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 ?
950119857^4928+4928^1985773326Hans Havermann12/2019
95022*5^104888-773314Lelio R Paula10/2014
9503(58695*2^243516-1)/98373308Lelio R Paula04/2015
9504(3^153648-2)/3342313809773299Lelio R Paula06/2012
9505(2^243467+470)/273291Stefano Morozzi01/2020
9506(2^243460+2410)/273289Stefano Morozzi01/2020
950718^58376-525573278Enzo Doria03/2013
950811^70363+3273276Lelio R Paula02/2015
95092^243413+425773275Lelio R Paula05/2013
9510104824^5+5^10482473269Andrey Kulsha07/2010
95117^86689-6^8668973261Predrag Minovic09/2004
9512(2^243355+3846)/273257Stefano Morozzi01/2020
9513(15954^17431-1)/1595373257Serge Batalov08/2020
95142^243296+9019573240Lelio R Paula05/2013
95152^243281-484373235Yves Minet05/2019
9517p(15433)#/2-473218Robert Price12/2016
9516(59*10^73217-77)/973218Robert Price11/2017
9518(18160^17191-1)/1815973215Serge Batalov08/2020
95192*10^73199+2373200Robert Price12/2020
95202^243127+7135573189Lelio R Paula05/2013
95212^243116-24941973186Paul Bourdelais03/2013
9522(58695*2^243085-1)/1173180Lelio R Paula04/2015
9523(2^243084+3406)/273176Stefano Morozzi01/2020
952411^70262-9873171Lelio R Paula02/2015
9525(2^243034+47)/72270330373152Lelio R Paula07/2012
9526(2^242966+47)/4688773136Lelio R Paula07/2012
9527(43^44773-1)/4273134Robert Price04/2014
95286^93980-15835973131Mike Oakes02/2011
952919953^4616+4616^1995373114Hans Havermann11/2019
9530(2^242855+2546)/273107Stefano Morozzi01/2020
9531(2^242845+3926)/273104Stefano Morozzi01/2020
95326^93915+5373081Lelio R Paula01/2015
9533(5*10^73079+211)/973079Robert Price12/2017
9534(74*10^73076+43)/973077Robert Price10/2015
9535(3^153125+2)/114495573054Lelio R Paula06/2012
95362^242632-11219973040Enzo Doria06/2014
9537V(351646)73029Serge Batalov03/2015
9538(2^242598+1090)/273029Stefano Morozzi01/2020
953918^58175-8573026Lelio R Paula01/2015
9540p(15395)#/2-473019Robert Price12/2016
9541(4^121271+3^121271)/773012Jean-Louis Charton03/2011
95428*6^93825-573011Lelio R Paula10/2014
9543(28123^16411-1)/2812273010Serge Batalov08/2020
954419090^6673+6673^1909073007Hans Havermann11/2019
9546(F(220)^1601-F(219)^1601)/F(218)73005Wayne Halsdorf08/2013
9545(73^39181+1)/7473005Paul Bourdelais08/2017
95476^93815+14373003Lelio R Paula01/2015
95496^93812+573000Wojciech Florek03/2006
954817874^12137+12137^1787473000Hans Havermann11/2019
955019^57078-6272989Lelio R Paula01/2015
9551(29*10^72985+91)/372986Robert Price03/2016
955220691^3368+3368^2069172985Hans Havermann10/2019
9553(2^242451+558)/272985Stefano Morozzi01/2020
955411^70082-252072983Enzo Doria12/2012
9555(2^242429+2142)/272979Stefano Morozzi01/2020
9556(27992^16411-1)/2799172976Serge Batalov08/2020
95576^93773+13372970Lelio R Paula01/2015
9558(2^242392+3762)/272967Stefano Morozzi01/2020
95592^242328-5972948Lelio R Paula03/2012
95605^104358-1301672944Enzo Doria02/2013
9561(75*10^72941-57)/9972941Ray Chandler03/2011
956212^67585-9572937Lelio R Paula02/2015
9563(2^242261+3834)/272928Stefano Morozzi01/2020
