PRP Records

Probable Primes Top 10000

(271023 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 ?
450176^53332-75100308Norbert Schneider02/2015
45026^128892-17573100298Enzo Doria03/2013
4503(47*10^100283-119)/9100284Robert Price05/2019
45042^333105-113215100275Enzo Doria07/2014
4505(31*2^333102+1)/2375100272Lelio R Paula11/2013
45064*10^100257-83100258Robert Price10/2018
450717^81476-74100253Lelio R Paula10/2016
450823392^19207+19207^23392100199Hans Havermann06/2018
4509(2^332830+750)/2100192Stefano Morozzi09/2020
4510(206*10^100189-17)/9100191Robert Price01/2020
451117^81417-16100180Theodore Burton11/2005
4512(2^332773+590)/2100175Stefano Morozzi09/2020
45132^332739-113215100165Enzo Doria07/2014
45142^332730-1865621100162Enzo Doria03/2016
451591^51127-2100160Lelio R Paula09/2013
451615^85159-32100155Lelio R Paula10/2016
45176^128661+97100118Lelio R Paula10/2016
451819^78285+40100108Lelio R Paula07/2016
45196^128640+5100102Lelio R Paula11/2014
452022779^22970-22970^22779100093Norbert Schneider08/2020
4521(2^332468+3130)/2100083Stefano Morozzi09/2020
4522(14*10^100075+61)/3100076Robert Price12/2018
4523(2^332435+3098)/2100073Stefano Morozzi09/2020
452428562^3189+3189^28562100072Hans Havermann05/2018
45256^128565-127100044Lelio R Paula08/2016
4526(2^332317+2106)/2100038Stefano Morozzi09/2020
45272^332309-133100035Lelio R Paula02/2011
45282^332307+731100035Lelio R Paula07/2011
45292^332301+12927100033Lelio R Paula04/2013
453023406^18781+18781^23406100031Hans Havermann04/2018
45312^332277-4573100026Yves Minet03/2019
453212^92684-13100023Lelio R Paula07/2016
453378557*2^332193+55669100005Jorge Menendez04/2019
453478557*2^332192+72689100005Jorge Menendez04/2019
453510^100003+45799100004Stefano Morozzi04/2019
453610^100003+155461100004Stefano Morozzi04/2019
453710^100003+211389100004Stefano Morozzi04/2019
453810^100003+381027100004Stefano Morozzi04/2019
453910^100003+540703100004Stefano Morozzi04/2019
454010^100003+823977100004Stefano Morozzi04/2019
455210^100002+236023100003Stefano Morozzi05/2018
455310^100002+433741100003Stefano Morozzi05/2018
45412^332202+104659100003Stefano Morozzi04/2019
45422^332202+857539100003Stefano Morozzi04/2019
45432^332202+181773100003Stefano Morozzi04/2019
45442^332202+687543100003Stefano Morozzi04/2019
45452^332202+941595100003Stefano Morozzi04/2019
45462^332202+445813100003Stefano Morozzi04/2019
45472^332202+1599727100003Stefano Morozzi04/2019
45482^332202+1389567100003Stefano Morozzi04/2019
45492^332202+1206315100003Stefano Morozzi04/2019
45502^332202+1958647100003Stefano Morozzi04/2019
455110^100003-562857100003Patrick De Geest07/2019
4554(10^100002-1)/9-10^33441100002Akihiko Yoshida03/2018
4555(10^100002-1)/9-10^44692100002Akihiko Yoshida03/2018
455610^100002-249519100002Patrick De Geest07/2018
455710^100001+314199100002Patrick De Geest07/2018
464125206!+p(4114)100001Henri Lifchitz09/2005
464225206!-p(5447)100001Henri Lifchitz10/2005
464325206!-p(12402)100001Henri Lifchitz04/2006
464425206!-p(16290)100001Henri Lifchitz09/2006
464525206!-p(19647)100001Henri Lifchitz02/2007
46462^332194+11473100001Henri Lifchitz03/2007
463610^100000+342909100001Milton L. Brown12/2007
463710^100000+346579100001Robert Price04/2012
463810^100000+829767100001Robert Price05/2012
463910^100000+871899100001Robert Price05/2012
464010^100000+1475997100001Robert Price07/2012
462910^100000+1751769100001Robert Price08/2012
463010^100000+2155489100001Robert Price10/2012
463110^100000+2483527100001Robert Price12/2012
463210^100000+2503087100001Robert Price12/2012
463310^100000+2686179100001Robert Price12/2012
463410^100000+2688933100001Robert Price12/2012
463510^100000+3667159100001Robert Price08/2013
457410^100000+3938473100001Robert Price05/2015
457510^100000+3979761100001Robert Price05/2015
457610^100000+4293973100001Robert Price09/2015
459510^100000+4858267100001Robert Price12/2015
459610^100000+5113299100001Robert Price02/2016
459710^100000+5169411100001Robert Price02/2016
459810^100000+5354043100001Robert Price05/2016
