PRP Records

Probable Primes Top 10000

(252932 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 ?
22512^409533+77747123282Enzo Doria05/2016
22522^409436-112799123253Enzo Doria06/2014
22532^409225+1873787123189Enzo Doria06/2016
22542^409174+73009123174Enzo Doria04/2016
22552^409058-112685123139Enzo Doria06/2014
2256(13*10^123137-61)/3123138Robert Price11/2018
22574*10^123113+21123114Robert Price12/2018
22582^408778+77689123055Enzo Doria05/2016
22592^408690-75123028Lelio R Paula11/2013
2260(29*10^122996+673)/9122997Robert Price12/2018
22612^408574-2787341122994Enzo Doria03/2016
22623*10^122977+37122978Robert Price08/2018
2263Phi(157825,10)122961Maksym Voznyy06/2015
2264(13*2^408283+1)/1665122904Lelio R Paula05/2014
2265(16*10^122871+77)/3122872Robert Price03/2019
2266(11*2^408100-1)/35122850Lelio R Paula04/2014
2267(19*10^122836-43)/3122837Robert Price05/2019
2268(2^407821-lucasV(1,2,407821)+1)/2122767Mike Oakes11/2016
2269(32*10^122733-77)/9122734Robert Price06/2018
2270(21*2^407604-1)/215122701Lelio R Paula04/2014
2271(22*10^122681+161)/3122682Robert Price05/2019
2272(21*2^407433-1)/13122650Lelio R Paula04/2014
2273(73*10^122592-1)/9122593Robert Price01/2015
2274(5*10^122592+91)/3122593Robert Price04/2018
22752^407179-112075122574Enzo Doria06/2014
2276(21*2^407131+1)/207517523122552Lelio R Paula04/2014
2277(66^67349+1)/67122543Paul Bourdelais09/2017
22782^407008-1867919122522Enzo Doria04/2016
227911^117642-300122512Enzo Doria10/2012
2280(F(3*97700+1)^2+L(3*97700+1)^2)/2122509Henri Lifchitz10/2017
22812^406949+72197122504Enzo Doria04/2016
2282(19*10^122501+149)/3122502Robert Price05/2019
22832^406826-65122467Lelio R Paula11/2013
22842^406821-2797363122466Enzo Doria04/2016
22852^406758-17122447Lelio R Paula11/2013
2286(30^82883-1)/29122427Robert Price12/2011
2287(2^406583-1)/813167122388Jens K. Andersen02/2009
22884*10^122377+19122378Robert Price10/2018
22893*10^122345-97122346Robert Price07/2018
229097^61575-2122336Lelio R Paula12/2014
22912^406298+2799109122308Enzo Doria04/2016
22927*10^122294+57122295Robert Price06/2019
2293(27*2^406241-1)/10277122289Lelio R Paula04/2014
22942^406229-1849993122288Enzo Doria08/2015
22953*10^122274+7122275Robert Price07/2015
22962^406117+1876577122254Enzo Doria07/2016
22973^256199-2^256199122238Mike Oakes06/2005
22982^405992-78557122216Jorge Menendez03/2018
2299(8*10^122203+43)/3122204Robert Price06/2018
2300(58*10^122170+329)/9122171Robert Price05/2019
23012^405774+179149122151Enzo Doria06/2016
23025*10^122082+41122083Robert Price03/2019
23032^405514-3311122072Yves Minet12/2014
23042^405514-115511122072Enzo Doria07/2015
23052^405422-113261122045Enzo Doria07/2014
23062^405173+71237121970Enzo Doria04/2016
2307(2^405016+1)/257121920Lelio R Paula04/2014
23082^404858+71329121875Enzo Doria04/2016
23092^404813-114703121861Enzo Doria04/2015
23102^404764+77791121847Enzo Doria05/2016
2311317^48694+48694^317121787Norbert Schneider08/2015
23122^404536-115259121778Enzo Doria06/2015
