PRP Records

Probable Primes Top 10000

(271019 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 ?
900110^73579-17637973579Patrick De Geest02/2020
90022^244404+384173573Yves Minet03/2011
900319770^5263+5263^1977073569Hans Havermann12/2019
90049*10^73565-4173566Robert Price08/2020
90052^244372-11062773564Enzo Doria05/2014
900619778^5241+5241^1977873563Hans Havermann12/2019
9007(2^244349+2186)/273557Stefano Morozzi01/2020
9008(2^244309+3710)/273545Stefano Morozzi01/2020
900918428^9783+9783^1842873537Hans Havermann01/2020
9010(3*2^244255+1)/24573527Lelio R Paula08/2012
9011(11*2^244245+1)/2373525Lelio R Paula08/2012
901218140^11301+11301^1814073524Hans Havermann12/2019
9013(15185*2^244187-1)/611173509Lelio R Paula04/2015
9014(9699^18439-1)/969873508Serge Batalov08/2020
9015(2^244152+2058)/273497Stefano Morozzi01/2020
9016(2^244109+1422)/273484Stefano Morozzi01/2020
901717063^17362+17362^1706373477Norbert Schneider04/2019
9018(91^37507+1)/9273476Paul Bourdelais08/2017
901918^58521+6573460Lelio R Paula01/2015
902013^65940+3673454Lelio R Paula01/2015
902119065^7112+7112^1906573439Hans Havermann12/2019
9022(625^26267+1)/62673437Richard Fischer12/2017
9023(16612^17401-1)/1661173436Serge Batalov08/2020
9024(2^243935+530)/273432Stefano Morozzi01/2020
90255^105050-1473427Lelio R Paula08/2014
9026(2^243850+1474)/273406Stefano Morozzi01/2020
9027(((((((((((((30201^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-273401Serge Batalov07/2016
902815^62410-4673400Lelio R Paula01/2015
9029(2^243806+2494)/273393Stefano Morozzi01/2020
9030(2^243790+2530)/273388Stefano Morozzi01/2020
9031(2^243766+2362)/273381Stefano Morozzi01/2020
90322^243733+186970773371Enzo Doria05/2016
903311^70439-543073355Enzo Doria01/2013
90342^243676-8773354Lelio R Paula03/2012
9035(101*10^73346-17)/373348Robert Price08/2016
903621639^2452+2452^2163973346Hans Havermann12/2019
9037(2^243647+2438)/273345Stefano Morozzi01/2020
90382^243621-11318573338Enzo Doria07/2014
9039(5*2^243610-1)/166973332Lelio R Paula01/2014
904019857^4928+4928^1985773326Hans Havermann12/2019
90412*5^104888-773314Lelio R Paula10/2014
9042(58695*2^243516-1)/98373308Lelio R Paula04/2015
9043(3^153648-2)/3342313809773299Lelio R Paula06/2012
9044(2^243467+470)/273291Stefano Morozzi01/2020
9045(2^243460+2410)/273289Stefano Morozzi01/2020
904618^58376-525573278Enzo Doria03/2013
904711^70363+3273276Lelio R Paula02/2015
90482^243413+425773275Lelio R Paula05/2013
9049104824^5+5^10482473269Andrey Kulsha07/2010
90507^86689-6^8668973261Predrag Minovic09/2004
9051(2^243355+3846)/273257Stefano Morozzi01/2020
9052(15954^17431-1)/1595373257Serge Batalov08/2020
90532^243296+9019573240Lelio R Paula05/2013
90542^243281-484373235Yves Minet05/2019
9056p(15433)#/2-473218Robert Price12/2016
9055(59*10^73217-77)/973218Robert Price11/2017
9057(18160^17191-1)/1815973215Serge Batalov08/2020
90582^243127+7135573189Lelio R Paula05/2013
90592^243116-24941973186Paul Bourdelais03/2013
9060(58695*2^243085-1)/1173180Lelio R Paula04/2015
9061(2^243084+3406)/273176Stefano Morozzi01/2020
