PRP Records

Probable Primes Top 10000

(259919 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 ?
77512^247311-101774449Lelio R Paula05/2013
7752(2^247288+1938)/274441Stefano Morozzi01/2020
77532^247280+774439Lelio R Paula03/2012
7754(68*10^74434+13)/974435Ray Chandler11/2010
77553^156004-6274433Lelio R Paula01/2015
775621865^2536+2536^2186574432Hans Havermann11/2019
7757(2^247223+1050)/274422Stefano Morozzi01/2020
775836095!2-6474416Robert Price06/2015
775967699!4+1674409Robert Price09/2019
77602^247165-374405M. Frind & P. Underwood07/2002
77612^247150+3276974400Lelio R Paula05/2013
7762(2^247130+3858)/274394Stefano Morozzi01/2020
7763(2^247055+2426)/274371Stefano Morozzi01/2020
776412^68911+7374368Lelio R Paula01/2015
77652^246999+7490374355Enzo Doria04/2016
77662^246989-11064374352Enzo Doria05/2014
776710^74350+27943974351Patrick De Geest07/2017
7770(10^74350+11)/374350Robert Price11/2014
776810^74350-40000000174350Robert Price07/2017
776910^74350-71624174350Patrick De Geest07/2017
777167647!4-51274346Robert Price11/2019
777210^74335+1365974336Patrick De Geest05/2013
777310^74335-5374335Robert Price05/2011
777423360^1521+1521^2336074335Hans Havermann11/2019
7775(2^246914+3418)/274329Stefano Morozzi01/2020
77762^246906-121574327Lelio R Paula05/2013
7777(2^246879+1494)/274318Stefano Morozzi01/2020
77782^246848+11174309Lelio R Paula03/2012
7779(2^246842+2490)/274307Stefano Morozzi01/2020
77816^95490-1844374306Enzo Doria03/2013
7780(2^246840+2902)/274306Stefano Morozzi01/2020
778218^59188-236974298Enzo Doria03/2013
7783(1363*2^246767+1)/(3*5*7*13^2*743)74281Jens K. Andersen09/2007
77842^246744+4075574278Lelio R Paula05/2013
7785(29*10^74276+91)/374277Robert Price03/2016
778617222^17533-17533^1722274272Norbert Schneider11/2019
7787(2^246720+3606)/274270Stefano Morozzi01/2020
77886^95441+16374268Lelio R Paula01/2015
7789V(390863)74258Serge Batalov03/2015
779010^74254+9174255Robert Price03/2011
7792(19*10^74253-1)/974254Ray Chandler02/2012
779110^74254-13056974254Patrick De Geest05/2013
7793771^25718+25718^77174250Norbert Schneider10/2016
77942^246618+42774240Henri Lifchitz02/2005
779588*10^74234+374236Robert Price11/2016
77968*10^74234-4974235Robert Price04/2016
77972^246578+1228574228Lelio R Paula05/2013
7798(3^155569-5)/274225Lelio R Paula06/2012
779913^66628+4674220Lelio R Paula01/2015
7800(2^246534+3034)/274214Stefano Morozzi01/2020
7801(2^246486+798)/274200Stefano Morozzi01/2020
78022^246476-1729574197Lelio R Paula05/2013
7803(2^246465+446)/274194Stefano Morozzi01/2020
7804(61*10^74189-1)/374191Robert Price11/2017
7805(15185*2^246432-1)/1374187Lelio R Paula04/2015
78065*2^246413-374179Lelio R Paula05/2014
78072^246386-2863574170Lelio R Paula05/2013
7808(2^246371+3050)/274165Stefano Morozzi01/2020
78092^246334-11124574154Enzo Doria05/2014
78103*9^77708+7^77708-2*4^77708-374153Mike Oakes12/2010
781115^63045+8274147Lelio R Paula01/2015
781219255!+19255#+174140D. Gazzoni Filho & Lucas Teixeira06/2005
