PRP Records

Probable Primes Top 10000

(252932 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 ?
7501(21181*2^224570+1)/567606Lelio R Paula06/2014
750289762!6-367606Robert Price08/2018
75032^224578-11104167605Enzo Doria05/2014
75042^224569-11323367603Enzo Doria07/2014
75052^224562-11317167600Enzo Doria07/2014
75062^224556-11312967599Enzo Doria07/2014
75076*7^79980-567592Lelio R Paula09/2014
7508(6883*2^224523-1)/1603167588Lelio R Paula04/2015
750910^67579+16477967580Patrick De Geest07/2017
7511(52*10^67578-61)/967579Robert Price09/2015
751010^67579-40167579Robert Price06/2017
7512(17^54919-1)/1667574Paul Bourdelais03/2010
7513((10^33771-1)*10000/9+6389)*10^33771+(10^33771-1)/967546Hans Havermann05/2019
7514(2^224363-9)/195167537Lelio R Paula04/2012
7515(709*10^67517-7)/967519Robert Price09/2017
751647719!3-5904967516Robert Price12/2015
7517(22^50287+1)/2367506Robert Price06/2013
75183*10^67499+6767500Robert Price11/2017
751911^64811-582067494Enzo Doria01/2013
7520131^31870+31870^13167478Serge Batalov05/2014
75219*10^67468+767469Dmitry Domanov11/2010
7522(31*2^224115-1)/4772367463Lelio R Paula01/2014
7523128^32001+32001^12867433Serge Batalov05/2014
7524(89*10^67431-17)/967432Robert Price11/2015
75252^223912-11105967405Enzo Doria05/2014
75262^223913+7369767405Enzo Doria04/2016
7527(2*10^67405-23)/367405Robert Price09/2017
7528(10^67404+179)/967404Serge Batalov12/2014
752918738^3955+3955^1873867404Hans Havermann09/2016
75309*7^79728-267379Lelio R Paula09/2014
7531(28*10^67378-43)/367379Robert Price04/2016
7532(3^141234-7)/43024128267378Lelio R Paula04/2012
7533211^28988-267377Lelio R Paula09/2013
75344*10^67375+9167376Robert Price11/2017
75352^223793-1806967369Enzo Doria05/2013
75362^223777-252167364Yves Minet07/2014
7537(15185*2^223775-1)/1518367363Lelio R Paula04/2015
7538(2^223759-lucasV(1,2,223759)+1)/267358Mike Oakes11/2016
7539V(340138)67336Serge Batalov03/2015
754043125^14528-10667334Enzo Doria07/2012
754115275^16086-16086^1527567304Norbert Schneider09/2018
75428*10^67302-5167303Robert Price10/2017
754317458^7153+7153^1745867292Hans Havermann08/2016
754416366^12925+12925^1636667288Hans Havermann08/2016
754537^42906-267286Lelio R Paula08/2013
754618^53592-1367273Lelio R Paula08/2013
7547V(396221)67256Serge Batalov03/2015
7549(34*10^67245-7)/9/3^4/193/138153767236Makoto Morimoto04/2016
7548(14*10^67235-101)/367236Robert Price04/2017
755053^38993-52^3899367235Robert Price01/2013
7551(2^223349-7)/648567231Lelio R Paula04/2012
75522^223333+31567230Lelio R Paula04/2012
75532^223278-11104167214Enzo Doria05/2014
7554(2347*2^223281+1)/(3*5*197*1213*1783)67208Jens K. Andersen09/2007
75552^223256-4567207Lelio R Paula02/2012
75562^223253-11211167206Enzo Doria06/2014
755718407^4474+4474^1840767199Hans Havermann08/2016
755847^40182+40182^4767189Norbert Schneider11/2014
755913^60309+9467181Lelio R Paula07/2013
756011^64503-8467173Lelio R Paula07/2013
75613^140781+23667170Lelio R Paula06/2013
