PRP Records

Probable Primes Top 10000

(247113 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 ?
7251(4^111231+23)/366968Robert Price02/2017
72522^222408-11127566952Enzo Doria05/2014
725310^66949-9^6694966949Jean-Louis Charton12/2005
72542^222378-100566943Lelio R Paula04/2012
7255(9*2^222366+1)/7366938Lelio R Paula08/2012
72567^79202-6^(79202+1)66934Robert Price06/2016
72572^222325-11225566927Enzo Doria06/2014
725820^51428+3366910Lelio R Paula08/2013
72592^222224-1850966897Enzo Doria05/2013
7260(38*10^66896+187)/966897Robert Price11/2017
72612^222192-86968810566887Lelio R Paula02/2016
7262(19*10^66878-43)/366879Robert Price10/2017
726311^64219-6466878Lelio R Paula07/2013
72642^222151-1729566875Lelio R Paula04/2012
7265gcd(V(799885),5*F(159977)*(F(159977)+1)+1)66867Serge Batalov04/2015
72662^222085-11103166855Enzo Doria05/2014
72678*10^66848-1366849Robert Price05/2017
7268(3^140087+4)/1366838Lelio R Paula04/2012
7269(3^140102+4)/884360943766836Lelio R Paula04/2012
727019^52265+5266835Lelio R Paula08/2013
72712*10^66826-2766827Robert Price02/2017
72724*6^85867+566819Lelio R Paula09/2014
727315^56800+866802Lelio R Paula08/2013
7274(2^221891-2^110946+1)/56679611/2006
727510^66793+6944166794Patrick De Geest05/2013
727610^66793-6366793Robert Price05/2011
727735^43256-170466791Enzo Doria03/2013
72783^139976+2^(139976-1)66786Robert Price05/2016
727988769!6-4866786Robert Price08/2018
72807^79023-5466783Lelio R Paula06/2013
7281104^33109-10366782Norbert Schneider11/2016
7282(34*10^66778-7)/9/37/35890166772Makoto Morimoto04/2016
7283(-lucasV(1,2,443622)+2)/(7*281*487)66766Mike Oakes04/2017
72842^221768+18366759Lelio R Paula02/2012
7285gcd(V(1197915),5*F(239583)*(F(239583)+1)+1)66759Serge Batalov04/2015
7286(154*10^66755-1)/966757Serge Batalov12/2014
728711^64097+4866751Lelio R Paula07/2013
7288(lucasV(1,2,443547)-2)/(7*13*79*1327*221773)66749Mike Oakes04/2017
7289(19*10^66748+413)/966749Robert Price10/2017
7290(3*2^221696-1)/1366737Lelio R Paula01/2014
72918*6^85758-766734Lelio R Paula09/2014
7292135^31325+266733Lelio R Paula05/2013
7293(49*10^66729+41)/966730Robert Price07/2015
7294(349*10^66720-7)/966722Robert Price03/2017
7295(-lucasV(1,2,443285)+2)/(3^2*307)66718Mike Oakes04/2017
7296(25*10^66714+71)/366715Robert Price01/2017
729711^64061-78066713Enzo Doria11/2012
72987^78929+466703Lelio R Paula06/2013
729911^64048-93066700Enzo Doria11/2012
7300120^32079-11966699Norbert Schneider09/2018
73012*7^78921+566697Lelio R Paula09/2014
7302(25*2^221526+1)/40966685Lelio R Paula08/2012
7303(2^221509-1)/29239188166673Jens K. Andersen02/2009
73042^221479+7295366672Enzo Doria04/2016
730510^66666+27540366667Patrick De Geest03/2010
730610^66666-11552166666Patrick De Geest03/2010
7307(18*10^66657-81)/9966657Ray Chandler01/2011
73084*10^66653+2166654Robert Price08/2016
7309(10^66650+149)/366650Serge Batalov12/2014
73109^69842+3*8^69842-2*4^69842-3*2^6984266647Mike Oakes12/2010
73112^221391-214566646Lelio R Paula04/2012
