PRP Records

Probable Primes Top 10000

(181746 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 ?
875110^52753+282643060952754Robert Price05/2015
875210^52753+18399752754Patrick De Geest01/2016
875310^52753-5015352753Patrick De Geest03/2016
875419846^455+455^1984652751Anatoly F. Selevich02/2007
87552^175217+7297752746Enzo Doria04/2016
8756p(11466)#/2-25652746Robert Price05/2017
8757(4*10^52740+41)/952740Robert Price11/2014
87582^175189+538552738Lelio R Paula08/2009
87592^175160+938552729Lelio R Paula07/2008
876012356^12885+12885^1235652724Norbert Schneider03/2016
87612^175137+1152722Lelio R Paula01/2011
876265^29077-64^2907752715Robert Price08/2013
87632*10^52713-8752714Robert Price06/2016
87642^175106-46552713Lelio R Paula08/2009
87652^175089-5869552708Lelio R Paula08/2009
87662^175045+19552694Lelio R Paula02/2011
87672^175025+14952688Lelio R Paula02/2011
8768(19^41201+1)/2052685Paul Bourdelais03/2010
87692*12^48815-5^4881552681Mike Oakes10/2010
8770335^20862-20862^33552678Norbert Schneider09/2015
87712^174983-760552676Lelio R Paula07/2009
87724*10^52667+1952668Robert Price04/2016
8773(10^52667+77)/352667Robert Price01/2017
877411434^12977+12977^1143452664Norbert Schneider04/2016
87752^174941-120352663Lelio R Paula07/2009
87762^174910+1270552654Lelio R Paula07/2012
87773^110338+7452645Lelio R Paula10/2012
87785^75303+1252635Lelio R Paula10/2012
87792^174836+25525552631Lelio R Paula07/2009
8780(66^28921+1)/6752622Paul Bourdelais08/2017
878120^40443+952618Lelio R Paula01/2013
8782(11*2^174788+1)/952617Lelio R Paula01/2012
8783(11*2^174786-1)/70352615Lelio R Paula01/2014
878411^50520-129052612Enzo Doria11/2012
8785(9913*2^174736-1)/33352603Lelio R Paula03/2015
878613145^10024+10024^1314552594Hans Havermann05/2016
87875003^14217-15052592Enzo Doria07/2012
878819^41123+1052587Lelio R Paula01/2013
87892^174683+1290952585Lelio R Paula01/2011
87902^174643+5952573Lelio R Paula01/2011
8791(1017*2^174640-1)/77352572Lelio R Paula03/2015
879213529^7662+7662^1352952552Hans Havermann06/2016
8793121421#+18876752548Makoto Morimoto02/2016
879420^40375-592352530Enzo Doria03/2013
8795(67607*2^174503+1)/9094807952528Lelio R Paula05/2014
8796(-lucasV(1,2,349014)+2)/(7*50873*1047043)52521Mike Oakes03/2017
87972^174462+34552519Lelio R Paula07/2009
8798t(178863)52509Robert Price10/2014
87992^174416+85552505Lelio R Paula07/2009
88006^67467-10352500Lelio R Paula10/2012
8801(2^174533-1)/(193594572654550537*91917886778031629891960890057)52494Dario Alpern06/2017
88022^174329-1126552479Enzo Doria06/2014
88032^174314-124152474Yves Minet05/2009
880452^30577-5152471Norbert Schneider08/2014
880515692^2205+2205^1569252465Hans Havermann06/2016
8806(2^174281-7)/62881702961552453Lelio R Paula02/2012
8807(2^174240+5)/352451Lelio R Paula02/2012
8808(86*10^52450-221)/952451Robert Price06/2017
8809(15*2^174221+1)/40352445Lelio R Paula07/2012
881026313!2-3252443Robert Price10/2015
8811(3*2^174214-1)/374872952438Lelio R Paula01/2014
88122*3^109900-552436Lelio R Paula03/2014
88144159^14488-15052432Enzo Doria07/2012
8813(89*10^52431-71)/952432Robert Price11/2015