75622^223107-86505767162Paul Bourdelais03/2013
75632^223100-5967160Lelio R Paula02/2012
75642^223087+7196367156Enzo Doria04/2016
756518^53481-377967134Enzo Doria03/2013
7566(326^26713-1)/32567134Eric Chen09/2017
75674^111473-6257367114Mike Oakes02/2011
75682^222943+2967113Henri Lifchitz08/2005
7569(2^222939-9)/10367110Lelio R Paula04/2012
75702^222862-45916167089Enzo Doria05/2015
75712^222828+819367078Lelio R Paula04/2012
75723^140570+266067069Lelio R Paula06/2013
75732^222744+85567053Lelio R Paula04/2012
757413^60189+8467048Lelio R Paula07/2013
75752*10^67043-5167044Robert Price11/2017
75762^222701+57729457567040Lelio R Paula02/2016
7577(13*10^67038-31)/967039Serge Batalov11/2008
7578(151*10^67027-7)/967029Robert Price07/2017
7579(58695*2^222620-1)/6167019Lelio R Paula04/2015
75802^222614-11104167014Enzo Doria05/2014
7581118^32333-11766991Norbert Schneider08/2018
75822^222520-190766986Yves Minet03/2013
7583(4^111231+23)/366968Robert Price02/2017
75842^222408-11127566952Enzo Doria05/2014
758510^66949-9^6694966949Jean-Louis Charton12/2005
75862^222378-100566943Lelio R Paula04/2012
7587(9*2^222366+1)/7366938Lelio R Paula08/2012
75887^79202-6^(79202+1)66934Robert Price06/2016
75892^222325-11225566927Enzo Doria06/2014
759020^51428+3366910Lelio R Paula08/2013
75912^222224-1850966897Enzo Doria05/2013
7592(38*10^66896+187)/966897Robert Price11/2017
75932^222192-86968810566887Lelio R Paula02/2016
7594(19*10^66878-43)/366879Robert Price10/2017
759511^64219-6466878Lelio R Paula07/2013
75962^222151-1729566875Lelio R Paula04/2012
7597gcd(V(799885),5*F(159977)*(F(159977)+1)+1)66867Serge Batalov04/2015
75982^222085-11103166855Enzo Doria05/2014
75998*10^66848-1366849Robert Price05/2017
7600(3^140087+4)/1366838Lelio R Paula04/2012
7601(3^140102+4)/884360943766836Lelio R Paula04/2012
760219^52265+5266835Lelio R Paula08/2013
76032*10^66826-2766827Robert Price02/2017
76044*6^85867+566819Lelio R Paula09/2014
760511955^16384+266807Matt Stath12/2018
760615^56800+866802Lelio R Paula08/2013
7607(2^221891-2^110946+1)/56679611/2006
760810^66793+6944166794Patrick De Geest05/2013
760910^66793-6366793Robert Price05/2011
761035^43256-170466791Enzo Doria03/2013
76113^139976+2^(139976-1)66786Robert Price05/2016
761288769!6-4866786Robert Price08/2018
76137^79023-5466783Lelio R Paula06/2013
7614104^33109-10366782Norbert Schneider11/2016
7615(34*10^66778-7)/9/37/35890166772Makoto Morimoto04/2016
7616(-lucasV(1,2,443622)+2)/(7*281*487)66766Mike Oakes04/2017
76172^221768+18366759Lelio R Paula02/2012
7618gcd(V(1197915),5*F(239583)*(F(239583)+1)+1)66759Serge Batalov04/2015
7619(154*10^66755-1)/966757Serge Batalov12/2014
762011^64097+4866751Lelio R Paula07/2013
7621(lucasV(1,2,443547)-2)/(7*13*79*1327*221773)66749Mike Oakes04/2017
7622(19*10^66748+413)/966749Robert Price10/2017
7623(3*2^221696-1)/1366737Lelio R Paula01/2014
76248*6^85758-766734Lelio R Paula09/2014
7625135^31325+266733Lelio R Paula05/2013
7626(49*10^66729+41)/966730Robert Price07/2015
