PRP Records

Probable Primes Top 10000

(202622 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 (> 30000) Who ? When ?
67512^222520-190766986Yves Minet03/2013
6752(4^111231+23)/366968Robert Price02/2017
67532^222408-11127566952Enzo Doria05/2014
675410^66949-9^6694966949Jean-Louis Charton12/2005
67552^222378-100566943Lelio R Paula04/2012
6756(9*2^222366+1)/7366938Lelio R Paula08/2012
67577^79202-6^(79202+1)66934Robert Price06/2016
67582^222325-11225566927Enzo Doria06/2014
675920^51428+3366910Lelio R Paula08/2013
67612^222224-1850966897Enzo Doria05/2013
6760(38*10^66896+187)/966897Robert Price11/2017
67622^222192-86968810566887Lelio R Paula02/2016
6763(19*10^66878-43)/366879Robert Price10/2017
676411^64219-6466878Lelio R Paula07/2013
67652^222151-1729566875Lelio R Paula04/2012
6766gcd(V(799885),5*F(159977)*(F(159977)+1)+1)66867Serge Batalov04/2015
67672^222085-11103166855Enzo Doria05/2014
67688*10^66848-1366849Robert Price05/2017
6769(3^140087+4)/1366838Lelio R Paula04/2012
6770(3^140102+4)/884360943766836Lelio R Paula04/2012
677119^52265+5266835Lelio R Paula08/2013
67722*10^66826-2766827Robert Price02/2017
67734*6^85867+566819Lelio R Paula09/2014
677415^56800+866802Lelio R Paula08/2013
6775(2^221891-2^110946+1)/56679611/2006
677610^66793+6944166794Patrick De Geest05/2013
677710^66793-6366793Robert Price05/2011
677835^43256-170466791Enzo Doria03/2013
67793^139976+2^(139976-1)66786Robert Price05/2016
67807^79023-5466783Lelio R Paula06/2013
6781104^33109-10366782Norbert Schneider11/2016
6782(34*10^66778-7)/9/37/35890166772Makoto Morimoto04/2016
6783(-lucasV(1,2,443622)+2)/(7*281*487)66766Mike Oakes04/2017
67842^221768+18366759Lelio R Paula02/2012
6785gcd(V(1197915),5*F(239583)*(F(239583)+1)+1)66759Serge Batalov04/2015
6786(154*10^66755-1)/966757Serge Batalov12/2014
678711^64097+4866751Lelio R Paula07/2013
6788(lucasV(1,2,443547)-2)/(7*13*79*1327*221773)66749Mike Oakes04/2017
6789(19*10^66748+413)/966749Robert Price10/2017
6790(3*2^221696-1)/1366737Lelio R Paula01/2014
67918*6^85758-766734Lelio R Paula09/2014
6792135^31325+266733Lelio R Paula05/2013
6793(49*10^66729+41)/966730Robert Price07/2015
6794(349*10^66720-7)/966722Robert Price03/2017
6795(-lucasV(1,2,443285)+2)/(3^2*307)66718Mike Oakes04/2017
6796(25*10^66714+71)/366715Robert Price01/2017
679711^64061-78066713Enzo Doria11/2012
67987^78929+466703Lelio R Paula06/2013
679911^64048-93066700Enzo Doria11/2012
68002*7^78921+566697Lelio R Paula09/2014
6801(25*2^221526+1)/40966685Lelio R Paula08/2012
6802(2^221509-1)/29239188166673Jens K. Andersen02/2009
68032^221479+7295366672Enzo Doria04/2016
680410^66666+27540366667Patrick De Geest03/2010
680510^66666-11552166666Patrick De Geest03/2010
6806(18*10^66657-81)/9966657Ray Chandler01/2011
68074*10^66653+2166654Robert Price08/2016
6808(10^66650+149)/366650Serge Batalov12/2014
68099^69842+3*8^69842-2*4^69842-3*2^6984266647Mike Oakes12/2010
68102^221391-214566646Lelio R Paula04/2012