88152^174170-394152431Yves Minet04/2017
8816(7*2^174171-1)/68552429Lelio R Paula01/2014
8818(260137^9679+1)/26013852409Faysal YAtim03/2008
88172^174098+7952409Lelio R Paula01/2011
881935^33940-221452406Enzo Doria03/2013
882015^44557+252404Ray Chandler07/2011
88212^174049-43952394Yves Minet01/2012
88226^67329+11552393Lelio R Paula10/2012
88242^174041+26214552392Lelio R Paula07/2009
8823141^24377+252392Lelio R Paula05/2013
8825lucasU(285,1,21339)-lucasU(285,1,21338)52382Mike Oakes05/2009
88262^174001-595552380Lelio R Paula07/2009
8827lucasV(-1,2,347969)52375Mike Oakes02/2017
88283^109764-14052371Lelio R Paula10/2012
88292*3^109761+752370Lelio R Paula03/2014
88302^173944-11225352363Enzo Doria06/2014
88322^173940+111152362Lelio R Paula01/2011
8831(3126^14983-1)/312552362Richard Fischer03/2015
883315214^2763+2763^1521452358Hans Havermann05/2016
883413200^9247+9247^1320052352Hans Havermann05/2016
8835(1017*2^173867-1)/717552339Lelio R Paula03/2015
883613732^6465+6465^1373252327Hans Havermann05/2016
8837(2^173867-1)/5253663750268952326Donovan Johnson06/2005
88382^173811-68487752323Paul Bourdelais11/2012
88392^173807-595552322Lelio R Paula06/2009
88402^173796-104468952318Paul Bourdelais11/2012
884110^52317+6449752318Patrick De Geest12/2012
884210^52317+6474352318Patrick De Geest12/2012
884310^52317-7152317Robert Price05/2011
884410821^12968+12968^1082152317Norbert Schneider04/2016
8845(298*10^52308-7)/352310Robert Price06/2017
8846(2^173778-3)/5795952308Lelio R Paula02/2012
884710232^13043-13043^1023252302Norbert Schneider08/2017
88492^173727+952298Lelio R Paula01/2011
8848(14^45631+13^45631)/2752298Robert Price04/2013
885037856!3+656152293Robert Price11/2015
88514*3^109596+552292Lelio R Paula03/2014
885215436^2441+2441^1543652291Hans Havermann05/2016
885343^32005+2452280Robert Price11/2013
88542^173650-16552274Lelio R Paula02/2011
88554*10^52272+9352273Robert Price01/2017
885619^40873+8452267Lelio R Paula01/2013
88572^173621+424242952266Jason Earls09/2008
8858numbpart(46909^2-1)52247Serge Batalov04/2017
885914^45579-3152240Lelio R Paula01/2013
8860(10223*2^173518+1)/90352236Lelio R Paula05/2014
886120^40147-612352233Enzo Doria03/2013
88624^86754-3^(86754+1)52232Robert Price04/2016
88632^173477-343352222Yves Minet04/2009
8864(25*2^173446+1)/6152213Lelio R Paula07/2012
88653^109431-3852212Lelio R Paula10/2012
88662^173424-395952206Yves Minet04/2017
886713^46861-7252201Lelio R Paula01/2013
88682^173373-136352191Yves Minet03/2009
886911^50114-174052189Enzo Doria11/2012
887013735^6304+6304^1373552188Hans Havermann05/2016
887111^50111-111052186Enzo Doria11/2012
8872lucasU(46,1,31387)+lucasU(46,1,31386)52181Mike Oakes04/2009
887320^40105-858352178Enzo Doria03/2013
8874(10322^13001+2679^13001)/13001^252175Lelio R Paula08/2008
88752^173314-394152173Yves Minet04/2017
88762^173294+115552167Lelio R Paula07/2012
8878(19*2^173301-1)/2348952166Lelio R Paula01/2014
887715146^2781+2781^1514652166Hans Havermann06/2016
887911^50088-3252162Lelio R Paula01/2013
88803^109320+23652159Lelio R Paula10/2012
88812^173246-2863552153Lelio R Paula06/2009