7627(349*10^66720-7)/966722Robert Price03/2017
7628(-lucasV(1,2,443285)+2)/(3^2*307)66718Mike Oakes04/2017
7629(25*10^66714+71)/366715Robert Price01/2017
763011^64061-78066713Enzo Doria11/2012
76317^78929+466703Lelio R Paula06/2013
763211^64048-93066700Enzo Doria11/2012
7633120^32079-11966699Norbert Schneider09/2018
76342*7^78921+566697Lelio R Paula09/2014
7635(25*2^221526+1)/40966685Lelio R Paula08/2012
7636(2^221509-1)/29239188166673Jens K. Andersen02/2009
76372^221479+7295366672Enzo Doria04/2016
763810^66666+27540366667Patrick De Geest03/2010
763910^66666-11552166666Patrick De Geest03/2010
7640(18*10^66657-81)/9966657Ray Chandler01/2011
76414*10^66653+2166654Robert Price08/2016
7642(10^66650+149)/366650Serge Batalov12/2014
76439^69842+3*8^69842-2*4^69842-3*2^6984266647Mike Oakes12/2010
76442^221391-214566646Lelio R Paula04/2012
7645(5*10^66613-119)/366614Robert Price04/2016
76462^221273-11323366610Enzo Doria07/2014
76473^139571-4666593Lelio R Paula06/2013
7648(4*10^(2*33295)-2*(10^33295)+1)/366591Robert Price04/2018
76492^221181-86968810566583Lelio R Paula02/2016
7650(61*10^66575-7)/966576Ray Chandler02/2012
76512^221126+13366566Lelio R Paula02/2012
765212^61680+9166564Lelio R Paula07/2013
7653(lucasV(1,2,442258)+2)/10366564Mike Oakes04/2017
7654(13*10^66551-73)/366552Robert Price12/2016
765511^63901-159066547Enzo Doria12/2012
765611^63901-150066547Enzo Doria12/2012
76576^85517+2366546Lelio R Paula07/2013
765817^54069-4066530Lelio R Paula08/2013
7659(2^110503+4725)^2+(2^110503+4725)+4166530Makoto Morimoto05/2016
7660(2^110503+8099)^2+(2^110503+8099)+4166530Makoto Morimoto05/2016
7661(2^221008-1017)/7853366526Lelio R Paula04/2012
76623^139432+2666526Lelio R Paula06/2013
7663((2^110503+5139)^2+(2^110503+5139)+41)/2086579766523Makoto Morimoto05/2016
7664((2^110503+6647)^2+(2^110503+6647)+41)/197/1732766523Makoto Morimoto05/2016
76656^85481+8548166518Henri Lifchitz08/2014
7666(9179*2^220913-1)/39966503Lelio R Paula04/2015
766713^59687+6666488Lelio R Paula07/2013
7668(49*10^66485-31)/966486Robert Price07/2015
7669(46*10^66469+17)/966470Robert Price06/2015
76702^220790+9766465Lelio R Paula02/2012
7671(23*2^220790+1)/80766463Lelio R Paula06/2012
767240009^14441-10266460Enzo Doria07/2012
76732^220736-14366449Lelio R Paula02/2012
7674(79*10^66447-97)/9966447Ray Chandler01/2011
76752^220675+6966430Lelio R Paula02/2012
767688323!6-1666419Robert Price08/2018
76772^220633-11138166418Enzo Doria05/2014
7678(2^220625-509203)/400032166409Lelio R Paula05/2012
76792^220596-1581366407Enzo Doria04/2013
7680(5*10^66394-17)/366395Serge Batalov05/2009
76812^220549-185917366392Enzo Doria04/2016
76822^220478-16166371Lelio R Paula02/2012
76835^94938-1463666359Enzo Doria02/2013
7684(F(67)^4861-F(66)^4861)/F(65)66353Wayne Halsdorf03/2012
768515444^15839-15839^1544466346Norbert Schneider08/2018
76862^220253-11487166303Enzo Doria05/2015
768712^61432+9566297Lelio R Paula07/2013
76882^220192-11156366285Enzo Doria05/2014