906211^70262-9873171Lelio R Paula02/2015
9063(2^243034+47)/72270330373152Lelio R Paula07/2012
9064(2^242966+47)/4688773136Lelio R Paula07/2012
9065(43^44773-1)/4273134Robert Price04/2014
90666^93980-15835973131Mike Oakes02/2011
906719953^4616+4616^1995373114Hans Havermann11/2019
9068(2^242855+2546)/273107Stefano Morozzi01/2020
9069(2^242845+3926)/273104Stefano Morozzi01/2020
90706^93915+5373081Lelio R Paula01/2015
9071(5*10^73079+211)/973079Robert Price12/2017
9072(74*10^73076+43)/973077Robert Price10/2015
9073(3^153125+2)/114495573054Lelio R Paula06/2012
90742^242632-11219973040Enzo Doria06/2014
9075V(351646)73029Serge Batalov03/2015
9076(2^242598+1090)/273029Stefano Morozzi01/2020
907718^58175-8573026Lelio R Paula01/2015
9078p(15395)#/2-473019Robert Price12/2016
9079(4^121271+3^121271)/773012Jean-Louis Charton03/2011
90808*6^93825-573011Lelio R Paula10/2014
9081(28123^16411-1)/2812273010Serge Batalov08/2020
908219090^6673+6673^1909073007Hans Havermann11/2019
9084(F(220)^1601-F(219)^1601)/F(218)73005Wayne Halsdorf08/2013
9083(73^39181+1)/7473005Paul Bourdelais08/2017
90856^93815+14373003Lelio R Paula01/2015
90876^93812+573000Wojciech Florek03/2006
908617874^12137+12137^1787473000Hans Havermann11/2019
908819^57078-6272989Lelio R Paula01/2015
9089(29*10^72985+91)/372986Robert Price03/2016
909020691^3368+3368^2069172985Hans Havermann10/2019
9091(2^242451+558)/272985Stefano Morozzi01/2020
909211^70082-252072983Enzo Doria12/2012
9093(2^242429+2142)/272979Stefano Morozzi01/2020
9094(27992^16411-1)/2799172976Serge Batalov08/2020
90956^93773+13372970Lelio R Paula01/2015
9096(2^242392+3762)/272967Stefano Morozzi01/2020
90972^242328-5972948Lelio R Paula03/2012
90985^104358-1301672944Enzo Doria02/2013
9099(75*10^72941-57)/9972941Ray Chandler03/2011
910012^67585-9572937Lelio R Paula02/2015
9101(2^242261+3834)/272928Stefano Morozzi01/2020
91022^242230-11328572919Enzo Doria07/2014
9103(2^242229+2742)/272918Stefano Morozzi01/2020
9104(5*10^72916-11)/372917Erik Branger12/2013
91052^242220-11039972916Enzo Doria05/2014
91062^242205-11341372911Enzo Doria07/2014
9107(3^152809+3^76405+1)/772908Serge Batalov03/2014
91082^242175+7424372902Yves Minet03/2011
9109(2^242168+3406)/272900Stefano Morozzi01/2020
91102^242150+1765972895Lelio R Paula11/2009
911118902^7179+7179^1890272888Hans Havermann11/2019
9112(17366^17191-1)/1736572881Serge Batalov08/2020
911311^69982-234072879Enzo Doria12/2012
9114(23*2^242093+1)/1011772875Lelio R Paula08/2012
9115(67607*2^242043+1)/3326372863Lelio R Paula06/2014
91162^242032+8772859Lelio R Paula03/2012
9117(194*10^72852-17)/372854Robert Price09/2020
9118(2^241983+2690)/272844Stefano Morozzi01/2020
91202^241968-11059572840Enzo Doria05/2014
9119(2^241968+598)/272840Stefano Morozzi01/2020
912118850^7313+7313^1885072839Hans Havermann11/2019
9122(2^241921+3290)/272826Stefano Morozzi01/2020
9123(10^72821+71)/972821Robert Price11/2014
91242^241852-6487572805Lelio R Paula05/2013
9125F(348307)/2056289086590809372776Donovan Johnson07/2007