6811(5*10^66613-119)/366614Robert Price04/2016
68122^221273-11323366610Enzo Doria07/2014
68133^139571-4666593Lelio R Paula06/2013
68142^221181-86968810566583Lelio R Paula02/2016
6815(61*10^66575-7)/966576Ray Chandler02/2012
68162^221126+13366566Lelio R Paula02/2012
681712^61680+9166564Lelio R Paula07/2013
6818(lucasV(1,2,442258)+2)/10366564Mike Oakes04/2017
6819(13*10^66551-73)/366552Robert Price12/2016
682011^63901-159066547Enzo Doria12/2012
682111^63901-150066547Enzo Doria12/2012
68226^85517+2366546Lelio R Paula07/2013
682317^54069-4066530Lelio R Paula08/2013
6824(2^110503+4725)^2+(2^110503+4725)+4166530Makoto Morimoto05/2016
6825(2^110503+8099)^2+(2^110503+8099)+4166530Makoto Morimoto05/2016
6827(2^221008-1017)/7853366526Lelio R Paula04/2012
68263^139432+2666526Lelio R Paula06/2013
6828((2^110503+5139)^2+(2^110503+5139)+41)/2086579766523Makoto Morimoto05/2016
6829((2^110503+6647)^2+(2^110503+6647)+41)/197/1732766523Makoto Morimoto05/2016
68306^85481+8548166518Henri Lifchitz08/2014
6831(9179*2^220913-1)/39966503Lelio R Paula04/2015
683213^59687+6666488Lelio R Paula07/2013
6833(49*10^66485-31)/966486Robert Price07/2015
6834(46*10^66469+17)/966470Robert Price06/2015
68352^220790+9766465Lelio R Paula02/2012
6836(23*2^220790+1)/80766463Lelio R Paula06/2012
683740009^14441-10266460Enzo Doria07/2012
68382^220736-14366449Lelio R Paula02/2012
6839(79*10^66447-97)/9966447Ray Chandler01/2011
68402^220675+6966430Lelio R Paula02/2012
68412^220633-11138166418Enzo Doria05/2014
6842(2^220625-509203)/400032166409Lelio R Paula05/2012
68432^220596-1581366407Enzo Doria04/2013
6844(5*10^66394-17)/366395Serge Batalov05/2009
68452^220549-185917366392Enzo Doria04/2016
68462^220478-16166371Lelio R Paula02/2012
68475^94938-1463666359Enzo Doria02/2013
6848(F(67)^4861-F(66)^4861)/F(65)66353Wayne Halsdorf03/2012
68492^220253-11487166303Enzo Doria05/2015
685012^61432+9566297Lelio R Paula07/2013
68512^220192-11156366285Enzo Doria05/2014
68522^220188-11144966284Enzo Doria05/2014
6853(4*10^66284+23)/966284Robert Price11/2014
685432501!2+266266Robert Price01/2015
6855(8*10^66261-101)/366262Robert Price10/2017
68561530*10^66254+R(66254)66258Patrick De Geest05/2016
6857(47^39623-1)/4666252Robert Price06/2014
68582^220044-9730566240Lelio R Paula04/2012
6859(77*10^66237-257)/966238Robert Price10/2017
686029^45285+266225Ray Chandler08/2011
686115^56289+3866202Lelio R Paula08/2013
68623^138749+9866201Lelio R Paula06/2013
6863(21*2^219912-1)/566201Lelio R Paula01/2014
68642^219904-1699566198Lelio R Paula10/2011
6865(3^138712-2)/529766179Lelio R Paula04/2012
6866Phi(198552,10)66177Ray Chandler07/2010
68674*6^85041+766176Lelio R Paula09/2014
68682^219812-314966171Yves Minet10/2009
68692^219795-61116766165Paul Bourdelais03/2013
687032455!2+51266162Robert Price02/2015
6871(27*2^219760-1)/22766154Lelio R Paula01/2014
6873(11^63521-4^63521)/766150Robert Price03/2013
68725*7^78274-666150Lelio R Paula09/2014