76892^220188-11144966284Enzo Doria05/2014
7690(4*10^66284+23)/966284Robert Price11/2014
769132501!2+266266Robert Price01/2015
7692(8*10^66261-101)/366262Robert Price10/2017
76931530*10^66254+R(66254)66258Patrick De Geest05/2016
7694(47^39623-1)/4666252Robert Price06/2014
76952^220044-9730566240Lelio R Paula04/2012
7696(77*10^66237-257)/966238Robert Price10/2017
769729^45285+266225Ray Chandler08/2011
769815^56289+3866202Lelio R Paula08/2013
76993^138749+9866201Lelio R Paula06/2013
7700(21*2^219912-1)/566201Lelio R Paula01/2014
77012^219904-1699566198Lelio R Paula10/2011
77022^219903-461566198Yves Minet05/2019
7703(3^138712-2)/529766179Lelio R Paula04/2012
7704Phi(198552,10)66177Ray Chandler07/2010
77054*6^85041+766176Lelio R Paula09/2014
77062^219812-314966171Yves Minet10/2009
77072^219795-61116766165Paul Bourdelais03/2013
770832455!2+51266162Robert Price02/2015
7709(27*2^219760-1)/22766154Lelio R Paula01/2014
7711(11^63521-4^63521)/766150Robert Price03/2013
77105*7^78274-666150Lelio R Paula09/2014
7712(-lucasV(1,2,439441)-2)/(3*11927*81359)66134Mike Oakes04/2017
77132^219679-11201566130Enzo Doria05/2014
77142^219653+15015*21965366123Henri Lifchitz04/2005
771515445^15782-15782^1544566108Norbert Schneider08/2018
77162^219600+7656166107Enzo Doria05/2016
77172^219594+25525566105Lelio R Paula10/2011
77184*7^78210-366096Lelio R Paula09/2014
7719(15185*2^219557-1)/6366096Lelio R Paula04/2015
7720(19*2^219499-1)/1366076Lelio R Paula01/2014
77212^219496+6661566075Lelio R Paula10/2011
7722(F(79021)^5-F(79020)^5)/F(79019)66057Wayne Halsdorf03/2012
7723(2^219414+7)/44365766045Lelio R Paula04/2012
7724(115*10^66043-1)/366045Serge Batalov12/2014
772510^66033+1966034Robert Price01/2011
772610^66033-7830966033Patrick De Geest05/2013
7727(lucasV(1,2,438701)+2)/759941966025Mike Oakes04/2017
77282^219304+45424566018Henri Lifchitz03/2007
7729(27*2^219293+1)/914566012Lelio R Paula08/2012
77302^219273-11263566008Enzo Doria06/2014
77312^219250+2566001Lelio R Paula08/2011
7732132^31123+13165999Norbert Schneider03/2015
7733V(319871)65987Serge Batalov03/2015
77342^219189-19565983Lelio R Paula08/2011
7735(7*2^219143-1)/5565968Lelio R Paula01/2014
7736(73^35401-1)/7265962Paul Bourdelais08/2017
77372^219112-1700965960Enzo Doria05/2013
77382^219093-11120165954Enzo Doria05/2014
77392^219089-11209965953Enzo Doria06/2014
774046714!3+8165950Robert Price09/2014
7741(11*10^65944-131)/365945Robert Price02/2017
77422^219021-355365932Yves Minet03/2017
7743Pell-LucasQ(172243)/265931Eric W. Weisstein01/2007
77442^218990+7351965923Enzo Doria04/2016
774558^37378-5765914Norbert Schneider09/2014
7747(2^218945-7)/167565906Lelio R Paula04/2012
77465*10^65905+8165906Robert Price08/2017
77483*10^65899-1365900Robert Price11/2017
7749(-lucasV(1,2,437845)-2)/167991765896Mike Oakes04/2017
7750127^31322-265896Lelio R Paula10/2017


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: June, 18 2019 07:14 (Time in France)

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