PRP Records

Probable Primes Top 10000

(183432 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 ?
6501(2^223759-lucasV(1,2,223759)+1)/267358Mike Oakes11/2016
6502V(340138)67336Serge Batalov03/2015
650343125^14528-10667334Enzo Doria07/2012
65048*10^67302-5167303Robert Price10/2017
650517458^7153+7153^1745867292Hans Havermann08/2016
650616366^12925+12925^1636667288Hans Havermann08/2016
650737^42906-267286Lelio R Paula08/2013
650818^53592-1367273Lelio R Paula08/2013
6509V(396221)67256Serge Batalov03/2015
6511(34*10^67245-7)/9/3^4/193/138153767236Makoto Morimoto04/2016
6510(14*10^67235-101)/367236Robert Price04/2017
651253^38993-52^3899367235Robert Price01/2013
6513(2^223349-7)/648567231Lelio R Paula04/2012
65142^223333+31567230Lelio R Paula04/2012
65152^223278-11104167214Enzo Doria05/2014
6516(2347*2^223281+1)/(3*5*197*1213*1783)67208Jens K. Andersen09/2007
65172^223256-4567207Lelio R Paula02/2012
65182^223253-11211167206Enzo Doria06/2014
651918407^4474+4474^1840767199Hans Havermann08/2016
652047^40182+40182^4767189Norbert Schneider11/2014
652113^60309+9467181Lelio R Paula07/2013
652211^64503-8467173Lelio R Paula07/2013
65233^140781+23667170Lelio R Paula06/2013
65242^223107-86505767162Paul Bourdelais03/2013
65252^223100-5967160Lelio R Paula02/2012
65262^223087+7196367156Enzo Doria04/2016
652718^53481-377967134Enzo Doria03/2013
6528(326^26713-1)/32567134Eric Chen09/2017
65294^111473-6257367114Mike Oakes02/2011
65302^222943+2967113Henri Lifchitz08/2005
6531(2^222939-9)/10367110Lelio R Paula04/2012
65322^222862-45916167089Enzo Doria05/2015
65332^222828+819367078Lelio R Paula04/2012
65343^140570+266067069Lelio R Paula06/2013
65352^222744+85567053Lelio R Paula04/2012
653613^60189+8467048Lelio R Paula07/2013
65372^222701+57729457567040Lelio R Paula02/2016
6538(13*10^67038-31)/967039Serge Batalov11/2008
6539(151*10^67027-7)/967029Robert Price07/2017
6540(58695*2^222620-1)/6167019Lelio R Paula04/2015
65412^222614-11104167014Enzo Doria05/2014
65422^222520-190766986Yves Minet03/2013
6543(4^111231+23)/366968Robert Price02/2017
65442^222408-11127566952Enzo Doria05/2014
654510^66949-9^6694966949Jean-Louis Charton12/2005
65462^222378-100566943Lelio R Paula04/2012
6547(9*2^222366+1)/7366938Lelio R Paula08/2012
65487^79202-6^(79202+1)66934Robert Price06/2016
65492^222325-11225566927Enzo Doria06/2014
655020^51428+3366910Lelio R Paula08/2013
65512^222224-1850966897Enzo Doria05/2013
65522^222192-86968810566887Lelio R Paula02/2016
655311^64219-6466878Lelio R Paula07/2013
65542^222151-1729566875Lelio R Paula04/2012
6555gcd(V(799885),5*F(159977)*(F(159977)+1)+1)66867Serge Batalov04/2015
65562^222085-11103166855Enzo Doria05/2014
65578*10^66848-1366849Robert Price05/2017
6558(3^140087+4)/1366838Lelio R Paula04/2012
6559(3^140102+4)/884360943766836Lelio R Paula04/2012
656019^52265+5266835Lelio R Paula08/2013
65612*10^66826-2766827Robert Price02/2017
65624*6^85867+566819Lelio R Paula09/2014
