PRP Records

Probable Primes Top 10000

(202632 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 ?
6751(151*10^67027-7)/967029Robert Price07/2017
6752(58695*2^222620-1)/6167019Lelio R Paula04/2015
67532^222614-11104167014Enzo Doria05/2014
67542^222520-190766986Yves Minet03/2013
6755(4^111231+23)/366968Robert Price02/2017
67562^222408-11127566952Enzo Doria05/2014
675710^66949-9^6694966949Jean-Louis Charton12/2005
67582^222378-100566943Lelio R Paula04/2012
6759(9*2^222366+1)/7366938Lelio R Paula08/2012
67607^79202-6^(79202+1)66934Robert Price06/2016
67612^222325-11225566927Enzo Doria06/2014
676220^51428+3366910Lelio R Paula08/2013
67642^222224-1850966897Enzo Doria05/2013
6763(38*10^66896+187)/966897Robert Price11/2017
67652^222192-86968810566887Lelio R Paula02/2016
6766(19*10^66878-43)/366879Robert Price10/2017
676711^64219-6466878Lelio R Paula07/2013
67682^222151-1729566875Lelio R Paula04/2012
6769gcd(V(799885),5*F(159977)*(F(159977)+1)+1)66867Serge Batalov04/2015
67702^222085-11103166855Enzo Doria05/2014
67718*10^66848-1366849Robert Price05/2017
6772(3^140087+4)/1366838Lelio R Paula04/2012
6773(3^140102+4)/884360943766836Lelio R Paula04/2012
677419^52265+5266835Lelio R Paula08/2013
67752*10^66826-2766827Robert Price02/2017
67764*6^85867+566819Lelio R Paula09/2014
677715^56800+866802Lelio R Paula08/2013
6778(2^221891-2^110946+1)/56679611/2006
677910^66793+6944166794Patrick De Geest05/2013
678010^66793-6366793Robert Price05/2011
678135^43256-170466791Enzo Doria03/2013
67823^139976+2^(139976-1)66786Robert Price05/2016
67837^79023-5466783Lelio R Paula06/2013
6784104^33109-10366782Norbert Schneider11/2016
6785(34*10^66778-7)/9/37/35890166772Makoto Morimoto04/2016
6786(-lucasV(1,2,443622)+2)/(7*281*487)66766Mike Oakes04/2017
67872^221768+18366759Lelio R Paula02/2012
6788gcd(V(1197915),5*F(239583)*(F(239583)+1)+1)66759Serge Batalov04/2015
6789(154*10^66755-1)/966757Serge Batalov12/2014
679011^64097+4866751Lelio R Paula07/2013
6791(lucasV(1,2,443547)-2)/(7*13*79*1327*221773)66749Mike Oakes04/2017
6792(19*10^66748+413)/966749Robert Price10/2017
6793(3*2^221696-1)/1366737Lelio R Paula01/2014
67948*6^85758-766734Lelio R Paula09/2014
6795135^31325+266733Lelio R Paula05/2013
6796(49*10^66729+41)/966730Robert Price07/2015
6797(349*10^66720-7)/966722Robert Price03/2017
6798(-lucasV(1,2,443285)+2)/(3^2*307)66718Mike Oakes04/2017
6799(25*10^66714+71)/366715Robert Price01/2017
680011^64061-78066713Enzo Doria11/2012
68017^78929+466703Lelio R Paula06/2013
680211^64048-93066700Enzo Doria11/2012
68032*7^78921+566697Lelio R Paula09/2014
6804(25*2^221526+1)/40966685Lelio R Paula08/2012
6805(2^221509-1)/29239188166673Jens K. Andersen02/2009
68062^221479+7295366672Enzo Doria04/2016
680710^66666+27540366667Patrick De Geest03/2010
680810^66666-11552166666Patrick De Geest03/2010
6809(18*10^66657-81)/9966657Ray Chandler01/2011
68104*10^66653+2166654Robert Price08/2016
6811(10^66650+149)/366650Serge Batalov12/2014