88822*10^52147+1152148Robert Price01/2015
88832^173208-11262552141Enzo Doria06/2014
8884(9179*2^173206-1)/203552141Lelio R Paula03/2015
888515^44333-7652140Lelio R Paula01/2013
88862^173187-318952135Yves Minet10/2014
88872^173167+7557952129Enzo Doria04/2016
8888(2^173169+7)/9279352125Lelio R Paula02/2012
8889(25*10^52119+23)/352120Robert Price06/2017
88909*7^61671+452119Lelio R Paula09/2014
88922^173130-922152118Lelio R Paula07/2008
8891(17*2^173129-1)/352118Lelio R Paula01/2014
88932^173100-11255952109Enzo Doria06/2014
88942^173091-11233952106Enzo Doria06/2014
889511^50030+2852101Lelio R Paula01/2013
8896(59*10^52099+13)/952100Robert Price09/2015
88972^173064-182952098Yves Minet09/2012
88982^173062-136152097Yves Minet08/2012
88993^109190-7052097Lelio R Paula10/2012
89002^173059+9019552096Lelio R Paula07/2012
89012^173048-11262552093Enzo Doria06/2014
890292^26524+9152088Norbert Schneider04/2013
890341^32295-4052085Theodore Burton02/2007
89042^173002+17752079Lelio R Paula02/2011
8905p(11334)#/2+852075Robert Price01/2017
89062^172965-11236352068Enzo Doria06/2014
89079*2^172935+752060Lelio R Paula03/2014
890811^49978-819052047Enzo Doria02/2013
890910^52041+63352042Patrick De Geest11/2012
891010^52041-9352041Robert Price05/2011
8911(21*2^172815-1)/86952021Lelio R Paula01/2014
8912(182*10^52018+1)/352020Robert Price02/2017
89134*6^66843-552015Lelio R Paula09/2014
891419^40670-5452007Lelio R Paula01/2013
89152^172756-11288352005Enzo Doria06/2014
891611832^12763-12763^1183251985Norbert Schneider02/2017
89177^61511-3651983Lelio R Paula10/2012
891810591^12914-12914^1059151979Norbert Schneider05/2017
89192^172640-7551970Lelio R Paula01/2011
8920gcd(V(932265),5*F(186453)*(F(186453)-1)+1)51953Serge Batalov04/2015
892112240^12709-12709^1224051952Norbert Schneider01/2017
8922t(173589)51951Robert Price12/2014
89237^61469+3451948Lelio R Paula10/2012
89259*2^172553-751945Lelio R Paula03/2014
892411542^12787+12787^1154251945Norbert Schneider01/2016
892635^33640-708651943Enzo Doria03/2013
8927(7*2^172534+1)/247951936Lelio R Paula07/2012
8928(2^86243+43467)^2+(2^86243+43467)+4151924Makoto Morimoto05/2016
8929(2^86243+84085)^2+(2^86243+84085)+4151924Makoto Morimoto05/2016
8930((2^86243+75146)^2+(2^86243+75146)+41)/6151922Makoto Morimoto05/2016
8931((2^86243+8692)^2+(2^86243+8692)+41)/301151920Makoto Morimoto05/2016
8932((2^86243+30085)^2+(2^86243+30085)+41)/41/19951920Makoto Morimoto05/2016
8933((2^86243+36540)^2+(2^86243+36540)+41)/43/64751920Makoto Morimoto05/2016
89352^172470+751919Lelio R Paula01/2011
8934((2^86243+76136)^2+(2^86243+76136)+41)/6050951919Makoto Morimoto05/2016
8936((2^86243+50999)^2+(2^86243+50999)+41)/249686951918Makoto Morimoto05/2016
8937((2^86243+80760)^2+(2^86243+80760)+41)/93048151918Makoto Morimoto05/2016
8938((2^86243+26732)^2+(2^86243+26732)+41)/223/9651751917Makoto Morimoto05/2016
8939((2^86243+51479)^2+(2^86243+51479)+41)/1607/2202751916Makoto Morimoto05/2016
89422^172455+1551915Lelio R Paula01/2011
8940((2^86243+27637)^2+(2^86243+27637)+41)/2693/51843151915Makoto Morimoto05/2016
8941((2^86243+82275)^2+(2^86243+82275)+41)/71/930992951915Makoto Morimoto05/2016