7312(5*10^66613-119)/366614Robert Price04/2016
73132^221273-11323366610Enzo Doria07/2014
73143^139571-4666593Lelio R Paula06/2013
7315(4*10^(2*33295)-2*(10^33295)+1)/366591Robert Price04/2018
73162^221181-86968810566583Lelio R Paula02/2016
7317(61*10^66575-7)/966576Ray Chandler02/2012
73182^221126+13366566Lelio R Paula02/2012
731912^61680+9166564Lelio R Paula07/2013
7320(lucasV(1,2,442258)+2)/10366564Mike Oakes04/2017
7321(13*10^66551-73)/366552Robert Price12/2016
732211^63901-159066547Enzo Doria12/2012
732311^63901-150066547Enzo Doria12/2012
73246^85517+2366546Lelio R Paula07/2013
732517^54069-4066530Lelio R Paula08/2013
7326(2^110503+4725)^2+(2^110503+4725)+4166530Makoto Morimoto05/2016
7327(2^110503+8099)^2+(2^110503+8099)+4166530Makoto Morimoto05/2016
7329(2^221008-1017)/7853366526Lelio R Paula04/2012
73283^139432+2666526Lelio R Paula06/2013
7330((2^110503+5139)^2+(2^110503+5139)+41)/2086579766523Makoto Morimoto05/2016
7331((2^110503+6647)^2+(2^110503+6647)+41)/197/1732766523Makoto Morimoto05/2016
73326^85481+8548166518Henri Lifchitz08/2014
7333(9179*2^220913-1)/39966503Lelio R Paula04/2015
733413^59687+6666488Lelio R Paula07/2013
7335(49*10^66485-31)/966486Robert Price07/2015
7336(46*10^66469+17)/966470Robert Price06/2015
73372^220790+9766465Lelio R Paula02/2012
7338(23*2^220790+1)/80766463Lelio R Paula06/2012
733940009^14441-10266460Enzo Doria07/2012
73402^220736-14366449Lelio R Paula02/2012
7341(79*10^66447-97)/9966447Ray Chandler01/2011
73422^220675+6966430Lelio R Paula02/2012
734388323!6-1666419Robert Price08/2018
73442^220633-11138166418Enzo Doria05/2014
7345(2^220625-509203)/400032166409Lelio R Paula05/2012
73462^220596-1581366407Enzo Doria04/2013
7347(5*10^66394-17)/366395Serge Batalov05/2009
73482^220549-185917366392Enzo Doria04/2016
73492^220478-16166371Lelio R Paula02/2012
73505^94938-1463666359Enzo Doria02/2013
7351(F(67)^4861-F(66)^4861)/F(65)66353Wayne Halsdorf03/2012
735215444^15839-15839^1544466346Norbert Schneider08/2018
73532^220253-11487166303Enzo Doria05/2015
735412^61432+9566297Lelio R Paula07/2013
73552^220192-11156366285Enzo Doria05/2014
73562^220188-11144966284Enzo Doria05/2014
7357(4*10^66284+23)/966284Robert Price11/2014
735832501!2+266266Robert Price01/2015
7359(8*10^66261-101)/366262Robert Price10/2017
73601530*10^66254+R(66254)66258Patrick De Geest05/2016
7361(47^39623-1)/4666252Robert Price06/2014
73622^220044-9730566240Lelio R Paula04/2012
7363(77*10^66237-257)/966238Robert Price10/2017
736429^45285+266225Ray Chandler08/2011
736515^56289+3866202Lelio R Paula08/2013
73663^138749+9866201Lelio R Paula06/2013
7367(21*2^219912-1)/566201Lelio R Paula01/2014
73682^219904-1699566198Lelio R Paula10/2011
7369(3^138712-2)/529766179Lelio R Paula04/2012
7370Phi(198552,10)66177Ray Chandler07/2010
73714*6^85041+766176Lelio R Paula09/2014
73722^219812-314966171Yves Minet10/2009
73732^219795-61116766165Paul Bourdelais03/2013
737432455!2+51266162Robert Price02/2015