7813(2^246277+2114)/274137Stefano Morozzi01/2020
78142^246268-11050774135Enzo Doria05/2014
78153^155328+266074111Lelio R Paula01/2015
78172^246148-278624974098Enzo Doria03/2016
781619740^5671+5671^1974074098Hans Havermann01/2020
7818(2^246135+3386)/274094Stefano Morozzi01/2020
7819(16*10^74092-19)/374093Robert Price03/2016
78202^246115-11076774088Enzo Doria05/2014
78217^87666-6874087Lelio R Paula08/2014
7822(2^246091+1938)/274081Stefano Morozzi01/2020
782310^74079+114514191974080Marisa Kirisame03/2015
782410^74079+621974080Patrick De Geest03/2016
782510^74079-28270774079Patrick De Geest03/2016
7826129^35098+274078Lelio R Paula05/2013
782722193^2176+2176^2219374073Hans Havermann12/2019
782817703^15278+15278^1770374071Hans Havermann12/2019
78292^246025-11212374061Enzo Doria06/2014
7830(67*10^74045+17)/374047Robert Price02/2017
7831(2^245944+2202)/274037Stefano Morozzi01/2020
7832(2^245885+1446)/274019Stefano Morozzi01/2020
78332^245823+6683174001Marek Hubal02/2017
78345^105869+4274000Lelio R Paula08/2014
7835(21*2^245806+1)/63455573991Lelio R Paula08/2012
7836(22699*2^245762+1)/11973985Lelio R Paula06/2014
7837(3^155048-7)/26273975Lelio R Paula06/2012
78389998*2^245696+373966Donovan Johnson10/2004
783913^66400-8073966Lelio R Paula01/2015
7841(2^245704+9)/2573963Lelio R Paula07/2012
784211^71023-717073963Enzo Doria01/2013
78403*10^73962+1373963Robert Price08/2017
7843(31*2^245660-1)/11419573948Lelio R Paula01/2014
78442^245629-279781373942Eric Chen03/2016
78452^245557-15373921Lelio R Paula03/2012
7846(77*10^73917-59)/973918Robert Price11/2017
784715010^17699+17699^1501073918Norbert Schneider11/2019
78482^245525+186988173911Enzo Doria06/2016
78492^245522+15973910Lelio R Paula03/2012
7850(2^245507+1986)/273905Stefano Morozzi01/2020
7851(13*10^73891-43)/373892Robert Price08/2017
785219^57783-5673891Lelio R Paula01/2015
78537*10^73888+7973889Robert Price02/2017
7854(2^245449+942)/273888Stefano Morozzi01/2020
78556^94948+17428173884Mike Oakes02/2011
7856(2^245431+3630)/273882Stefano Morozzi01/2020
785711^70939-486073876Enzo Doria01/2013
785818637^9196+9196^1863773870Hans Havermann01/2020
78592^245372+5461573865Lelio R Paula05/2013
78602^245362-14373862Lelio R Paula03/2012
78617^87396+6^(87396-1)73859Robert Price03/2016
7862(22*10^73853-37)/373854Robert Price05/2017
78635^105646-1424673844Enzo Doria02/2013
78652^245290-4173840Lelio R Paula03/2012
78642^245290-9439573840Lelio R Paula05/2013
786615770^17589+17589^1577073836Norbert Schneider10/2019
786712352^18043+18043^1235273828Norbert Schneider11/2019
7868(2^245240+3598)/273825Stefano Morozzi01/2020
7869(2^245242+498)/273825Stefano Morozzi01/2020
78708*5^105600-773813Lelio R Paula10/2014
78717*5^105573-473794Lelio R Paula10/2014
7872(2^245112+1122)/273786Stefano Morozzi01/2020
787320151^4570+4570^2015173751Hans Havermann12/2019
7874(2^244968+1318)/273743Stefano Morozzi01/2020
787518^58742-480573738Enzo Doria03/2013
787613^66179+6673720Lelio R Paula01/2015
7877(2^244881+942)/273717Stefano Morozzi01/2020