656315^56800+866802Lelio R Paula08/2013
6564(2^221891-2^110946+1)/56679611/2006
656510^66793+6944166794Patrick De Geest05/2013
656610^66793-6366793Robert Price05/2011
656735^43256-170466791Enzo Doria03/2013
65683^139976+2^(139976-1)66786Robert Price05/2016
65697^79023-5466783Lelio R Paula06/2013
6570104^33109-10366782Norbert Schneider11/2016
6571(34*10^66778-7)/9/37/35890166772Makoto Morimoto04/2016
6572(-lucasV(1,2,443622)+2)/(7*281*487)66766Mike Oakes04/2017
65742^221768+18366759Lelio R Paula02/2012
6573gcd(V(1197915),5*F(239583)*(F(239583)+1)+1)66759Serge Batalov04/2015
6575(154*10^66755-1)/966757Serge Batalov12/2014
657611^64097+4866751Lelio R Paula07/2013
6577(lucasV(1,2,443547)-2)/(7*13*79*1327*221773)66749Mike Oakes04/2017
6578(19*10^66748+413)/966749Robert Price10/2017
6579(3*2^221696-1)/1366737Lelio R Paula01/2014
65808*6^85758-766734Lelio R Paula09/2014
6581135^31325+266733Lelio R Paula05/2013
6582(49*10^66729+41)/966730Robert Price07/2015
6583(349*10^66720-7)/966722Robert Price03/2017
6584(-lucasV(1,2,443285)+2)/(3^2*307)66718Mike Oakes04/2017
6585(25*10^66714+71)/366715Robert Price01/2017
658611^64061-78066713Enzo Doria11/2012
65877^78929+466703Lelio R Paula06/2013
658811^64048-93066700Enzo Doria11/2012
65892*7^78921+566697Lelio R Paula09/2014
6590(25*2^221526+1)/40966685Lelio R Paula08/2012
6591(2^221509-1)/29239188166673Jens K. Andersen02/2009
65922^221479+7295366672Enzo Doria04/2016
659310^66666+27540366667Patrick De Geest03/2010
659410^66666-11552166666Patrick De Geest03/2010
6595(18*10^66657-81)/9966657Ray Chandler01/2011
65964*10^66653+2166654Robert Price08/2016
6597(10^66650+149)/366650Serge Batalov12/2014
65989^69842+3*8^69842-2*4^69842-3*2^6984266647Mike Oakes12/2010
65992^221391-214566646Lelio R Paula04/2012
6600(5*10^66613-119)/366614Robert Price04/2016
66012^221273-11323366610Enzo Doria07/2014
66023^139571-4666593Lelio R Paula06/2013
66032^221181-86968810566583Lelio R Paula02/2016
6604(61*10^66575-7)/966576Ray Chandler02/2012
66052^221126+13366566Lelio R Paula02/2012
660712^61680+9166564Lelio R Paula07/2013
6606(lucasV(1,2,442258)+2)/10366564Mike Oakes04/2017
6608(13*10^66551-73)/366552Robert Price12/2016
660911^63901-159066547Enzo Doria12/2012
661011^63901-150066547Enzo Doria12/2012
66116^85517+2366546Lelio R Paula07/2013
661217^54069-4066530Lelio R Paula08/2013
6613(2^110503+4725)^2+(2^110503+4725)+4166530Makoto Morimoto05/2016
6614(2^110503+8099)^2+(2^110503+8099)+4166530Makoto Morimoto05/2016
6615(2^221008-1017)/7853366526Lelio R Paula04/2012
66163^139432+2666526Lelio R Paula06/2013
6617((2^110503+5139)^2+(2^110503+5139)+41)/2086579766523Makoto Morimoto05/2016
6618((2^110503+6647)^2+(2^110503+6647)+41)/197/1732766523Makoto Morimoto05/2016
66196^85481+8548166518Henri Lifchitz08/2014
6620(9179*2^220913-1)/39966503Lelio R Paula04/2015
662113^59687+6666488Lelio R Paula07/2013
6622(49*10^66485-31)/966486Robert Price07/2015
6623(46*10^66469+17)/966470Robert Price06/2015