7375(27*2^219760-1)/22766154Lelio R Paula01/2014
7377(11^63521-4^63521)/766150Robert Price03/2013
73765*7^78274-666150Lelio R Paula09/2014
7378(-lucasV(1,2,439441)-2)/(3*11927*81359)66134Mike Oakes04/2017
73792^219679-11201566130Enzo Doria05/2014
73802^219653+15015*21965366123Henri Lifchitz04/2005
738115445^15782-15782^1544566108Norbert Schneider08/2018
73822^219600+7656166107Enzo Doria05/2016
73832^219594+25525566105Lelio R Paula10/2011
73844*7^78210-366096Lelio R Paula09/2014
7385(15185*2^219557-1)/6366096Lelio R Paula04/2015
7386(19*2^219499-1)/1366076Lelio R Paula01/2014
73872^219496+6661566075Lelio R Paula10/2011
7388(F(79021)^5-F(79020)^5)/F(79019)66057Wayne Halsdorf03/2012
7389(2^219414+7)/44365766045Lelio R Paula04/2012
7390(115*10^66043-1)/366045Serge Batalov12/2014
739110^66033+1966034Robert Price01/2011
739210^66033-7830966033Patrick De Geest05/2013
7393(lucasV(1,2,438701)+2)/759941966025Mike Oakes04/2017
73942^219304+45424566018Henri Lifchitz03/2007
7395(27*2^219293+1)/914566012Lelio R Paula08/2012
73962^219273-11263566008Enzo Doria06/2014
73972^219250+2566001Lelio R Paula08/2011
7398132^31123+13165999Norbert Schneider03/2015
7399V(319871)65987Serge Batalov03/2015
74002^219189-19565983Lelio R Paula08/2011
7401(7*2^219143-1)/5565968Lelio R Paula01/2014
7402(73^35401-1)/7265962Paul Bourdelais08/2017
74032^219112-1700965960Enzo Doria05/2013
74042^219093-11120165954Enzo Doria05/2014
74052^219089-11209965953Enzo Doria06/2014
740646714!3+8165950Robert Price09/2014
7407(11*10^65944-131)/365945Robert Price02/2017
74082^219021-355365932Yves Minet03/2017
7409Pell-LucasQ(172243)/265931Eric W. Weisstein01/2007
74102^218990+7351965923Enzo Doria04/2016
741158^37378-5765914Norbert Schneider09/2014
7413(2^218945-7)/167565906Lelio R Paula04/2012
74125*10^65905+8165906Robert Price08/2017
74143*10^65899-1365900Robert Price11/2017
7415(-lucasV(1,2,437845)-2)/167991765896Mike Oakes04/2017
7416127^31322-265896Lelio R Paula10/2017
74182^218897-11188965895Enzo Doria05/2014
74172^218896+186945165895Enzo Doria05/2016
741963^36616+265885Lelio R Paula05/2013
7420(3*2^218822-1)/1165872Lelio R Paula01/2014
74212^218796-11329765865Enzo Doria07/2014
74222^218797+7372765865Enzo Doria04/2016
74233^138040-11065862Lelio R Paula06/2013
742411^63240-195065858Enzo Doria12/2012
74252^218764-11187365855Enzo Doria05/2014
7426(34*10^65839-7)/9/3765839Makoto Morimoto04/2016
74273^137988+2665838Lelio R Paula06/2013
74282^218680-71965830Yves Minet05/2012
742918^52424+1765807Lelio R Paula08/2013
7430(2*15683^15683+1)/73238442565789David Broadhurst09/2010
7431(23*2^218517+1)/1900365778Lelio R Paula07/2012
7432(5*10^65773+1)/365774Erik Branger12/2013
74332^218457-1732965763Enzo Doria05/2013
7434151703#+22338165759Nicolas PALAU10/2016
74352^218436+4075565756Lelio R Paula10/2011
7436(F(44)^7433-F(43)^7433)/F(42)65744Wayne Halsdorf03/2012
7437157^29934+29934^15765733Serge Batalov05/2014
7438211^28273-265715Lelio R Paula09/2013
