefano Morozzi01/2020
862423969^1842+1842^2396978266Hans Havermann05/2020
862519297^11370+11370^1929778265Hans Havermann05/2020
8626(21^59183+1)/2278252Paul Bourdelais03/2010
862719090^12561+12561^1909078251Hans Havermann04/2020
8628(88*10^78242-7)/978243Robert Price11/2014
86292*6^100547+778242Lelio R Paula10/2014
8630(2^259913+3470)/278242Stefano Morozzi01/2020
8631(2^259885+3726)/278233Stefano Morozzi01/2020
86322^259860-11108978226Enzo Doria05/2014
863318226^18359+18359^1822678223Norbert Schneider02/2020
8634(2^259833+3342)/278218Stefano Morozzi01/2020
863537^49875-278215Lelio R Paula09/2013
8636(13*10^78213+401)/978214Robert Price10/2017
86377*5^111893-478211Lelio R Paula10/2014
8638(11*2^259809-1)/143778209Lelio R Paula02/2014
86397^92511-678181Theodore Burton11/2005
8640(3^163859-4)/25378179Lelio R Paula10/2012
8641(2^259689+1346)/278174Stefano Morozzi01/2020
8642(27*2^259666-1)/62569178163Lelio R Paula02/2014
8643(2^259642+3202)/278160Stefano Morozzi01/2020
8644(2^259624+442)/278155Stefano Morozzi01/2020
86453*10^78146+1778147Robert Price03/2017
8646(2^259594+1558)/278146Stefano Morozzi01/2020
8647(576^28307+1)/57778137Richard Fischer01/2018
86482^259503+7433378119Enzo Doria04/2016
8649(2^259503+2438)/278118Stefano Morozzi01/2020
8650(31*2^259504-1)/1336578116Lelio R Paula02/2014
8652(58547^16384+1)/278111Lelio R Paula11/2011
86516^100379+1378111Lelio R Paula03/2015
86532^259469-10990978108Enzo Doria04/2014
865415^66413-2678108Lelio R Paula02/2015
865518550^16229+16229^1855078101Hans Havermann05/2020
86567^92410-926678096Mike Oakes02/2010
86572^259398+7579978087Enzo Doria04/2016
86582^259394+187618978086Enzo Doria07/2016
8659PIPrime(78073)78073Eric W. Weisstein07/2006
86605*2^259344-778072Lelio R Paula06/2014
8661(2^259347+990)/278071Stefano Morozzi01/2020
866221702^3955+3955^2170278066Hans Havermann04/2020
866314^68097-8778048Lelio R Paula02/2015
86642^259233-47557378037Paul Bourdelais03/2013
8665181^34554-278012Lelio R Paula10/2017
86663^163500-2878010Robert Price12/2013
8667(206*10^78005+7)/378007Robert Price07/2020
8668(65*10^77992+691)/977993Robert Price08/2016
8669(2^259035+3930)/277978Stefano Morozzi01/2020
86702^259013-11259177971Enzo Doria06/2014
86727*10^77969-1177970Robert Price10/2017
8671(2^259011+2430)/277970Stefano Morozzi01/2020
86736^100193-100193^677966Norbert Schneider04/2017
8674(2^258974+2638)/277959Stefano Morozzi01/2020
867524214^1657+1657^2421477953Hans Havermann03/2020
8676(2^258945+674)/277950Stefano Morozzi01/2020
8677(2^258939+2450)/277949Stefano Morozzi01/2020
867818090^18307+18307^1809077941Norbert Schneider02/2020
8679(11259^19237-1)/1125877935Serge Batalov08/2020
86802^258863-11023577926Enzo Doria05/2014
86812^258852+160577923Lelio R Paula06/2013
868210^77919+23802777920Patrick De Geest04/2020
868310^77919-12345678977919Robert Price02/2020
868410^77919-2543377919Patrick De Geest04/2020
8685(11*10^77909+49)/377910Robert Price05/2016
86862*7^92187-977908Lelio R Paula10/2014
86872^258763-11015577896Enzo Doria04/2014
8688(2^258738+1062)/277888Stefano Morozzi01/2020