68129^69842+3*8^69842-2*4^69842-3*2^6984266647Mike Oakes12/2010
68132^221391-214566646Lelio R Paula04/2012
6814(5*10^66613-119)/366614Robert Price04/2016
68152^221273-11323366610Enzo Doria07/2014
68163^139571-4666593Lelio R Paula06/2013
68172^221181-86968810566583Lelio R Paula02/2016
6818(61*10^66575-7)/966576Ray Chandler02/2012
68192^221126+13366566Lelio R Paula02/2012
682012^61680+9166564Lelio R Paula07/2013
6821(lucasV(1,2,442258)+2)/10366564Mike Oakes04/2017
6822(13*10^66551-73)/366552Robert Price12/2016
682311^63901-159066547Enzo Doria12/2012
682411^63901-150066547Enzo Doria12/2012
68256^85517+2366546Lelio R Paula07/2013
682617^54069-4066530Lelio R Paula08/2013
6827(2^110503+4725)^2+(2^110503+4725)+4166530Makoto Morimoto05/2016
6828(2^110503+8099)^2+(2^110503+8099)+4166530Makoto Morimoto05/2016
6830(2^221008-1017)/7853366526Lelio R Paula04/2012
68293^139432+2666526Lelio R Paula06/2013
6831((2^110503+5139)^2+(2^110503+5139)+41)/2086579766523Makoto Morimoto05/2016
6832((2^110503+6647)^2+(2^110503+6647)+41)/197/1732766523Makoto Morimoto05/2016
68336^85481+8548166518Henri Lifchitz08/2014
6834(9179*2^220913-1)/39966503Lelio R Paula04/2015
683513^59687+6666488Lelio R Paula07/2013
6836(49*10^66485-31)/966486Robert Price07/2015
6837(46*10^66469+17)/966470Robert Price06/2015
68382^220790+9766465Lelio R Paula02/2012
6839(23*2^220790+1)/80766463Lelio R Paula06/2012
684040009^14441-10266460Enzo Doria07/2012
68412^220736-14366449Lelio R Paula02/2012
6842(79*10^66447-97)/9966447Ray Chandler01/2011
68432^220675+6966430Lelio R Paula02/2012
68442^220633-11138166418Enzo Doria05/2014
6845(2^220625-509203)/400032166409Lelio R Paula05/2012
68462^220596-1581366407Enzo Doria04/2013
6847(5*10^66394-17)/366395Serge Batalov05/2009
68482^220549-185917366392Enzo Doria04/2016
68492^220478-16166371Lelio R Paula02/2012
68505^94938-1463666359Enzo Doria02/2013
6851(F(67)^4861-F(66)^4861)/F(65)66353Wayne Halsdorf03/2012
68522^220253-11487166303Enzo Doria05/2015
685312^61432+9566297Lelio R Paula07/2013
68542^220192-11156366285Enzo Doria05/2014
68552^220188-11144966284Enzo Doria05/2014
6856(4*10^66284+23)/966284Robert Price11/2014
685732501!2+266266Robert Price01/2015
6858(8*10^66261-101)/366262Robert Price10/2017
68591530*10^66254+R(66254)66258Patrick De Geest05/2016
6860(47^39623-1)/4666252Robert Price06/2014
68612^220044-9730566240Lelio R Paula04/2012
6862(77*10^66237-257)/966238Robert Price10/2017
686329^45285+266225Ray Chandler08/2011
686415^56289+3866202Lelio R Paula08/2013
68653^138749+9866201Lelio R Paula06/2013
6866(21*2^219912-1)/566201Lelio R Paula01/2014
68672^219904-1699566198Lelio R Paula10/2011
6868(3^138712-2)/529766179Lelio R Paula04/2012
6869Phi(198552,10)66177Ray Chandler07/2010
68704*6^85041+766176Lelio R Paula09/2014
68712^219812-314966171Yves Minet10/2009
68722^219795-61116766165Paul Bourdelais03/2013
687332455!2+51266162Robert Price02/2015
6874(27*2^219760-1)/22766154Lelio R Paula01/2014
