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 ?
3251(112*10^120395-1)/3120397Serge Batalov12/2014
32522^399918-95120388Lelio R Paula04/2013
3253(28*10^120381-67)/3120382Robert Price10/2020
3254(49*10^120380-139)/9120381Robert Price03/2019
3255(2^399874+2194)/2120374Stefano Morozzi09/2020
32562^399792-1849259120350Enzo Doria08/2015
32579*10^120342-7120343Robert Price09/2015
3258(2^399751+786)/2120337Stefano Morozzi09/2020
3259(13*10^120306-37)/3120307Robert Price01/2019
3260(2^399604+3070)/2120293Stefano Morozzi09/2020
3261(2^399549+1062)/2120276Stefano Morozzi09/2020
32622^399526-1861721120270Enzo Doria11/2015
3263(10^(2*60126+1)+36*10^60126-1)/9120253Robert Price10/2015
326432016^5687+5687^32016120217Hans Havermann01/2021
32652^399322-2798111120208Enzo Doria04/2016
326630438^8867+8867^30438120163Hans Havermann02/2021
326872^64693-71^64693120157Robert Price03/2014
3267(17*10^120156-161)/9120157Robert Price02/2021
32692^399111-28489120145Enzo Doria08/2015
3270(2^399014+1318)/2120115Stefano Morozzi02/2021
327130254^9333+9333^30254120110Hans Havermann02/2021
327230882^7745+7745^30882120101Hans Havermann02/2021
32742^398877+105120074Donovan Johnson01/2006
3273(101*10^120072-87)/7120074Hans Havermann02/2015
3275(88^61751+1)/89120072Paul Bourdelais09/2017
32762^398710+57120024Lelio R Paula04/2013
3277(2^398698+1138)/2120020Stefano Morozzi09/2020
32782^398691-115057120018Enzo Doria06/2015
3279L(574219)120005Renaud Lifchitz03/2004
32802^398571+60413119982Yves Minet03/2011
328128623^15538+15538^28623119971Hans Havermann02/2021
3282p(24179)#/2-64119949Robert Price04/2017
32832^398448+1872001119945Enzo Doria05/2016
3284634^42803+42803^634119938Norbert Schneider07/2019
328531083^7220+7220^31083119935Hans Havermann01/2021
3286(68*10^119931-11)/3119933Robert Price01/2020
32878*10^119930-3119931Ray Chandler04/2011
3288(2^398398+774)/2119930Stefano Morozzi09/2020
3289(10^119880+179)/9119880Serge Batalov12/2014
3290(9*2^398145+1)/73119853Lelio R Paula04/2014
3291(10^119836+77)/3119836Robert Price01/2018
329228179^17870+17870^28179119821Hans Havermann02/2021
32932^398029+1872527119819Enzo Doria05/2016
329433142^4119+4119^33142119802Hans Havermann01/2021
32952^397897-113541119779Enzo Doria08/2014
329628636^15171+15171^28636119728Hans Havermann02/2021
3297(2^397696+1042)/2119719Stefano Morozzi09/2020
3298(19*10^119716+101)/3119717Robert Price09/2019
329929563^11208+11208^29563119717Hans Havermann02/2021
3300(21*2^397661-1)/27593119705Lelio R Paula04/2014
330128243^17308+17308^28243119701Hans Havermann02/2021
330277*10^119688+3119690Robert Price06/2020
3303(2^397504+1698)/2119661Stefano Morozzi09/2020
3304(58^67853-1)/57119653Paul Bourdelais09/2017
33052^397426+73849119638Enzo Doria04/2016
33062^396933-112723119489Enzo Doria06/2014
330711^114738-150119488Enzo Doria10/2012
3308(4*10^119474+149)/9119474Robert Price04/2018
33092^396790-21119446Lelio R Paula04/2013
331032061^5300+5300^32061119405Hans Havermann01/2021
3311(2^396633-7)/5119398Lelio R Paula04/2014
331227382^22913+22913^27382119388Hans Havermann03/2021
3313(2^396577+2522)/2119382Stefano Morozzi09/2020