86892^258694-11038777875Enzo Doria05/2014
869011^74773-9477869Lelio R Paula02/2015
86916^100067+12577868Lelio R Paula03/2015
869215^66205+877864Lelio R Paula07/2014
8693(2^258637+17)/1860500377851Stefano Morozzi03/2020
86945^111373-1813677847Enzo Doria05/2014
8695(2^258566+1974)/277836Stefano Morozzi01/2020
86962^258524-10987777824Enzo Doria04/2014
869722828^2565+2565^2282877823Hans Havermann04/2020
8698(2^258515+3914)/277821Stefano Morozzi01/2020
86996^100002-1664377817Enzo Doria02/2013
8700(13*10^77811+347)/977812Robert Price10/2017
870119376^10365+10365^1937677806Hans Havermann04/2020
870265^42916+2877803Lelio R Paula01/2016
8703(2^258405+3302)/277788Stefano Morozzi01/2020
8704(89*10^77781-17)/977782Robert Price11/2015
87052^258382-11040577781Enzo Doria05/2014
87075^111278-1499677780Enzo Doria02/2013
8706(2^258378+2314)/277780Stefano Morozzi01/2020
870814^67862+6177779Lelio R Paula02/2015
870910^77777+4848377778Patrick De Geest11/2010
871010^77777-18324377777Patrick De Geest11/2010
87117*((10^77777-1)/9)-81432*277777Matt Stath10/2020
8712(27*2^258352+1)/4377772Lelio R Paula08/2012
8713(22329^17881-1)/2232877758Serge Batalov08/2020
8714(2^258294+2454)/277754Stefano Morozzi01/2020
8715337^30756-1000277740Enzo Doria07/2012
871610^77726+9977727Robert Price03/2011
871710^77726-8594777726Patrick De Geest06/2013
871889^39870-277723Lelio R Paula08/2013
87197^91966-3277721Lelio R Paula02/2015
872035^50327+277709Lelio R Paula05/2013
872224^56298+2377704Norbert Schneider12/2016
8721(2^258128+3502)/277704Stefano Morozzi01/2020
8724(2^258105+78557)/1977697Lelio R Paula10/2012
8723(2^258102+2842)/277697Stefano Morozzi01/2020
87252^258079+17977690Lelio R Paula03/2012
87272^258062-11311177685Enzo Doria07/2014
8726(21752^17911-1)/2175177685Serge Batalov08/2020
8728(2^258022+2422)/277673Stefano Morozzi01/2020
872910^77669+12345678977670Robert Price10/2019
873010^77669+5912777670Patrick De Geest12/2019
873110^77669-10910377669Patrick De Geest12/2019
8732(2^258002+3822)/277667Stefano Morozzi01/2020
873380^40807-7977660Norbert Schneider03/2015
873470385!4-477658Robert Price11/2019
8735(10^77637+359)/977637Serge Batalov12/2014
87362^257862-16577625Lelio R Paula03/2012
8737(25*2^257853+1)/377623Lelio R Paula07/2012
8738(2^257832+1362)/277615Stefano Morozzi01/2020
8739(2^257869+1)/(3*18645362967379)77613Henri Lifchitz04/2005
87406^99728+7177604Lelio R Paula01/2015
87412^257778-11276777599Enzo Doria06/2014
8742(31*2^257771+1)/53777596Lelio R Paula07/2012
8743(2^257762+2214)/277594Stefano Morozzi01/2020
87442^257729-7377585Lelio R Paula03/2012
8745(2^257728+1890)/277584Stefano Morozzi01/2020
87472^257689-6377573Lelio R Paula03/2012
8746(47*10^77572+493)/977573Robert Price11/2017
8748(78557*2^257665+1)/610872577564Lelio R Paula06/2014
8749(5570^20707-1)/556977562Serge Batalov08/2020
8750(3^162563+8)/288577559Lelio R Paula10/2012


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: January, 25 2021 11:23 (Time in France)

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