912613952^17559+17559^1395272776Norbert Schneider09/2019
9127(67*10^72772+23)/972773Ray Chandler11/2010
9128(8*10^72759+67)/372760Robert Price01/2017
91292^241670+14572750Lelio R Paula03/2012
91305^104074+5272745Lelio R Paula08/2014
9131(3^152466-5)/72472742Lelio R Paula06/2012
913220^55908-4172738Lelio R Paula01/2015
9133(73*10^72735+53)/972736Robert Price10/2015
913410^72730+22401172731Patrick De Geest05/2013
913510^72730-9972730Robert Price05/2011
91363*10^72723+6772724Robert Price11/2017
9138(11^69833+3^69833)/1472723Robert Price03/2013
9137(10^72723-79)/372723Robert Price10/2017
913918706^7719+7719^1870672721Hans Havermann11/2019
9140(88*10^72711-43)/972712Robert Price11/2015
91413^152379+28072704Lelio R Paula01/2015
9143(25*10^72703-241)/972704Robert Price01/2017
9142(2^241517+3774)/272704Stefano Morozzi01/2020
9144(2^241515+3518)/272703Stefano Morozzi01/2020
9145(47*10^72696+133)/972697Robert Price04/2017
914617^59077-9072692Lelio R Paula01/2015
914765^40096+5872691Lelio R Paula01/2016
9148(29*2^241446-1)/24572682Lelio R Paula01/2014
915011^69783-3840000072672Enzo Doria01/2013
91492^241409-11290372672Enzo Doria06/2014
915118895^7014+7014^1889572670Hans Havermann11/2019
9152(3^152287+1)/472659Paul Bourdelais04/2008
9153(2^241353+3186)/272655Stefano Morozzi01/2020
915417638^13137+13137^1763872643Hans Havermann11/2019
91553^152249-5672642Lelio R Paula01/2015
915610^72631+3772632Robert Price01/2011
915710^72631-881372631Patrick De Geest05/2013
9158(19*2^241254+1)/10172624Lelio R Paula08/2012
9159(32202^16111-1)/3220172622Serge Batalov08/2020
9160(9^76103+8^76103)/1772620Robert Price12/2012
91622^241220-11233772615Enzo Doria06/2014
91617*10^72614+3372615Robert Price06/2020
9163(82*10^72612+449)/972613Robert Price02/2017
91642^241169-1579372600Enzo Doria04/2013
91659*10^72595+1172596Robert Kinser01/2017
9166(2^241152+2478)/272594Stefano Morozzi01/2020
9167(2^241143+2438)/272591Stefano Morozzi01/2020
9168(2^241115+1598)/272583Stefano Morozzi01/2020
9169(1003^24179-1)/100272566Serge Batalov07/2020
9170(25*2^241048+1)/8972563Lelio R Paula08/2012
9171(2^241045+1550)/272562Stefano Morozzi01/2020
9172(22*10^72560+17)/372561Robert Price09/2015
91732^241032-2372558Lelio R Paula02/2012
917434485*10^72550+2^241004-372555Gilbert Mozzo12/2012
917519460^5349+5349^1946072553Hans Havermann11/2019
9176(2^241016+3850)/272553Stefano Morozzi01/2020
91772^241004-372550M. Frind & P. Underwood07/2002
917822061^1942+1942^2206172543Hans Havermann11/2019
91799*10^72528-8972529Robert Price04/2020
918197*10^72522-372524Robert Price01/2017
9180(29*10^72523-107)/372524Robert Price08/2020
9182(68*10^72516+7)/372518Robert Price03/2016
9183(13993^17491-1)/1399272512Serge Batalov08/2020
9184(78557*2^240844+1)/6372505Lelio R Paula06/2014
918567^39701-6672497Norbert Schneider11/2014
9186(185*10^72484+7)/372486Robert Price02/2017
9187(2^240780+2686)/272482Stefano Morozzi01/2020
9188(2^240759+1106)/272476Stefano Morozzi01/2020
9190(293*27^50631-1736)/1372473Curtis Bright05/2015
9189103^36005-10272473Norbert Schneider10/2016