459910^100000+5717979100001Robert Price05/2016
460010^100000+6080631100001Robert Price07/2016
460110^100000+6308469100001Robert Price07/2016
460210^100000+6512023100001Robert Price08/2016
460310^100000+6596557100001Robert Price08/2016
460410^100000+7115409100001Robert Price10/2016
460510^100000+7235803100001Robert Price10/2016
458210^100000+7867333100001Robert Price12/2016
458310^100000+8743093100001Robert Price02/2017
458410^100000+8955391100001Robert Price03/2017
458510^100000+9180019100001Robert Price03/2017
458610^100000+9225987100001Robert Price04/2017
458710^100000+9265587100001Robert Price04/2017
458810^100000+9287049100001Robert Price04/2017
458910^100000+9425053100001Robert Price05/2017
459010^100000+9450769100001Robert Price05/2017
459110^100000+9528747100001Robert Smith05/2017
459210^100000+9548071100001Robert Price06/2017
459310^100000+10064287100001Robert Price08/2017
459410^100000+10229569100001Robert Price10/2017
455810^100000+11187931100001Robert Price03/2018
455910^100000+11264721100001Robert Price04/2018
456010^100000+11477661100001Robert Price05/2018
456110^100000+11644653100001Robert Price07/2018
456210^100001-431439100001Patrick De Geest07/2018
456310^100000+11769399100001Robert Price08/2018
456410^100000+11848159100001Robert Price08/2018
456510^100000+11863467100001Robert Price08/2018
462610^100000+11992051100001Robert Price09/2018
46272^332196-1-2*29696100001Matt Stath11/2018
462810^100000+12363957100001Robert Price11/2018
45662^332196+1+2*17152100001Matt Stath12/2018
456710^100000+12778033100001Robert Price02/2019
456810^100000+13581679100001Robert Price05/2019
456910^100000+13613199100001Robert Price05/2019
457010^100000+13752327100001Robert Price05/2019
457110^100000+14139243100001Robert Price06/2019
457210^100000+14151057100001Robert Price06/2019
457310^100000+14218923100001Robert Price06/2019
460610^100000+15136771100001Robert Price09/2019
460710^100000+15219873100001Robert Price10/2019
460810^100000+15274039100001Robert Price10/2019
460910^100000+15394069100001Robert Price10/2019
461010^100000+15547119100001Robert Price10/2019
461110^100000+15932923100001Robert Price11/2019
461210^100000+16345467100001Robert Price12/2019
461310^100000+16672143100001Robert Price01/2020
461410^100000+16731939100001Robert Price02/2020
461510^100000+16907049100001Robert Price03/2020
461610^100000+17652523100001Robert Price05/2020
461710^100000+18047167100001Robert Price05/2020
461810^100000+18471819100001Robert Price06/2020
461910^100000+18494793100001Robert Price07/2020
462010^100000+18762609100001Robert Price07/2020
462110^100000+19204141100001Robert Price08/2020
462210^100000+19349793100001Robert Price08/2020
462310^100000+19495699100001Robert Price09/2020
462410^100000+19668927100001Robert Price09/2020
462510^100000+19704313100001Robert Price09/2020
458110^100000+19956229100001Robert Price09/2020
457810^100000+3*(10^37093-1)/9*10^31454+1100001Makoto Morimoto09/2020
458010^100000+4*(10^36149-1)/9*10^31926+1100001Makoto Morimoto09/2020
457910^100000+6*(10^41029-1)/9*10^29486+1100001Makoto Morimoto09/2020
457710^100000+7*(10^55505-1)/9*10^22248+1100001Makoto Morimoto09/2020
464710^99999+309403100000Daniel Heuer01/2004
464810^100000-260199100000Patrick De Geest01/2010
464910^99999-5951199999Patrick De Geest07/2009
465010^99998+23543799999Patrick De Geest02/2020
465110^99998-28658799998Patrick De Geest02/2020
465210^99997+7229799998Patrick De Geest02/2020
465310^99997-40262799997Patrick De Geest02/2020
465410^99996+27985399997Patrick De Geest02/2020
465510^99996-9496199996Patrick De Geest02/2020
465610^99995+5463399996Patrick De Geest02/2020
465710^99995-10142999995Patrick De Geest02/2020
465810^99994+11727199995Patrick De Geest02/2020
465910^99994-45228999994Patrick De Geest02/2020
466010^99993+37131199994Patrick De Geest02/2020
466110^99993-18649199993Patrick De Geest02/2020
466210^99992+1743199993Patrick De Geest02/2020
466310^99992-2860799992Patrick De Geest02/2020
466410^99991+12539199992Patrick De Geest02/2020
466510^99991-20457399991Patrick De Geest02/2020