95642^242230-11328572919Enzo Doria07/2014
9565(2^242229+2742)/272918Stefano Morozzi01/2020
9566(5*10^72916-11)/372917Erik Branger12/2013
95672^242220-11039972916Enzo Doria05/2014
95682^242205-11341372911Enzo Doria07/2014
9569(3^152809+3^76405+1)/772908Serge Batalov03/2014
95702^242175+7424372902Yves Minet03/2011
9571(2^242168+3406)/272900Stefano Morozzi01/2020
95722^242150+1765972895Lelio R Paula11/2009
957318902^7179+7179^1890272888Hans Havermann11/2019
9574(17366^17191-1)/1736572881Serge Batalov08/2020
957511^69982-234072879Enzo Doria12/2012
9576(23*2^242093+1)/1011772875Lelio R Paula08/2012
9577(67607*2^242043+1)/3326372863Lelio R Paula06/2014
95782^242032+8772859Lelio R Paula03/2012
9579(194*10^72852-17)/372854Robert Price09/2020
9580(2^241983+2690)/272844Stefano Morozzi01/2020
95822^241968-11059572840Enzo Doria05/2014
9581(2^241968+598)/272840Stefano Morozzi01/2020
958318850^7313+7313^1885072839Hans Havermann11/2019
9584(2^241921+3290)/272826Stefano Morozzi01/2020
9585(10^72821+71)/972821Robert Price11/2014
95862^241852-6487572805Lelio R Paula05/2013
9587F(348307)/2056289086590809372776Donovan Johnson07/2007
958813952^17559+17559^1395272776Norbert Schneider09/2019
9589(67*10^72772+23)/972773Ray Chandler11/2010
9590(8*10^72759+67)/372760Robert Price01/2017
95912^241670+14572750Lelio R Paula03/2012
95925^104074+5272745Lelio R Paula08/2014
9593(3^152466-5)/72472742Lelio R Paula06/2012
959420^55908-4172738Lelio R Paula01/2015
9595(73*10^72735+53)/972736Robert Price10/2015
959610^72730+22401172731Patrick De Geest05/2013
959710^72730-9972730Robert Price05/2011
95983*10^72723+6772724Robert Price11/2017
9600(11^69833+3^69833)/1472723Robert Price03/2013
9599(10^72723-79)/372723Robert Price10/2017
960118706^7719+7719^1870672721Hans Havermann11/2019
9602(88*10^72711-43)/972712Robert Price11/2015
96033^152379+28072704Lelio R Paula01/2015
9605(25*10^72703-241)/972704Robert Price01/2017
9604(2^241517+3774)/272704Stefano Morozzi01/2020
9606(2^241515+3518)/272703Stefano Morozzi01/2020
9607(47*10^72696+133)/972697Robert Price04/2017
960817^59077-9072692Lelio R Paula01/2015
960965^40096+5872691Lelio R Paula01/2016
9610(29*2^241446-1)/24572682Lelio R Paula01/2014
961211^69783-3840000072672Enzo Doria01/2013
96112^241409-11290372672Enzo Doria06/2014
961318895^7014+7014^1889572670Hans Havermann11/2019
9614(3^152287+1)/472659Paul Bourdelais04/2008
9615(2^241353+3186)/272655Stefano Morozzi01/2020
961617638^13137+13137^1763872643Hans Havermann11/2019
96173^152249-5672642Lelio R Paula01/2015
961810^72631+3772632Robert Price01/2011
961910^72631-881372631Patrick De Geest05/2013
9620(19*2^241254+1)/10172624Lelio R Paula08/2012
9621(32202^16111-1)/3220172622Serge Batalov08/2020
9622(9^76103+8^76103)/1772620Robert Price12/2012
96242^241220-11233772615Enzo Doria06/2014
96237*10^72614+3372615Robert Price06/2020
9625(82*10^72612+449)/972613Robert Price02/2017
96262^241169-1579372600Enzo Doria04/2013
96279*10^72595+1172596Robert Kinser01/2017