66242^220790+9766465Lelio R Paula02/2012
6625(23*2^220790+1)/80766463Lelio R Paula06/2012
662640009^14441-10266460Enzo Doria07/2012
66272^220736-14366449Lelio R Paula02/2012
6628(79*10^66447-97)/9966447Ray Chandler01/2011
66292^220675+6966430Lelio R Paula02/2012
66302^220633-11138166418Enzo Doria05/2014
6631(2^220625-509203)/400032166409Lelio R Paula05/2012
66322^220596-1581366407Enzo Doria04/2013
6633(5*10^66394-17)/366395Serge Batalov05/2009
66342^220549-185917366392Enzo Doria04/2016
66352^220478-16166371Lelio R Paula02/2012
66365^94938-1463666359Enzo Doria02/2013
6637(F(67)^4861-F(66)^4861)/F(65)66353Wayne Halsdorf03/2012
66382^220253-11487166303Enzo Doria05/2015
663912^61432+9566297Lelio R Paula07/2013
66402^220192-11156366285Enzo Doria05/2014
66412^220188-11144966284Enzo Doria05/2014
6642(4*10^66284+23)/966284Robert Price11/2014
664332501!2+266266Robert Price01/2015
66441530*10^66254+R(66254)66258Patrick De Geest05/2016
6645(47^39623-1)/4666252Robert Price06/2014
66462^220044-9730566240Lelio R Paula04/2012
6647(77*10^66237-257)/966238Robert Price10/2017
664829^45285+266225Ray Chandler08/2011
664915^56289+3866202Lelio R Paula08/2013
66503^138749+9866201Lelio R Paula06/2013
6651(21*2^219912-1)/566201Lelio R Paula01/2014
66522^219904-1699566198Lelio R Paula10/2011
6653(3^138712-2)/529766179Lelio R Paula04/2012
6654Phi(198552,10)66177Ray Chandler07/2010
66554*6^85041+766176Lelio R Paula09/2014
66562^219812-314966171Yves Minet10/2009
66572^219795-61116766165Paul Bourdelais03/2013
665832455!2+51266162Robert Price02/2015
6659(27*2^219760-1)/22766154Lelio R Paula01/2014
6661(11^63521-4^63521)/766150Robert Price03/2013
66605*7^78274-666150Lelio R Paula09/2014
6662(-lucasV(1,2,439441)-2)/(3*11927*81359)66134Mike Oakes04/2017
66632^219679-11201566130Enzo Doria05/2014
66642^219653+15015*21965366123Henri Lifchitz04/2005
66652^219600+7656166107Enzo Doria05/2016
66662^219594+25525566105Lelio R Paula10/2011
66674*7^78210-366096Lelio R Paula09/2014
6668(15185*2^219557-1)/6366096Lelio R Paula04/2015
6669(19*2^219499-1)/1366076Lelio R Paula01/2014
66702^219496+6661566075Lelio R Paula10/2011
6671(F(79021)^5-F(79020)^5)/F(79019)66057Wayne Halsdorf03/2012
6672(2^219414+7)/44365766045Lelio R Paula04/2012
6673(115*10^66043-1)/366045Serge Batalov12/2014
667410^66033+1966034Robert Price01/2011
667510^66033-7830966033Patrick De Geest05/2013
6676(lucasV(1,2,438701)+2)/759941966025Mike Oakes04/2017
66772^219304+45424566018Henri Lifchitz03/2007
6678(27*2^219293+1)/914566012Lelio R Paula08/2012
66792^219273-11263566008Enzo Doria06/2014
66802^219250+2566001Lelio R Paula08/2011
6681132^31123+13165999Norbert Schneider03/2015
6682V(319871)65987Serge Batalov03/2015
66832^219189-19565983Lelio R Paula08/2011
6684(7*2^219143-1)/5565968Lelio R Paula01/2014
6685(73^35401-1)/7265962Paul Bourdelais08/2017
66862^219112-1700965960Enzo Doria05/2013
66872^219093-11120165954Enzo Doria05/2014
66882^219089-11209965953Enzo Doria06/2014