6874(-lucasV(1,2,439441)-2)/(3*11927*81359)66134Mike Oakes04/2017
68752^219679-11201566130Enzo Doria05/2014
68762^219653+15015*21965366123Henri Lifchitz04/2005
68772^219600+7656166107Enzo Doria05/2016
68782^219594+25525566105Lelio R Paula10/2011
68794*7^78210-366096Lelio R Paula09/2014
6880(15185*2^219557-1)/6366096Lelio R Paula04/2015
6881(19*2^219499-1)/1366076Lelio R Paula01/2014
68822^219496+6661566075Lelio R Paula10/2011
6883(F(79021)^5-F(79020)^5)/F(79019)66057Wayne Halsdorf03/2012
6884(2^219414+7)/44365766045Lelio R Paula04/2012
6885(115*10^66043-1)/366045Serge Batalov12/2014
688610^66033+1966034Robert Price01/2011
688710^66033-7830966033Patrick De Geest05/2013
6888(lucasV(1,2,438701)+2)/759941966025Mike Oakes04/2017
68892^219304+45424566018Henri Lifchitz03/2007
6890(27*2^219293+1)/914566012Lelio R Paula08/2012
68912^219273-11263566008Enzo Doria06/2014
68922^219250+2566001Lelio R Paula08/2011
6893132^31123+13165999Norbert Schneider03/2015
6894V(319871)65987Serge Batalov03/2015
68952^219189-19565983Lelio R Paula08/2011
6896(7*2^219143-1)/5565968Lelio R Paula01/2014
6897(73^35401-1)/7265962Paul Bourdelais08/2017
68982^219112-1700965960Enzo Doria05/2013
68992^219093-11120165954Enzo Doria05/2014
69002^219089-11209965953Enzo Doria06/2014
690146714!3+8165950Robert Price09/2014
6902(11*10^65944-131)/365945Robert Price02/2017
69032^219021-355365932Yves Minet03/2017
6904Pell-LucasQ(172243)/265931Eric W. Weisstein01/2007
69052^218990+7351965923Enzo Doria04/2016
690658^37378-5765914Norbert Schneider09/2014
6908(2^218945-7)/167565906Lelio R Paula04/2012
69075*10^65905+8165906Robert Price08/2017
69093*10^65899-1365900Robert Price11/2017
6910(-lucasV(1,2,437845)-2)/167991765896Mike Oakes04/2017
6911127^31322-265896Lelio R Paula10/2017
69122^218897-11188965895Enzo Doria05/2014
69132^218896+186945165895Enzo Doria05/2016
691463^36616+265885Lelio R Paula05/2013
6915(3*2^218822-1)/1165872Lelio R Paula01/2014
69162^218796-11329765865Enzo Doria07/2014
69172^218797+7372765865Enzo Doria04/2016
69183^138040-11065862Lelio R Paula06/2013
691911^63240-195065858Enzo Doria12/2012
69202^218764-11187365855Enzo Doria05/2014
6921(34*10^65839-7)/9/3765839Makoto Morimoto04/2016
69223^137988+2665838Lelio R Paula06/2013
69232^218680-71965830Yves Minet05/2012
692418^52424+1765807Lelio R Paula08/2013
6925(2*15683^15683+1)/73238442565789David Broadhurst09/2010
6926(23*2^218517+1)/1900365778Lelio R Paula07/2012
6927(5*10^65773+1)/365774Erik Branger12/2013
69282^218457-1732965763Enzo Doria05/2013
6929151703#+22338165759Nicolas PALAU10/2016
69302^218436+4075565756Lelio R Paula10/2011
6931(F(44)^7433-F(43)^7433)/F(42)65744Wayne Halsdorf03/2012
6932157^29934+29934^15765733Serge Batalov05/2014
6933211^28273-265715Lelio R Paula09/2013
6934(59*10^65712+31)/965713Robert Price09/2015
6936611^23586+23586^61165712Norbert Schneider08/2016
6935p(13991)#/2+3265712Robert Price12/2016
69372^218282-1848565710Enzo Doria05/2013
69382^218274-11125165708Enzo Doria05/2014