23132^404501-631121767Yves Minet07/2012
231463^67620+2121672Lelio R Paula08/2015
2315(17*10^121621+1)/9121622Serge Batalov05/2010
2316(15*2^403912+1)/271121589Lelio R Paula05/2014
2317(10^121543-79)/3121543Robert Price01/2018
23182^403676+76831121519Enzo Doria05/2016
2319(7*10^121487+143)/3121488Robert Price03/2018
23202^403363-113635121425Enzo Doria08/2014
23212^403336-1861469121417Enzo Doria03/2016
2322p(24442)#/2-64121381Robert Price04/2017
232311^116555-720121380Enzo Doria11/2012
23242^403100-461267121346Enzo Doria07/2015
23252^403093-112213121344Enzo Doria06/2014
2326(316^48539+1)/317121330Eric Chen10/2017
23272^403004+1866361121317Enzo Doria03/2016
23282^402953+89121301Lelio R Paula10/2013
23292^402944-2788319121299Enzo Doria03/2016
2330(44*10^121297-719)/9121298Robert Price12/2018
2331(27*2^402865+1)/5121276Lelio R Paula04/2014
23322^402828-113183121264Enzo Doria07/2014
2333(17*10^121242+1)/9121243Serge Batalov05/2010
2334(15*2^402757+1)/101121242Lelio R Paula05/2014
23362^402715+1874223121230Enzo Doria06/2016
2335(35*10^121229-593)/9121230Robert Price07/2018
2337(91^61879+1)/92121222Paul Bourdelais09/2017
23387*10^121144+9121145Robert Price09/2015
23392^401725-113251120932Enzo Doria07/2014
2340(15*2^401677-1)/19120917Lelio R Paula05/2014
23412^401652+73711120910Enzo Doria04/2016
2342(2^401632+3)/79120902Lelio R Paula04/2014
23432^401406-2791331120836Enzo Doria03/2016
2344(28^83497+1)/29120832Robert Price07/2013
2345(22*10^120828+161)/3120829Robert Price05/2019
23462^401369+1867367120825Enzo Doria03/2016
2347(10^120782+29)/3120782Serge Batalov12/2014
23482^401215-1657120778Yves Minet07/2014
23492^401159+53120761Lelio R Paula10/2013
23502^401031-113047120723Enzo Doria07/2014
2351(29*2^400909-1)/303120685Lelio R Paula04/2014
23522^400571-15120584Lelio R Paula10/2013
2353(10^120574+359)/9120574Serge Batalov12/2014
23542^400424-216413120540Enzo Doria04/2013
2355(17*2^400200-1)/587120471Lelio R Paula05/2014
23562^400166+1874899120462Enzo Doria06/2016
2357(3*2^400045-1)/865120424Lelio R Paula04/2014
23582^399966+73759120402Enzo Doria04/2016
2359(112*10^120395-1)/3120397Serge Batalov12/2014
23602^399918-95120388Lelio R Paula04/2013
2361(49*10^120380-139)/9120381Robert Price03/2019
23622^399792-1849259120350Enzo Doria08/2015
23639*10^120342-7120343Robert Price09/2015
2364(13*10^120306-37)/3120307Robert Price01/2019
23652^399526-1861721120270Enzo Doria11/2015
2366(10^(2*60126+1)+36*10^60126-1)/9120253Robert Price10/2015
23672^399322-2798111120208Enzo Doria04/2016
236872^64693-71^64693120157Robert Price03/2014
23692^399111-28489120145Enzo Doria08/2015
23712^398877+105120074Donovan Johnson01/2006
2370(101*10^120072-87)/7120074Hans Havermann02/2015
2372(88^61751+1)/89120072Paul Bourdelais09/2017
23732^398710+57120024Lelio R Paula04/2013
23742^398691-115057120018Enzo Doria06/2015
2375L(574219)120005Renaud Lifchitz03/2004
23762^398571+60413119982Yves Minet03/2011
2377p(24179)#/2-64119949Robert Price04/2017
23782^398448+1872001119945Enzo Doria05/2016