9628(2^241152+2478)/272594Stefano Morozzi01/2020
9629(2^241143+2438)/272591Stefano Morozzi01/2020
9630(2^241115+1598)/272583Stefano Morozzi01/2020
9631(1003^24179-1)/100272566Serge Batalov07/2020
9632(25*2^241048+1)/8972563Lelio R Paula08/2012
9633(2^241045+1550)/272562Stefano Morozzi01/2020
9634(22*10^72560+17)/372561Robert Price09/2015
96352^241032-2372558Lelio R Paula02/2012
963634485*10^72550+2^241004-372555Gilbert Mozzo12/2012
963719460^5349+5349^1946072553Hans Havermann11/2019
9638(2^241016+3850)/272553Stefano Morozzi01/2020
96392^241004-372550M. Frind & P. Underwood07/2002
964022061^1942+1942^2206172543Hans Havermann11/2019
96419*10^72528-8972529Robert Price04/2020
964397*10^72522-372524Robert Price01/2017
9642(29*10^72523-107)/372524Robert Price08/2020
9644(68*10^72516+7)/372518Robert Price03/2016
9645(13993^17491-1)/1399272512Serge Batalov08/2020
9646(78557*2^240844+1)/6372505Lelio R Paula06/2014
964767^39701-6672497Norbert Schneider11/2014
9648(185*10^72484+7)/372486Robert Price02/2017
9649(2^240780+2686)/272482Stefano Morozzi01/2020
9650(2^240759+1106)/272476Stefano Morozzi01/2020
9652(293*27^50631-1736)/1372473Curtis Bright05/2015
9651103^36005-10272473Norbert Schneider10/2016
965315^61616+8872467Lelio R Paula01/2015
965445^43831+272462Lelio R Paula05/2013
96552^240692-49238972456Paul Bourdelais03/2013
9656(646*10^72446-7)/972448Robert Price07/2016
96579*6^93083+772434Lelio R Paula10/2014
96582^240617-364572433Lelio R Paula05/2013
9659(9391^18229-1)/939072415Serge Batalov08/2020
966011^69531-2400072410Enzo Doria12/2012
9661(259*10^72400-1)/372402Robert Price12/2020
966218714^7367+7367^1871472373Hans Havermann11/2019
9663(22699*2^240396+1)/5572370Lelio R Paula06/2014
96646^92995+1372365Lelio R Paula01/2015
9665(11*10^72362-149)/372363Robert Price01/2017
966618567^7892+7892^1856772360Hans Havermann11/2019
9667(2^240381+3)/5165572358Lelio R Paula05/2012
96686^92974-5572348Lelio R Paula01/2015
96692^240295+1172337Lelio R Paula02/2012
9670(2^240294+1342)/272336Stefano Morozzi01/2020
9671(14*10^72326-53)/372327Robert Price12/2016
967215^61493-4672322Lelio R Paula01/2015
9673(2^240245+2094)/272321Stefano Morozzi01/2020
9674(2^240237+1554)/272319Stefano Morozzi01/2020
9675lucasU(46,1,43497)-lucasU(46,1,43496)72315Mike Oakes04/2009
9676(2^240211+1514)/272311Stefano Morozzi01/2020
96785*10^72302+972303Dmitry Domanov11/2010
9677(9787*2^240179-1)/26572303Lelio R Paula04/2015
9679(2^240171+3246)/272299Stefano Morozzi01/2020
968011^69419-312072293Enzo Doria12/2012
968118069^10016+10016^1806972289Hans Havermann11/2019
9682(25883^16381-1)/2588272286Serge Batalov08/2020
9683(2^240095+594)/272276Stefano Morozzi01/2020
9684(25848^16381-1)/2584772276Serge Batalov08/2020
96854*10^72274-8372275Robert Price10/2017
9686(2^240075+2790)/272270Stefano Morozzi01/2020
968710^72267+3372268Robert Price01/2011
968810^72267-55394772267Patrick De Geest05/2013
9689(2^240066+1030)/272267Stefano Morozzi01/2020
969111^69389-138072262Enzo Doria12/2012