3314(2^396492+2230)/2119356Stefano Morozzi01/2021
3315105^59050+104119352Norbert Schneider11/2016
3316126^56824-125119352Norbert Schneider12/2018
3317139^55690-138119345Norbert Schneider04/2019
3318790^41179+41179^790119322Norbert Schneider04/2019
33192^396374+73729119321Enzo Doria04/2016
332088*10^119295+3119297Robert Price05/2020
33212^396258-459491119286Enzo Doria05/2015
3322(2^396248+3126)/2119283Stefano Morozzi09/2020
33232^396128-396128-1119247Karsten Bonath06/2018
3324(28*10^119206-67)/3119207Robert Price10/2020
3325(2^395986+5)/76881119199Lelio R Paula04/2014
332611^114458+6119196Paul Bourdelais02/2021
3327(23*2^395942-1)/91119190Lelio R Paula04/2014
3328(2^395902+202)/2119179Stefano Morozzi09/2020
3329(2^395825+582)/2119155Stefano Morozzi09/2020
3330(2^395733+1130)/2119128Stefano Morozzi09/2020
333129548^10725+10725^29548119091Hans Havermann02/2021
3332(11*2^395548+1)/3119073Lelio R Paula04/2014
3333(30^80599+1)/31119054Robert Price07/2013
3334(232*10^119047+17)/3119049Robert Price04/2021
3335(43*10^119024-403)/9119025Robert Price01/2019
33366*10^118964+43118965Robert Price07/2020
3337(8*10^118960+49)/3118961Robert Price05/2020
333831253^6402+6402^31253118959Hans Havermann02/2021
3339(194*10^118925-17)/3118927Robert Price09/2020
33402^395062-109121118926Enzo Doria04/2014
33412^395055-4627118924Yves Minet05/2019
3342(2^395054+702)/2118923Stefano Morozzi09/2020
3343(2^395011+2526)/2118910Stefano Morozzi09/2020
3344(2^394918+78557)/3118882Lelio R Paula01/2015
3345(2^394858+1018)/2118864Stefano Morozzi09/2020
3346(16*10^118852+77)/3118853Robert Price03/2019
3347(2^394739+3)/1883118826Lelio R Paula04/2014
334810^118772+163599118773Patrick De Geest02/2021
335010^118772-40000000001118772Robert Price09/2020
334910^118772-207603118772Patrick De Geest02/2021
335126842^26577+26577^26842118763Hans Havermann02/2021
3352(2^394513+2034)/2118760Stefano Morozzi09/2020
3353(2^394473+2774)/2118748Stefano Morozzi02/2021
335427949^17710+17710^27949118734Hans Havermann02/2021
33552^394266+71389118686Enzo Doria04/2016
33562^394215-51261118671Tony Prest / Never Odd Or Even04/2018
3357(2^394215-48793)/5/5118670Tony Prest / Never Odd Or Even04/2018
3358(2^394215-17063)/3/3/5118669Tony Prest / Never Odd Or Even04/2018
3359(2^394215-24393)/5/5/5/5/5118668Tony Prest / Never Odd Or Even04/2018
3360(2^394215-35885)/3/71/173118666Tony Prest / Never Odd Or Even04/2018
3361(2^394215-47925)/353/2269118665Tony Prest / Never Odd Or Even04/2018
336229201^11568+11568^29201118652Hans Havermann02/2021
3363(2^394215-62819)/3/3/3/3/3/3/3/7/21737/1082153/1953673118650Tony Prest / Never Odd Or Even04/2018
3364(2^394131+2214)/2118645Stefano Morozzi09/2020
3365(17*10^118635+13)/3118636Robert Price01/2019
33665^169727+2118635Lelio R Paula08/2013
33672^394034-3118617M. Frind & P. Underwood09/2002
3368(7*10^118607+179)/3118608Robert Price09/2018
33693^248572-6242118599Enzo Doria05/2014
3370(3*2^393964-1)/181118594Lelio R Paula04/2014
33717^140303-6118570Robert Price11/2014
3372(2^393864+2686)/2118565Stefano Morozzi09/2020
3373(2^393862+3150)/2118564Stefano Morozzi09/2020
3374(2^393849+3762)/2118561Stefano Morozzi01/2021