8943((2^86243+57757)^2+(2^86243+57757)+41)/30871/62272951914Makoto Morimoto05/2016
8944((2^86243+18643)^2+(2^86243+18643)+41)/47/23071/6529351913Makoto Morimoto05/2016
8945((2^86243+8693)^2+(2^86243+8693)+41)/494107/293389151912Makoto Morimoto05/2016
8946((2^86243+8250)^2+(2^86243+8250)+41)/223/34877/147262351911Makoto Morimoto05/2016
8947((2^86243+51745)^2+(2^86243+51745)+41)/71/95891/217129351911Makoto Morimoto05/2016
8948((2^86243+29592)^2+(2^86243+29592)+41)/7717/11933/1256650951909Makoto Morimoto05/2016
89495^74263+5451908Lelio R Paula10/2012
895013804^5755+5755^1380451904Hans Havermann05/2016
89517*2^172403-351900Henri Lifchitz06/2003
8952t(196078)51892Robert Price02/2014
89532*3^108759-751892Lelio R Paula03/2014
8954(94*10^51889+11)/351891Robert Price02/2017
8955(73*10^51889+17)/951890Robert Price10/2015
895635^33603-402651886Enzo Doria03/2013
89572^172350-10751883Lelio R Paula02/2011
895814419^3960+3960^1441951876Hans Havermann05/2016
89592^172325-11318551875Enzo Doria07/2014
896010^51872+10068351873Patrick De Geest06/2016
896110^51872-100000000151872Robert Price05/2016
896210^51872-10014951872Patrick De Geest06/2016
89632147092^8192+6351871Jens K. Andersen04/2009
896413^46564-2451870Lelio R Paula01/2013
896510524^12893-12893^1052451858Norbert Schneider05/2017
896613981^5110+5110^1398151848Hans Havermann05/2016
89672^172228+7626151846Enzo Doria04/2016
896811^49772-126051833Enzo Doria11/2012
8969(11*2^172157-1)/35151823Lelio R Paula01/2014
8970(43*10^51816-403)/951817Robert Price04/2017
89719001^13102-11451810Enzo Doria07/2012
8972(80051^10567+1)/8005251809Faysal YAtim07/2007
89742^172101-6151808Lelio R Paula01/2011
8973(2^172125+3)/3112550551808Lelio R Paula02/2012
89759*7^61301+451807Lelio R Paula09/2014
8976(23*2^172090-1)/3650951802Lelio R Paula01/2014
89772^172074+145951800Lelio R Paula07/2008
89782^172063+16551797Lelio R Paula02/2011
8979(21181*2^172061+1)/1814751796Lelio R Paula05/2014
898028^35785-2751787Norbert Schneider01/2014
8981(65*10^51778+43)/951779Ray Chandler09/2010
8982(15185*2^171975-1)/351774Lelio R Paula03/2015
89832^171978-11329751771Enzo Doria07/2014
898411^49708+7851766Lelio R Paula01/2013
8985(26*10^51764-107)/951765Robert Price07/2016
898612^47956-9751754Lelio R Paula12/2012
89872^171907-351151750Yves Minet03/2017
898810306^12885-12885^1030651709Norbert Schneider05/2017
8989(12611^12611+311)/2/13/1357790351707Makoto Morimoto07/2016
8990(3*2^171761+1)/2951705Lelio R Paula07/2012
8991t(195346)51699Robert Price07/2014
899213^46409+4651697Lelio R Paula01/2013
89932^171663+1155*17166351676Henri Lifchitz01/2005
899415^43937+2651674Lelio R Paula01/2013
8995(3^108312-7)/12452651673Lelio R Paula03/2012
8996(12601^12601+465)/2/13151667Makoto Morimoto07/2016
8997(79*10^51663-97)/9951663Ray Chandler11/2010
899848589!4+102451656Robert Price08/2017
8999(10^51652-31)/351652Serge Batalov12/2014
90002^171583+7379351652Enzo Doria04/2016


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: September, 14 2017 17:05 (Time in France)

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