9692(16^60013-5^60013)/1172262Robert Price07/2013
96907^85507-3072262Lelio R Paula08/2014
9693(19*2^240026-1)/1572256Lelio R Paula02/2014
9694(3^151426-2)/66133772243Lelio R Paula06/2012
9695(2^239940+3850)/272229Stefano Morozzi01/2020
9696gcd(V(1296375),5*F(259275)*(F(259275)-1)+1)72227Serge Batalov04/2015
9697(2789^20959-1)/278872210Serge Batalov08/2020
96982^239863-11226772206Enzo Doria06/2014
96992^239853-11485372203Enzo Doria05/2015
9700(14068^17401-1)/1406772180Serge Batalov08/2020
9701(5669^19231-1)/566872180Serge Batalov08/2020
9702(4*10^72174+149)/972174Robert Price03/2017
97034*10^72166+6772167Robert Price01/2021
9705(2^239671+9)/29613172143Lelio R Paula05/2012
97042^239651-11066572143Enzo Doria05/2014
9706(29*2^239650-1)/330572140Lelio R Paula01/2014
9707(17099^17041-1)/1709872130Serge Batalov08/2020
9709241^30280+30280^24172128Norbert Schneider11/2014
9708(2^239603+950)/272128Stefano Morozzi01/2020
9710(2^239594+3058)/272125Stefano Morozzi01/2020
9711(68*10^72120-23)/972121Robert Price10/2015
9712(9^75571+8^75571)/1772112Robert Price12/2012
9713(15661^17191-1)/1566072109Serge Batalov08/2020
9714(3508^20341-1)/350772107Serge Batalov08/2020
9715(15*2^239530-1)/17372105Lelio R Paula01/2014
9716(2^239523+2378)/272104Stefano Morozzi01/2020
97172^239513-11251972101Enzo Doria06/2014
9718(10^72097+149)/372097Serge Batalov12/2014
97192^239442-655572080Lelio R Paula05/2012
97202*5^103106+372069Lelio R Paula10/2014
97212^239402-19772068Lelio R Paula02/2012
97222^239356-11187572054Enzo Doria05/2014
9723(38*10^72050-119)/972051Robert Price11/2016
97242^239339+1501572049Lelio R Paula01/2013
9725159^32728+272048Lelio R Paula05/2013
972615^61259-3872047Lelio R Paula01/2015
972792^36683-91^3668372038Robert Price08/2015
97282^239280+5461572031Lelio R Paula05/2012
9729(47*2^239267+1)/7772027Lelio R Paula04/2015
9730(85*10^72025-1)/372027Robert Price07/2017
9731(2^239269+1730)/272027Stefano Morozzi01/2020
97322^239236-9730572018Lelio R Paula05/2012
9734144^33361-14372006Norbert Schneider11/2018
9733(2^239198+1422)/272006Stefano Morozzi01/2020
97352^239169+5971998Lelio R Paula02/2012
9736lucasU(2010,1,21796)-lucasU(2010,1,21795)71994Mike Oakes05/2009
9737(15*2^239171-1)/10630171994Lelio R Paula01/2014
9738(2^239121+1926)/271983Stefano Morozzi01/2020
9740(29^49211-1)/2871965Robert Price04/2012
9739(299*10^71963+1)/371965Robert Price11/2017
9741(58729^15091-1)/5872871962Anonymous11/2020
9743L(344293)71953Renaud Lifchitz09/2003
9742V(344293)71953Serge Batalov03/2015
97446*10^71951+771952Dmitry Domanov11/2010
97453^150798+4071949Lelio R Paula01/2015
97462^238961+9571935Lelio R Paula02/2012
974712511^17556+17556^1251171933Norbert Schneider09/2019
97482^238936-40771927Yves Minet02/2012
9749(2^238930+2982)/271925Stefano Morozzi01/2020
97502^238923-2863571923Lelio R Paula05/2012


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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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