23798*10^119930-3119931Ray Chandler04/2011
2380(10^119880+179)/9119880Serge Batalov12/2014
2381(9*2^398145+1)/73119853Lelio R Paula04/2014
2382(10^119836+77)/3119836Robert Price01/2018
23832^398029+1872527119819Enzo Doria05/2016
23842^397897-113541119779Enzo Doria08/2014
2385(21*2^397661-1)/27593119705Lelio R Paula04/2014
2386(58^67853-1)/57119653Paul Bourdelais09/2017
23872^397426+73849119638Enzo Doria04/2016
23882^396933-112723119489Enzo Doria06/2014
238911^114738-150119488Enzo Doria10/2012
2390(4*10^119474+149)/9119474Robert Price04/2018
23912^396790-21119446Lelio R Paula04/2013
2392(2^396633-7)/5119398Lelio R Paula04/2014
2393105^59050+104119352Norbert Schneider11/2016
2394126^56824-125119352Norbert Schneider12/2018
2395139^55690-138119345Norbert Schneider04/2019
2396790^41179+41179^790119322Norbert Schneider04/2019
23972^396374+73729119321Enzo Doria04/2016
23982^396258-459491119286Enzo Doria05/2015
23992^396128-396128-1119247Karsten Bonath06/2018
2400(2^395986+5)/76881119199Lelio R Paula04/2014
2401(23*2^395942-1)/91119190Lelio R Paula04/2014
2402(11*2^395548+1)/3119073Lelio R Paula04/2014
2403(30^80599+1)/31119054Robert Price07/2013
2404(43*10^119024-403)/9119025Robert Price01/2019
24052^395062-109121118926Enzo Doria04/2014
24062^395055-4627118924Yves Minet05/2019
2407(2^394918+78557)/3118882Lelio R Paula01/2015
2408(16*10^118852+77)/3118853Robert Price03/2019
2409(2^394739+3)/1883118826Lelio R Paula04/2014
24102^394266+71389118686Enzo Doria04/2016
24112^394215-51261118671Tony Prest / Never Odd Or Even04/2018
2412(2^394215-48793)/5/5118670Tony Prest / Never Odd Or Even04/2018
2413(2^394215-17063)/3/3/5118669Tony Prest / Never Odd Or Even04/2018
2414(2^394215-24393)/5/5/5/5/5118668Tony Prest / Never Odd Or Even04/2018
2415(2^394215-35885)/3/71/173118666Tony Prest / Never Odd Or Even04/2018
2416(2^394215-47925)/353/2269118665Tony Prest / Never Odd Or Even04/2018
2417(2^394215-62819)/3/3/3/3/3/3/3/7/21737/1082153/1953673118650Tony Prest / Never Odd Or Even04/2018
2418(17*10^118635+13)/3118636Robert Price01/2019
24195^169727+2118635Lelio R Paula08/2013
24202^394034-3118617M. Frind & P. Underwood09/2002
2421(7*10^118607+179)/3118608Robert Price09/2018
24223^248572-6242118599Enzo Doria05/2014
2423(3*2^393964-1)/181118594Lelio R Paula04/2014
24247^140303-6118570Robert Price11/2014
24252^393427+75683118434Enzo Doria04/2016
24262^393376-114749118418Enzo Doria04/2015
24272^393180+73118359Lelio R Paula04/2013
2428p(23881)#/2+256118328Robert Price05/2017
2429(10^118324+359)/9118324Serge Batalov12/2014
2430p(23879)#/2+64118317Robert Price03/2017
2431(53*10^118216+1)/9118217Serge Batalov11/2010
2432(7*2^392697+1)/15118214Renaud Lifchitz03/2011
2433(157^53819-1)/156118179Alexander Zhirkov06/2016
2434(19*2^392551+1)/3118171Lelio R Paula04/2014
24352^392516-29219118160Enzo Doria07/2015
2436Phi(177231,10)118152Maksym Voznyy09/2015
24372^392413-112123118129Enzo Doria06/2014
2438(2^392342+5)/27118106Lelio R Paula04/2014