6876(11^63521-4^63521)/766150Robert Price03/2013
68755*7^78274-666150Lelio R Paula09/2014
6877(-lucasV(1,2,439441)-2)/(3*11927*81359)66134Mike Oakes04/2017
68782^219679-11201566130Enzo Doria05/2014
68792^219653+15015*21965366123Henri Lifchitz04/2005
68802^219600+7656166107Enzo Doria05/2016
68812^219594+25525566105Lelio R Paula10/2011
68824*7^78210-366096Lelio R Paula09/2014
6883(15185*2^219557-1)/6366096Lelio R Paula04/2015
6884(19*2^219499-1)/1366076Lelio R Paula01/2014
68852^219496+6661566075Lelio R Paula10/2011
6886(F(79021)^5-F(79020)^5)/F(79019)66057Wayne Halsdorf03/2012
6887(2^219414+7)/44365766045Lelio R Paula04/2012
6888(115*10^66043-1)/366045Serge Batalov12/2014
688910^66033+1966034Robert Price01/2011
689010^66033-7830966033Patrick De Geest05/2013
6891(lucasV(1,2,438701)+2)/759941966025Mike Oakes04/2017
68922^219304+45424566018Henri Lifchitz03/2007
6893(27*2^219293+1)/914566012Lelio R Paula08/2012
68942^219273-11263566008Enzo Doria06/2014
68952^219250+2566001Lelio R Paula08/2011
6896132^31123+13165999Norbert Schneider03/2015
6897V(319871)65987Serge Batalov03/2015
68982^219189-19565983Lelio R Paula08/2011
6899(7*2^219143-1)/5565968Lelio R Paula01/2014
6900(73^35401-1)/7265962Paul Bourdelais08/2017
69012^219112-1700965960Enzo Doria05/2013
69022^219093-11120165954Enzo Doria05/2014
69032^219089-11209965953Enzo Doria06/2014
690446714!3+8165950Robert Price09/2014
6905(11*10^65944-131)/365945Robert Price02/2017
69062^219021-355365932Yves Minet03/2017
6907Pell-LucasQ(172243)/265931Eric W. Weisstein01/2007
69082^218990+7351965923Enzo Doria04/2016
690958^37378-5765914Norbert Schneider09/2014
6911(2^218945-7)/167565906Lelio R Paula04/2012
69105*10^65905+8165906Robert Price08/2017
69123*10^65899-1365900Robert Price11/2017
6913(-lucasV(1,2,437845)-2)/167991765896Mike Oakes04/2017
6914127^31322-265896Lelio R Paula10/2017
69152^218897-11188965895Enzo Doria05/2014
69162^218896+186945165895Enzo Doria05/2016
691763^36616+265885Lelio R Paula05/2013
6918(3*2^218822-1)/1165872Lelio R Paula01/2014
69192^218796-11329765865Enzo Doria07/2014
69202^218797+7372765865Enzo Doria04/2016
69213^138040-11065862Lelio R Paula06/2013
692211^63240-195065858Enzo Doria12/2012
69232^218764-11187365855Enzo Doria05/2014
6924(34*10^65839-7)/9/3765839Makoto Morimoto04/2016
69253^137988+2665838Lelio R Paula06/2013
69262^218680-71965830Yves Minet05/2012
692718^52424+1765807Lelio R Paula08/2013
6928(2*15683^15683+1)/73238442565789David Broadhurst09/2010
6929(23*2^218517+1)/1900365778Lelio R Paula07/2012
6930(5*10^65773+1)/365774Erik Branger12/2013
69312^218457-1732965763Enzo Doria05/2013
6932151703#+22338165759Nicolas PALAU10/2016
69332^218436+4075565756Lelio R Paula10/2011
6934(F(44)^7433-F(43)^7433)/F(42)65744Wayne Halsdorf03/2012
6935157^29934+29934^15765733Serge Batalov05/2014
6936211^28273-265715Lelio R Paula09/2013
6937(59*10^65712+31)/965713Robert Price09/2015
6939611^23586+23586^61165712Norbert Schneider08/2016