7878(2^244883+1946)/273717Stefano Morozzi01/2020
7879(82*10^73714-1)/973715Robert Price12/2014
7880(2^244862+3682)/273711Stefano Morozzi01/2020
7881(29*2^244856-1)/18612173706Lelio R Paula01/2014
7882(13*2^244840-1)/279973702Lelio R Paula01/2014
7883(13*10^73701+17)/373702Robert Price06/2015
7884(2^244787-1017)/2841173684Lelio R Paula07/2012
788521213^2974+2974^2121373680Hans Havermann01/2020
7886(3^154421-4)/2373677Lelio R Paula06/2012
788714596^17691+17691^1459673670Norbert Schneider11/2019
78888*7^87170+573669Lelio R Paula10/2014
7889(29*10^73659-113)/373660Robert Price11/2017
7890Phi(40100,-40100)73651Henri Lifchitz06/2013
7891(4*10^73647-19)/373648Robert Price06/2017
78922^244618-229773638Yves Minet10/2009
78933*5^105344+873633Lelio R Paula10/2014
7894(2^244588+2562)/273629Stefano Morozzi01/2020
78955^105334-1409673626Enzo Doria02/2013
7896(2^244562+1534)/273621Stefano Morozzi01/2020
7897(2^244584-7)/1323707424303373614Lelio R Paula07/2012
78982^244465-11018573592Enzo Doria05/2014
7899(2^244465+2934)/273591Stefano Morozzi01/2020
79002^244443+4075573585Lelio R Paula05/2013
790123155^1506+1506^2315573583Hans Havermann12/2019
790210^73579+98765432173580Robert Price12/2019
790310^73579+12417373580Patrick De Geest02/2020
790410^73579-17637973579Patrick De Geest02/2020
79052^244404+384173573Yves Minet03/2011
790619770^5263+5263^1977073569Hans Havermann12/2019
79072^244372-11062773564Enzo Doria05/2014
790819778^5241+5241^1977873563Hans Havermann12/2019
7909(2^244349+2186)/273557Stefano Morozzi01/2020
7910(2^244309+3710)/273545Stefano Morozzi01/2020
791118428^9783+9783^1842873537Hans Havermann01/2020
7912(3*2^244255+1)/24573527Lelio R Paula08/2012
7913(11*2^244245+1)/2373525Lelio R Paula08/2012
791418140^11301+11301^1814073524Hans Havermann12/2019
7915(15185*2^244187-1)/611173509Lelio R Paula04/2015
7916(2^244152+2058)/273497Stefano Morozzi01/2020
7917(2^244109+1422)/273484Stefano Morozzi01/2020
791817063^17362+17362^1706373477Norbert Schneider04/2019
7919(91^37507+1)/9273476Paul Bourdelais08/2017
792018^58521+6573460Lelio R Paula01/2015
792113^65940+3673454Lelio R Paula01/2015
792219065^7112+7112^1906573439Hans Havermann12/2019
7923(625^26267+1)/62673437Richard Fischer12/2017
7924(2^243935+530)/273432Stefano Morozzi01/2020
79255^105050-1473427Lelio R Paula08/2014
7926(2^243850+1474)/273406Stefano Morozzi01/2020
7927(((((((((((((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
792815^62410-4673400Lelio R Paula01/2015
7929(2^243806+2494)/273393Stefano Morozzi01/2020
7930(2^243790+2530)/273388Stefano Morozzi01/2020
7931(2^243766+2362)/273381Stefano Morozzi01/2020
79322^243733+186970773371Enzo Doria05/2016
793311^70439-543073355Enzo Doria01/2013
79342^243676-8773354Lelio R Paula03/2012
7935(101*10^73346-17)/373348Robert Price08/2016
793621639^2452+2452^2163973346Hans Havermann12/2019
7937(2^243647+2438)/273345Stefano Morozzi01/2020
79382^243621-11318573338Enzo Doria07/2014
7939(5*2^243610-1)/166973332Lelio R Paula01/2014