24392^392300-1841429118095Enzo Doria06/2015
24402^392220+75241118070Enzo Doria04/2016
244110^118009+664447118010Patrick De Geest07/2018
244210^118009-20001118009Robert Price01/2018
2443(14*10^117991+61)/3117992Robert Price12/2018
24442^391933+5897117984Yves Minet02/2011
24452^391912-1849259117978Enzo Doria08/2015
2446(2^391812+5)/14181117944Lelio R Paula04/2014
2447(46*10^117902+683)/9117903Robert Price03/2019
2448(7*2^391521+1)/285117858Lelio R Paula04/2014
24492^391324+90901117801Yves Minet02/2011
24502^391301-1859923117794Enzo Doria03/2016
24512^391261-4131117782Yves Minet02/2018
2452(2^391115-7)/11791117734Lelio R Paula04/2014
24532^390960+1880881117691Enzo Doria11/2016
24542^390897-1860553117672Enzo Doria11/2015
24552^390889-115003117670Enzo Doria06/2015
24562^390779-30337117637Paul Bourdelais02/2012
245711^112916-780117590Enzo Doria12/2012
2458(16^97613-5^97613)/11117537Robert Price07/2013
2459(17*2^390272+1)/1983117482Lelio R Paula04/2014
246031^78759-30117459Theodore Burton02/2007
24612^389998+37117402Lelio R Paula03/2013
2462(13*10^117249+161)/3117250Robert Price11/2018
24632^389478+43117245Lelio R Paula03/2013
2464(29*2^389351-1)/9117207Lelio R Paula04/2014
24655*10^117205+23117206Robert Price03/2019
2466(2^389341-7)/3865117200Lelio R Paula03/2014
246710^117142+209223117143Patrick De Geest04/2018
246910^117142-1000000001117142Robert Price03/2018
246810^117142-966057117142Patrick De Geest04/2018
247010^117135+360577117136Patrick De Geest07/2018
247110^117135-401117135Robert Price01/2018
24724*10^117123+79117124Robert Price08/2018
24732^389033-12797413117111Enzo Doria04/2016
24742^388960-109505117089Enzo Doria04/2014
2475(2^388928-5)/569117077Lelio R Paula03/2014
24762^388888-1529117067Yves Minet01/2013
247710^117059+28879117060Patrick De Geest05/2016
2478(10^117059-71)/1117059Serge Batalov12/2014
2479(26*10^116999-503)/9117000Robert Price07/2018
24803^245154-6256116969Enzo Doria05/2014
24815*10^116966-43116967Robert Price01/2019
24822^388536-113495116961Enzo Doria08/2014
24832^388469-43116941Lelio R Paula03/2013
2484(7*2^388372-1)/111116911Lelio R Paula04/2014
2485(7*2^388335-1)/25116900Lelio R Paula04/2014
24862^388180+93116854Donovan Johnson07/2008
2487(2^388081+7)/1179116821Lelio R Paula03/2014
24882^387946-113261116784Enzo Doria07/2014
24892^387745+75557116723Enzo Doria04/2016
2490(7*10^116684+179)/3116685Robert Price09/2018
24912^387554+71455116666Enzo Doria04/2016
2492(2^387447+78557)/365116631Lelio R Paula12/2014
2493(145*10^116610-1)/9116612Serge Batalov12/2014
2494(25*10^116601-331)/9116602Robert Price08/2018
2495(17*2^387284-1)/59116584Lelio R Paula04/2014
2496(31*2^386968+1)/7116490Lelio R Paula03/2014
24972^386947+1869143116483Enzo Doria05/2016
2498(30^78857-1)/29116480Robert Price12/2011
2499(2^386903-3)/5116469Lelio R Paula03/2014
25002^386389-1864783116315Enzo Doria03/2016


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: June, 18 2019 07:14 (Time in France)

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