466610^99990+1389999991Patrick De Geest02/2020
466710^99990-811199990Patrick De Geest02/2020
46682^332141-11307399985Enzo Doria07/2014
4670(3^209561+2)/72810125599978Lelio R Paula09/2013
466923827^15702+15702^2382799978Hans Havermann04/2018
46712^332085+186589799968Enzo Doria03/2016
4672(9787*2^332070-1)/93640236999959Lelio R Paula05/2015
46732^332023+19199949Lelio R Paula02/2011
46742^331938+7114999924Enzo Doria04/2016
46752^331932-7879599922Lelio R Paula09/2016
46762^331921+77199919Lelio R Paula01/2013
4677(3^209419-2)/513275599912Lelio R Paula09/2013
46782^331860-11498999900Enzo Doria05/2015
46792^331746-1165599866Lelio R Paula09/2016
468011^95891-2899861Lelio R Paula08/2016
4681(2^331694-5)/1199849Lelio R Paula10/2013
4682(3^209246+7)/6499834Lelio R Paula09/2013
468325062^9617+9617^2506299823Hans Havermann04/2018
468415^84866-5299811Lelio R Paula08/2016
468513^89600+3099810Lelio R Paula08/2016
468622950^22309+22309^2295099798Hans Havermann03/2018
46875^142772-3899794Lelio R Paula08/2016
4688(23*2^331459+1)/47599778Lelio R Paula11/2013
46892^331416-331416+199767Robert Price10/2014
46902^331256-5799718Lelio R Paula12/2012
469128192^3443+3443^2819299714Hans Havermann03/2018
46922^331185+73799697Lelio R Paula01/2013
4693(4*10^99693+149)/999693Robert Price03/2017
46942^331154+188052799688Enzo Doria10/2016
4696(19^77951+1)/2099679Paul Bourdelais03/2010
469524354^12385+12385^2435499679Hans Havermann03/2018
46972^331110+187045999675Enzo Doria05/2016
46985*2^331075+799665Lelio R Paula08/2014
469925776^7351+7351^2577699659Hans Havermann02/2018
4700(16*10^99656-31)/399657Robert Price03/2016
47022^330968+34599632Lelio R Paula09/2016
4701(2^330969+690)/299632Stefano Morozzi09/2020
47042*5^142528-799624Lelio R Paula11/2014
47032^330942+7732999624Enzo Doria05/2016
470514^86914-9999615Lelio R Paula08/2016
4706(19*2^330902+1)/7799611Lelio R Paula11/2013
470722971^21692+21692^2297199610Hans Havermann03/2018
47082^330845+7168799595Enzo Doria04/2016
4709(23*2^330770+1)/399573Lelio R Paula11/2013
471024494^11613+11613^2449499567Hans Havermann03/2018
47112^330735+841599562Lelio R Paula09/2016
47122^330720+7407199557Enzo Doria04/2016
471331^66738-299531Lelio R Paula09/2013
47147*3^208567+499513Lelio R Paula08/2014
4715(13*10^99508+47)/399509Robert Price01/2017
47162^330553+77999507Lelio R Paula01/2013
471715^84606-9499505Lelio R Paula08/2016
47186^127858+4799493Lelio R Paula08/2016
47195^142337+4899490Lelio R Paula08/2016
47207^117724-2099489Lelio R Paula08/2016
4721(29*10^99474-17)/399475Erik Branger09/2014
4722(2^330410+2038)/299464Stefano Morozzi09/2020
4723(9*2^330407-1)/799463Lelio R Paula03/2014
4724(2^330373+2114)/299452Stefano Morozzi09/2020
4725(68*10^99441+7)/399443Robert Price03/2016
472610^99434+15557199435Patrick De Geest04/2020
472710^99434-12345678999434Robert Price02/2020
472810^99434-19123799434Patrick De Geest04/2020
472946^59791-45^5979199418Jean-Louis Charton01/2013
473023839^14802+14802^2383999417Hans Havermann02/2018
4731(2*10^99408+529)/999408Robert Price01/2017
4732(2^330216+3510)/299405Stefano Morozzi09/2020
473353^57646-299398Lelio R Paula09/2013
47342^330165+187002599390Enzo Doria05/2016
47352^330142-15599383Lelio R Paula12/2012
47362^330088-11525999367Enzo Doria06/2015
473824216^12671+12671^2421699354Hans Havermann01/2018
4737Phi(200548,10)/320876999354Makoto Kamada04/2019
4739(746*10^99303+1)/999305Robert Price02/2017
47403^208107+4099293Lelio R Paula08/2016
4741(5*2^329833-1)/36999288Lelio R Paula02/2014
47428*3^208093+599287Lelio R Paula08/2014
47435^142043+5699284Lelio R Paula08/2016
474422*10^99275+799277Robert Price04/2016
47452^329778+187618999274Enzo Doria07/2016
4746(10^99239-13)/399239Robert Price02/2017
47473^207987+6299236Lelio R Paula08/2016
47482^329638+4999231Lelio R Paula12/2012
47497^117413-1899226Lelio R Paula08/2016
47502^329586-45890399216Enzo Doria04/2015


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: September, 30 2020 00:02 (Time in France)

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