3375(2^393661+2666)/2118504Stefano Morozzi09/2020
3376(2^393650+1614)/2118501Stefano Morozzi09/2020
337727655^19264+19264^27655118495Hans Havermann02/2021
337810^118485-50001118485Robert Price08/2020
3379(2^393528+1030)/2118464Stefano Morozzi09/2020
33802^393427+75683118434Enzo Doria04/2016
33812^393376-114749118418Enzo Doria04/2015
338230960^6671+6671^30960118397Hans Havermann02/2021
3383(2^393234+2010)/2118375Stefano Morozzi09/2020
3384(2^393205+3030)/2118367Stefano Morozzi09/2020
3385(2^393191+2174)/2118362Stefano Morozzi09/2020
33862^393180+73118359Lelio R Paula04/2013
338727546^19771+19771^27546118339Hans Havermann02/2021
3388p(23881)#/2+256118328Robert Price05/2017
3389(10^118324+359)/9118324Serge Batalov12/2014
3390(2^393048+570)/2118319Stefano Morozzi09/2020
3391p(23879)#/2+64118317Robert Price03/2017
3392(238*10^118265-1)/3118267Robert Price04/2020
3394(53*10^118216+1)/9118217Serge Batalov11/2010
3393(2^392707+1710)/2118217Stefano Morozzi09/2020
3395(7*2^392697+1)/15118214Renaud Lifchitz03/2011
3396(157^53819-1)/156118179Alexander Zhirkov06/2016
3397(2^392567+2750)/2118175Stefano Morozzi01/2021
3398(19*2^392551+1)/3118171Lelio R Paula04/2014
339927185^22222+22222^27185118168Hans Havermann01/2021
34002^392516-29219118160Enzo Doria07/2015
340166*10^118155+7118157Robert Price07/2020
3402Phi(177231,10)118152Maksym Voznyy09/2015
34032^392413-112123118129Enzo Doria06/2014
340427491^19798+19798^27491118119Hans Havermann02/2021
3405(2^392342+5)/27118106Lelio R Paula04/2014
3406(2^392333+1782)/2118104Stefano Morozzi01/2021
34072^392300-1841429118095Enzo Doria06/2015
34082^392220+75241118070Enzo Doria04/2016
340927836^17409+17409^27836118047Hans Havermann02/2021
341010^118009+664447118010Patrick De Geest07/2018
341110^118009-20001118009Robert Price01/2018
3412(14*10^117991+61)/3117992Robert Price12/2018
34132^391933+5897117984Yves Minet02/2011
34142^391912-1849259117978Enzo Doria08/2015
341528357^14440+14440^28357117953Hans Havermann02/2021
3416(2^391812+5)/14181117944Lelio R Paula04/2014
3417(7*10^117930-79)/9117930Robert Price01/2021
341827531^19168+19168^27531117904Hans Havermann02/2021
3419(46*10^117902+683)/9117903Robert Price03/2019
342027670^18189+18189^27670117869Hans Havermann02/2021
3421(7*2^391521+1)/285117858Lelio R Paula04/2014
342232169^4606+4606^32169117846Hans Havermann02/2021
34232^391324+90901117801Yves Minet02/2011
34242^391301-1859923117794Enzo Doria03/2016
34252^391261-4131117782Yves Minet02/2018
3426(2^391211+554)/2117766Stefano Morozzi09/2020
342738434^1157+1157^38434117737Hans Havermann01/2021
3428(2^391115-7)/11791117734Lelio R Paula04/2014
3429(85*10^117719+473)/9117720Robert Price01/2020
3430(2^391049+582)/2117718Stefano Morozzi09/2020
343131083^6122+6122^31083117709Hans Havermann02/2021
34322^390960+1880881117691Enzo Doria11/2016
34332^390897-1860553117672Enzo Doria11/2015
34342^390889-115003117670Enzo Doria06/2015
34352^390779-30337117637Paul Bourdelais02/2012
3436(2^390735+378)/2117623Stefano Morozzi02/2021
343711^112916-780117590Enzo Doria12/2012
343827641^17916+17916^27641117564Hans Havermann02/2021
343927906^16321+16321^27906117561Hans Havermann02/2021