668946714!3+8165950Robert Price09/2014
6690(11*10^65944-131)/365945Robert Price02/2017
66912^219021-355365932Yves Minet03/2017
6692Pell-LucasQ(172243)/265931Eric W. Weisstein01/2007
66932^218990+7351965923Enzo Doria04/2016
669458^37378-5765914Norbert Schneider09/2014
6695(2^218945-7)/167565906Lelio R Paula04/2012
66965*10^65905+8165906Robert Price08/2017
6697(-lucasV(1,2,437845)-2)/167991765896Mike Oakes04/2017
6698127^31322-265896Lelio R Paula10/2017
66992^218897-11188965895Enzo Doria05/2014
67002^218896+186945165895Enzo Doria05/2016
670163^36616+265885Lelio R Paula05/2013
6702(3*2^218822-1)/1165872Lelio R Paula01/2014
67032^218796-11329765865Enzo Doria07/2014
67042^218797+7372765865Enzo Doria04/2016
67053^138040-11065862Lelio R Paula06/2013
670611^63240-195065858Enzo Doria12/2012
67072^218764-11187365855Enzo Doria05/2014
6708(34*10^65839-7)/9/3765839Makoto Morimoto04/2016
67093^137988+2665838Lelio R Paula06/2013
67102^218680-71965830Yves Minet05/2012
671118^52424+1765807Lelio R Paula08/2013
6712(2*15683^15683+1)/73238442565789David Broadhurst09/2010
6713(23*2^218517+1)/1900365778Lelio R Paula07/2012
6714(5*10^65773+1)/365774Erik Branger12/2013
67152^218457-1732965763Enzo Doria05/2013
6716151703#+22338165759Nicolas PALAU10/2016
67172^218436+4075565756Lelio R Paula10/2011
6718(F(44)^7433-F(43)^7433)/F(42)65744Wayne Halsdorf03/2012
6719157^29934+29934^15765733Serge Batalov05/2014
6720211^28273-265715Lelio R Paula09/2013
6721(59*10^65712+31)/965713Robert Price09/2015
6723611^23586+23586^61165712Norbert Schneider08/2016
6722p(13991)#/2+3265712Robert Price12/2016
67242^218282-1848565710Enzo Doria05/2013
67252^218274-11125165708Enzo Doria05/2014
67262*F(314335)-165693Henri Lifchitz12/2009
67272^218200+42765685Henri Lifchitz01/2005
672846532!3+365667Robert Price10/2014
67292^218120-14765661Lelio R Paula08/2011
6730452^24729+24729^45265659Norbert Schneider09/2016
67312^218102-11489365656Enzo Doria05/2015
6732(15*2^218083-1)/1765650Lelio R Paula01/2014
6733(15*2^218081+1)/1894165646Lelio R Paula08/2012
6734(306^26407-1)/30565638Eric Chen09/2017
673619^51326+3665634Lelio R Paula08/2013
6735(21*2^218045-1)/45158365634Lelio R Paula01/2014
67372^217989-3365622Lelio R Paula08/2011
6738(13*2^217961+1)/365614Lelio R Paula06/2012
67394*6^84315-565611Lelio R Paula09/2014
6740(315047^11933+1)/31504865607Faysal YAtim06/2008
67416^84303+5565601Lelio R Paula07/2013
6742(-lucasV(1,2,435857)+2)/(173*859*8017)65595Mike Oakes04/2017
6743(9787*2^217873-1)/3765589Lelio R Paula04/2015
67445*2^217858+365583Lelio R Paula04/2014
6745(19*10^65572+119)/365573Robert Price02/2017
674620^50399+5165571Lelio R Paula08/2013
674711^62946-567065552Enzo Doria01/2013
67482^217742-391165547Yves Minet08/2009
6749(19*10^65545+77)/365546Robert Price08/2016
67502^217731+13165544Lelio R Paula08/2011


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: October, 17 2017 09:44 (Time in France)

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