69392*F(314335)-165693Henri Lifchitz12/2009
69402^218200+42765685Henri Lifchitz01/2005
694146532!3+365667Robert Price10/2014
69422^218120-14765661Lelio R Paula08/2011
6943452^24729+24729^45265659Norbert Schneider09/2016
69442^218102-11489365656Enzo Doria05/2015
6945(15*2^218083-1)/1765650Lelio R Paula01/2014
6946(15*2^218081+1)/1894165646Lelio R Paula08/2012
6947(306^26407-1)/30565638Eric Chen09/2017
694919^51326+3665634Lelio R Paula08/2013
6948(21*2^218045-1)/45158365634Lelio R Paula01/2014
69502^217989-3365622Lelio R Paula08/2011
6951(13*2^217961+1)/365614Lelio R Paula06/2012
69524*6^84315-565611Lelio R Paula09/2014
6953(315047^11933+1)/31504865607Faysal YAtim06/2008
69546^84303+5565601Lelio R Paula07/2013
6955(-lucasV(1,2,435857)+2)/(173*859*8017)65595Mike Oakes04/2017
6956(9787*2^217873-1)/3765589Lelio R Paula04/2015
69575*2^217858+365583Lelio R Paula04/2014
6958(19*10^65572+119)/365573Robert Price02/2017
695920^50399+5165571Lelio R Paula08/2013
696011^62946-567065552Enzo Doria01/2013
69612^217742-391165547Yves Minet08/2009
6962(19*10^65545+77)/365546Robert Price08/2016
69632^217731+13165544Lelio R Paula08/2011
69642^217720-11128765541Enzo Doria05/2014
6965(365^25579+1)/36665539Eric Chen10/2017
696610^65537+2765538Robert Price01/2011
696710^65537-7685965537Patrick De Geest05/2013
6968(28*10^65532+359)/965533Robert Price11/2017
6969(10223*2^217676+1)/365531Lelio R Paula06/2014
6970PadovanNumber[536485]65518Eric W. Weisstein05/2009
69715*10^65509+2365510Robert Price11/2017
6972(8*10^65507-83)/365508Robert Price10/2017
69737*10^65492-4765493Robert Price02/2017
69742^217547-186840765489Enzo Doria04/2016
69752^217531-11176965484Enzo Doria05/2014
69767^77484-1865482Lelio R Paula06/2013
69772^217488-11328565471Enzo Doria07/2014
6978151153#/30-3065468Henri Lifchitz12/2011
69792^217466+425765464Lelio R Paula10/2011
698046396!3-8165455Robert Price09/2014
69812^217421-11318565451Enzo Doria07/2014
6982(6883*2^217440-1)/106119329589365448Lelio R Paula04/2015
69832^217408-214565447Lelio R Paula10/2011
69842^217398-1694765444Enzo Doria05/2013
69858*5^93613+365434Lelio R Paula09/2014
698611^62828-531065429Enzo Doria01/2013
698710^65426+1365427Robert Price01/2011
69882^217341-655565427Lelio R Paula10/2011
698910^65426-5484965426Patrick De Geest05/2013
6990(21*2^217363-1)/5600362666765424Lelio R Paula01/2014
699130011^14608-10865405Enzo Doria07/2012
6992119^31504-265389Lelio R Paula10/2017
6993(43^40031-1)/4265388Robert Price04/2014
69942^217190+9439565381Henri Lifchitz02/2005
699515^55587+4665376Lelio R Paula08/2013
69962^217088-11183365350Enzo Doria05/2014
6997(13*2^217069-1)/168294565340Lelio R Paula01/2014
6998(10^65340+47)/365340Robert Price11/2017
6999(62*10^65331+1)/965332Serge Batalov11/2010
70002^216947-11135165308Enzo Doria05/2014


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: February, 19 2018 09:17 (Time in France)

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