344027294^20275+20275^27294117555Hans Havermann02/2021
3441(2^390473+1002)/2117544Stefano Morozzi09/2020
344235912^1875+1875^35912117541Hans Havermann02/2021
3443(16^97613-5^97613)/11117537Robert Price07/2013
3444(2^390438+1774)/2117534Stefano Morozzi01/2021
3445(2^390418+1722)/2117528Stefano Morozzi09/2020
3446(2^390403+654)/2117523Stefano Morozzi09/2020
3447(2^390343+2246)/2117505Stefano Morozzi01/2021
344828043^15478+15478^28043117493Hans Havermann02/2021
3449(17*2^390272+1)/1983117482Lelio R Paula04/2014
345037077^1474+1474^37077117479Hans Havermann01/2021
345131^78759-30117459Theodore Burton02/2007
3452(2^390176+1222)/2117455Stefano Morozzi09/2020
3453(2^390133+1242)/2117442Stefano Morozzi09/2020
3454(2^390013+2634)/2117406Stefano Morozzi09/2020
34553*10^117402+61117403Robert Price09/2020
34562^389998+37117402Lelio R Paula03/2013
3457(2^389977+314)/2117395Stefano Morozzi09/2020
3458(2^389921+342)/2117378Stefano Morozzi01/2021
345971830^43+43^71830117333Hans Havermann01/2021
3460(2^389768+1582)/2117332Stefano Morozzi09/2020
346133802^2951+2951^33802117292Hans Havermann02/2021
346226789^23866+23866^26789117277Hans Havermann02/2021
346329^80192-1*80192^29117273Dylan Delgado12/2019
3464(13*10^117249+161)/3117250Robert Price11/2018
34652^389478+43117245Lelio R Paula03/2013
3466(298*10^117229-7)/3117231Robert Price06/2020
3467(2^389416+342)/2117226Stefano Morozzi01/2021
3468(29*2^389351-1)/9117207Lelio R Paula04/2014
34695*10^117205+23117206Robert Price03/2019
3470(2^389341-7)/3865117200Lelio R Paula03/2014
347127272^19827+19827^27272117195Hans Havermann01/2021
3472(2^389276+2650)/2117184Stefano Morozzi09/2020
347310^117142+209223117143Patrick De Geest04/2018
347510^117142-1000000001117142Robert Price03/2018
347410^117142-966057117142Patrick De Geest04/2018
347610^117135+360577117136Patrick De Geest07/2018
347710^117135-401117135Robert Price01/2018
34784*10^117123+79117124Robert Price08/2018
34792^389033-12797413117111Enzo Doria04/2016
3480(2^388987+2634)/2117097Stefano Morozzi09/2020
34812^388960-109505117089Enzo Doria04/2014
34827*10^117082-57117083Robert Price06/2020
3483(2^388928-5)/569117077Lelio R Paula03/2014
34842^388888-1529117067Yves Minet01/2013
348510^117059+28879117060Patrick De Geest05/2016
3486(10^117059-71)/1117059Serge Batalov12/2014
3487(2^388854+3630)/2117057Stefano Morozzi09/2020
3488(2^388842+2098)/2117053Stefano Morozzi09/2020
3489(2^388789+3150)/2117037Stefano Morozzi09/2020
3490(2^388748+378)/2117025Stefano Morozzi02/2021
3491(693^41189-1)/692117005Michael Stocker05/2020
3492(26*10^116999-503)/9117000Robert Price07/2018
3493(2^388609+1554)/2116983Stefano Morozzi09/2020
349438496^1093+1093^38496116975Hans Havermann02/2021
34953^245154-6256116969Enzo Doria05/2014
34965*10^116966-43116967Robert Price01/2019
34972^388536-113495116961Enzo Doria08/2014
3498(2^388512+382)/2116954Stefano Morozzi02/2021
34992^388469-43116941Lelio R Paula03/2013
350027417^18416+18416^27417116939Hans Havermann02/2021


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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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