6938p(13991)#/2+3265712Robert Price12/2016
69402^218282-1848565710Enzo Doria05/2013
69412^218274-11125165708Enzo Doria05/2014
69422*F(314335)-165693Henri Lifchitz12/2009
69432^218200+42765685Henri Lifchitz01/2005
694446532!3+365667Robert Price10/2014
69452^218120-14765661Lelio R Paula08/2011
6946452^24729+24729^45265659Norbert Schneider09/2016
69472^218102-11489365656Enzo Doria05/2015
6948(15*2^218083-1)/1765650Lelio R Paula01/2014
6949(15*2^218081+1)/1894165646Lelio R Paula08/2012
6950(306^26407-1)/30565638Eric Chen09/2017
695219^51326+3665634Lelio R Paula08/2013
6951(21*2^218045-1)/45158365634Lelio R Paula01/2014
69532^217989-3365622Lelio R Paula08/2011
6954(13*2^217961+1)/365614Lelio R Paula06/2012
69554*6^84315-565611Lelio R Paula09/2014
6956(315047^11933+1)/31504865607Faysal YAtim06/2008
69576^84303+5565601Lelio R Paula07/2013
6958(-lucasV(1,2,435857)+2)/(173*859*8017)65595Mike Oakes04/2017
6959(9787*2^217873-1)/3765589Lelio R Paula04/2015
69605*2^217858+365583Lelio R Paula04/2014
6961(19*10^65572+119)/365573Robert Price02/2017
696220^50399+5165571Lelio R Paula08/2013
696311^62946-567065552Enzo Doria01/2013
69642^217742-391165547Yves Minet08/2009
6965(19*10^65545+77)/365546Robert Price08/2016
69662^217731+13165544Lelio R Paula08/2011
69672^217720-11128765541Enzo Doria05/2014
6968(365^25579+1)/36665539Eric Chen10/2017
696910^65537+2765538Robert Price01/2011
697010^65537-7685965537Patrick De Geest05/2013
6971(28*10^65532+359)/965533Robert Price11/2017
6972(10223*2^217676+1)/365531Lelio R Paula06/2014
6973PadovanNumber[536485]65518Eric W. Weisstein05/2009
69745*10^65509+2365510Robert Price11/2017
6975(8*10^65507-83)/365508Robert Price10/2017
69767*10^65492-4765493Robert Price02/2017
69772^217547-186840765489Enzo Doria04/2016
69782^217531-11176965484Enzo Doria05/2014
69797^77484-1865482Lelio R Paula06/2013
69802^217488-11328565471Enzo Doria07/2014
6981151153#/30-3065468Henri Lifchitz12/2011
69822^217466+425765464Lelio R Paula10/2011
698346396!3-8165455Robert Price09/2014
69842^217421-11318565451Enzo Doria07/2014
6985(6883*2^217440-1)/106119329589365448Lelio R Paula04/2015
69862^217408-214565447Lelio R Paula10/2011
69872^217398-1694765444Enzo Doria05/2013
69888*5^93613+365434Lelio R Paula09/2014
698911^62828-531065429Enzo Doria01/2013
699010^65426+1365427Robert Price01/2011
69912^217341-655565427Lelio R Paula10/2011
699210^65426-5484965426Patrick De Geest05/2013
6993(21*2^217363-1)/5600362666765424Lelio R Paula01/2014
699430011^14608-10865405Enzo Doria07/2012
6995119^31504-265389Lelio R Paula10/2017
6996(43^40031-1)/4265388Robert Price04/2014
69972^217190+9439565381Henri Lifchitz02/2005
699815^55587+4665376Lelio R Paula08/2013
69992^217088-11183365350Enzo Doria05/2014
7000(13*2^217069-1)/168294565340Lelio R Paula01/2014


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: February, 20 2018 10:36 (Time in France)

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