7439(59*10^65712+31)/965713Robert Price09/2015
7440611^23586+23586^61165712Norbert Schneider08/2016
7441p(13991)#/2+3265712Robert Price12/2016
74422^218282-1848565710Enzo Doria05/2013
74432^218274-11125165708Enzo Doria05/2014
74442*F(314335)-165693Henri Lifchitz12/2009
74452^218200+42765685Henri Lifchitz01/2005
7446(10199^16384+10197^16384)/265676Jeppe Stig Nielsen04/2018
7447(10199^(2^14)+(10197)^(2^14))/265676Robert Price05/2018
744846532!3+365667Robert Price10/2014
74492^218120-14765661Lelio R Paula08/2011
7450452^24729+24729^45265659Norbert Schneider09/2016
74512^218102-11489365656Enzo Doria05/2015
7452(15*2^218083-1)/1765650Lelio R Paula01/2014
7453(15*2^218081+1)/1894165646Lelio R Paula08/2012
7454(306^26407-1)/30565638Eric Chen09/2017
745519^51326+3665634Lelio R Paula08/2013
7456(21*2^218045-1)/45158365634Lelio R Paula01/2014
74572^217989-3365622Lelio R Paula08/2011
7458(13*2^217961+1)/365614Lelio R Paula06/2012
74594*6^84315-565611Lelio R Paula09/2014
7460(315047^11933+1)/31504865607Faysal YAtim06/2008
74616^84303+5565601Lelio R Paula07/2013
7462(-lucasV(1,2,435857)+2)/(173*859*8017)65595Mike Oakes04/2017
7463(9787*2^217873-1)/3765589Lelio R Paula04/2015
74645*2^217858+365583Lelio R Paula04/2014
7465(19*10^65572+119)/365573Robert Price02/2017
746720^50399+5165571Lelio R Paula08/2013
74667162^17009+17009^716265571Norbert Schneider07/2018
746811^62946-567065552Enzo Doria01/2013
74692^217742-391165547Yves Minet08/2009
7470(19*10^65545+77)/365546Robert Price08/2016
74712^217731+13165544Lelio R Paula08/2011
74722^217720-11128765541Enzo Doria05/2014
7473(365^25579+1)/36665539Eric Chen10/2017
747410^65537+2765538Robert Price01/2011
747510^65537-7685965537Patrick De Geest05/2013
7476(28*10^65532+359)/965533Robert Price11/2017
7477(10223*2^217676+1)/365531Lelio R Paula06/2014
7478PadovanNumber[536485]65518Eric W. Weisstein05/2009
74795*10^65509+2365510Robert Price11/2017
7480(8*10^65507-83)/365508Robert Price10/2017
74817*10^65492-4765493Robert Price02/2017
74822^217547-186840765489Enzo Doria04/2016
74832^217531-11176965484Enzo Doria05/2014
74847^77484-1865482Lelio R Paula06/2013
74852^217488-11328565471Enzo Doria07/2014
7486151153#/30-3065468Henri Lifchitz12/2011
74872^217466+425765464Lelio R Paula10/2011
748846396!3-8165455Robert Price09/2014
74892^217421-11318565451Enzo Doria07/2014
7490(6883*2^217440-1)/106119329589365448Lelio R Paula04/2015
74912^217408-214565447Lelio R Paula10/2011
74922^217398-1694765444Enzo Doria05/2013
74938*5^93613+365434Lelio R Paula09/2014
749411^62828-531065429Enzo Doria01/2013
749510^65426+1365427Robert Price01/2011
74962^217341-655565427Lelio R Paula10/2011
749710^65426-5484965426Patrick De Geest05/2013
7498(21*2^217363-1)/5600362666765424Lelio R Paula01/2014
749930011^14608-10865405Enzo Doria07/2012
7500119^31504-265389Lelio R Paula10/2017


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: December, 11 2018 05:54 (Time in France)

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