919115^61616+8872467Lelio R Paula01/2015
919245^43831+272462Lelio R Paula05/2013
91932^240692-49238972456Paul Bourdelais03/2013
9194(646*10^72446-7)/972448Robert Price07/2016
91959*6^93083+772434Lelio R Paula10/2014
91962^240617-364572433Lelio R Paula05/2013
9197(9391^18229-1)/939072415Serge Batalov08/2020
919811^69531-2400072410Enzo Doria12/2012
919918714^7367+7367^1871472373Hans Havermann11/2019
9200(22699*2^240396+1)/5572370Lelio R Paula06/2014
92016^92995+1372365Lelio R Paula01/2015
9202(11*10^72362-149)/372363Robert Price01/2017
920318567^7892+7892^1856772360Hans Havermann11/2019
9204(2^240381+3)/5165572358Lelio R Paula05/2012
92056^92974-5572348Lelio R Paula01/2015
92062^240295+1172337Lelio R Paula02/2012
9207(2^240294+1342)/272336Stefano Morozzi01/2020
9208(14*10^72326-53)/372327Robert Price12/2016
920915^61493-4672322Lelio R Paula01/2015
9210(2^240245+2094)/272321Stefano Morozzi01/2020
9211(2^240237+1554)/272319Stefano Morozzi01/2020
9212lucasU(46,1,43497)-lucasU(46,1,43496)72315Mike Oakes04/2009
9213(2^240211+1514)/272311Stefano Morozzi01/2020
92155*10^72302+972303Dmitry Domanov11/2010
9214(9787*2^240179-1)/26572303Lelio R Paula04/2015
9216(2^240171+3246)/272299Stefano Morozzi01/2020
921711^69419-312072293Enzo Doria12/2012
921818069^10016+10016^1806972289Hans Havermann11/2019
9219(25883^16381-1)/2588272286Serge Batalov08/2020
9220(2^240095+594)/272276Stefano Morozzi01/2020
9221(25848^16381-1)/2584772276Serge Batalov08/2020
92224*10^72274-8372275Robert Price10/2017
9223(2^240075+2790)/272270Stefano Morozzi01/2020
922410^72267+3372268Robert Price01/2011
922510^72267-55394772267Patrick De Geest05/2013
9226(2^240066+1030)/272267Stefano Morozzi01/2020
922811^69389-138072262Enzo Doria12/2012
9229(16^60013-5^60013)/1172262Robert Price07/2013
92277^85507-3072262Lelio R Paula08/2014
9230(19*2^240026-1)/1572256Lelio R Paula02/2014
9231(3^151426-2)/66133772243Lelio R Paula06/2012
9232(2^239940+3850)/272229Stefano Morozzi01/2020
9233gcd(V(1296375),5*F(259275)*(F(259275)-1)+1)72227Serge Batalov04/2015
9234(2789^20959-1)/278872210Serge Batalov08/2020
92352^239863-11226772206Enzo Doria06/2014
92362^239853-11485372203Enzo Doria05/2015
9237(14068^17401-1)/1406772180Serge Batalov08/2020
9238(5669^19231-1)/566872180Serge Batalov08/2020
9239(4*10^72174+149)/972174Robert Price03/2017
9241(2^239671+9)/29613172143Lelio R Paula05/2012
92402^239651-11066572143Enzo Doria05/2014
9242(29*2^239650-1)/330572140Lelio R Paula01/2014
9243(17099^17041-1)/1709872130Serge Batalov08/2020
9245241^30280+30280^24172128Norbert Schneider11/2014
9244(2^239603+950)/272128Stefano Morozzi01/2020
9246(2^239594+3058)/272125Stefano Morozzi01/2020
9247(68*10^72120-23)/972121Robert Price10/2015
9248(9^75571+8^75571)/1772112Robert Price12/2012
9249(15661^17191-1)/1566072109Serge Batalov08/2020
9250(3508^20341-1)/350772107Serge Batalov08/2020


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: September, 29 2020 15:45 (Time in France)

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