794019857^4928+4928^1985773326Hans Havermann12/2019
79412*5^104888-773314Lelio R Paula10/2014
7942(58695*2^243516-1)/98373308Lelio R Paula04/2015
7943(3^153648-2)/3342313809773299Lelio R Paula06/2012
7944(2^243467+470)/273291Stefano Morozzi01/2020
7945(2^243460+2410)/273289Stefano Morozzi01/2020
794618^58376-525573278Enzo Doria03/2013
794711^70363+3273276Lelio R Paula02/2015
79482^243413+425773275Lelio R Paula05/2013
7949104824^5+5^10482473269Andrey Kulsha07/2010
79507^86689-6^8668973261Predrag Minovic09/2004
7951(2^243355+3846)/273257Stefano Morozzi01/2020
79522^243296+9019573240Lelio R Paula05/2013
79532^243281-484373235Yves Minet05/2019
7955p(15433)#/2-473218Robert Price12/2016
7954(59*10^73217-77)/973218Robert Price11/2017
79562^243127+7135573189Lelio R Paula05/2013
79572^243116-24941973186Paul Bourdelais03/2013
7958(58695*2^243085-1)/1173180Lelio R Paula04/2015
7959(2^243084+3406)/273176Stefano Morozzi01/2020
796011^70262-9873171Lelio R Paula02/2015
7961(2^243034+47)/72270330373152Lelio R Paula07/2012
7962(2^242966+47)/4688773136Lelio R Paula07/2012
7963(43^44773-1)/4273134Robert Price04/2014
79646^93980-15835973131Mike Oakes02/2011
796519953^4616+4616^1995373114Hans Havermann11/2019
7966(2^242855+2546)/273107Stefano Morozzi01/2020
7967(2^242845+3926)/273104Stefano Morozzi01/2020
79686^93915+5373081Lelio R Paula01/2015
7969(5*10^73079+211)/973079Robert Price12/2017
7970(74*10^73076+43)/973077Robert Price10/2015
7971(3^153125+2)/114495573054Lelio R Paula06/2012
79722^242632-11219973040Enzo Doria06/2014
7973V(351646)73029Serge Batalov03/2015
7974(2^242598+1090)/273029Stefano Morozzi01/2020
797518^58175-8573026Lelio R Paula01/2015
7976p(15395)#/2-473019Robert Price12/2016
7977(4^121271+3^121271)/773012Jean-Louis Charton03/2011
79788*6^93825-573011Lelio R Paula10/2014
797919090^6673+6673^1909073007Hans Havermann11/2019
7981(F(220)^1601-F(219)^1601)/F(218)73005Wayne Halsdorf08/2013
7980(73^39181+1)/7473005Paul Bourdelais08/2017
79826^93815+14373003Lelio R Paula01/2015
79846^93812+573000Wojciech Florek03/2006
798317874^12137+12137^1787473000Hans Havermann11/2019
798519^57078-6272989Lelio R Paula01/2015
7986(29*10^72985+91)/372986Robert Price03/2016
798720691^3368+3368^2069172985Hans Havermann10/2019
7988(2^242451+558)/272985Stefano Morozzi01/2020
798911^70082-252072983Enzo Doria12/2012
7990(2^242429+2142)/272979Stefano Morozzi01/2020
79916^93773+13372970Lelio R Paula01/2015
7992(2^242392+3762)/272967Stefano Morozzi01/2020
79932^242328-5972948Lelio R Paula03/2012
79945^104358-1301672944Enzo Doria02/2013
7995(75*10^72941-57)/9972941Ray Chandler03/2011
799612^67585-9572937Lelio R Paula02/2015
7997(2^242261+3834)/272928Stefano Morozzi01/2020
79982^242230-11328572919Enzo Doria07/2014
7999(2^242229+2742)/272918Stefano Morozzi01/2020
8000(5*10^72916-11)/372917Erik Branger12/2013


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: March, 29 2020 17:41 (Time in France)

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