PRP Records

Probable Primes Top 10000

(172213 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 ?
9501(791013^8192+1)/248318Lelio R Paula12/2014
950210^48314+7146948315Patrick De Geest06/2016
950511^46393-795048314Enzo Doria02/2013
950310^48314-2*10^4988-148314Serge Batalov01/2015
950410^48314-42379748314Patrick De Geest03/2016
95062^160491+8771348313Yves Minet03/2010
95078*6^62084-748312Lelio R Paula09/2014
95082^160477+7297748309Enzo Doria04/2016
95092^160471+9948307Lelio R Paula07/2009
9510(9913*2^160481-1)/419187548307Lelio R Paula03/2015
9512(43^29573+1)/4448305Robert Price11/2013
95112^160463-290748305Yves Minet09/2014
9513Phi(77061,10)/4151276071/1520798835148301Maksym Voznyy02/2010
95145^69098-1457648298Enzo Doria02/2013
9515(2*10^48297-17)/348297Erik Branger03/2013
951610^48292+10470748293Patrick De Geest06/2016
951810^48292-2*10^392-148292Serge Batalov01/2015
951710^48292-6680348292Patrick De Geest03/2016
951945709!4+248291Robert Price03/2017
95202^160402-112748286Yves Minet05/2013
95212^160398-145148285Yves Minet08/2012
952211^46365+2648285Lelio R Paula10/2012
9523t(160462)48285Robert Price05/2015
9524(3^50599-75)^2-7748284Jorge Menendez02/2017
95253^101192+2^10119348281Mike Oakes10/2009
95265^69063-1848273Lelio R Paula05/2012
95275^69060-1541648271Enzo Doria02/2013
95282^160343-66748269Yves Minet01/2012
95292^160302-214548256Lelio R Paula04/2009
953012^44705-8548245Lelio R Paula10/2012
9531(58695*2^160249-1)/14948243Lelio R Paula03/2015
95322^160218+1270548231Lelio R Paula10/2011
9533(F(14425)^17-F(14424)^17)/F(14423)48230Wayne Halsdorf02/2010
9534(771035^8192+1)/248227Lelio R Paula12/2014
953618348^425+425^1834848226Anatoly F. Selevich12/2006
9535(29*2^160204-1)/6748226Lelio R Paula01/2014
95372^160166+577548215Lelio R Paula04/2009
953811875^11478+11478^1187548211Anatoly F. Selevich10/2009
953917^39177-4048206Lelio R Paula11/2012
9540(5*2^160135-1)/429039948200Lelio R Paula01/2014
9541(763957^8192+1)/248194Lelio R Paula12/2014
9542(11833^11833+1278)/7/89/10748193Makoto Morimoto06/2016
9543gcd(V(576505),5*F(115301)*(F(115301)+1)+1)48192Serge Batalov04/2015
95448788^12217+12217^878848183Norbert Schneider01/2014
9545(11831^11831+1584)/5/23/97/140948181Makoto Morimoto07/2016
9546(760473^8192+1)/248178Lelio R Paula12/2014
9547-lucasV(-1,2,320104)/3148178Mike Oakes01/2017
9548gcd(V(864525),5*F(172905)*(F(172905)-1)+1)48176Serge Batalov04/2015
9549(760135^8192+1)/29491448171Lelio R Paula12/2014
95514357^13236-11048169Enzo Doria06/2012
9550(11827^11827+4120)/1748169Makoto Morimoto07/2016
9552(3*2^160013-1)/242548166Lelio R Paula01/2014
955313^43238+8248165Lelio R Paula11/2012
95542^159992+65748163Lelio R Paula02/2013
95552^159984-38300948160Gary Barnes08/2009
95562^159958-5869548153Lelio R Paula03/2009
95576408*10^48143+11821^11821-2448147Gilbert Mozzo12/2012
9558(755045^8192+1)/22937848147Lelio R Paula12/2014
955911821^11821-2448143Henri Lifchitz10/2011
9560(33*2^159934+1)/193696948141Michael Porter10/2015
9561(11821^11821+1240)/19/1378948138Makoto Morimoto06/2016
956220^36997-5148135Lelio R Paula11/2012
9563(3^100895+7)/2432177503448129Lelio R Paula03/2012
9564(15185*2^159869-1)/182748127Lelio R Paula03/2015
95653*7^56945+848125Lelio R Paula09/2014
9566(749655^8192+1)/13107448122Lelio R Paula12/2014
95674*5^68835+948115Lelio R Paula09/2014
9568(148^22171+1)/14948115Richard Fischer12/2016
9569(2^159841+78557)/92348114Lelio R Paula05/2012
9570(3^50420+59)^2+6148113Jorge Menendez02/2017
957110^48109+948110Jason Earls12/2007
957210^48108+3953148109Patrick De Geest01/2009
957310^48109-10459148109Patrick De Geest07/2009
957610^48107-4810748108Henri Lifchitz07/2002
957410^48107+12622948108Patrick De Geest04/2007
957510^48108-6134348108Patrick De Geest07/2009
957723^35328+2248108Norbert Schneider12/2013
95796213^12682+12682^621348107Norbert Schneider01/2016
9578(64*10^48106+287)/948107Robert Price04/2016
958018^38321-9748104Lelio R Paula11/2012
9581(11813^11813+748)/3/67980748101Makoto Morimoto06/2016
9582(743679^8192+1)/248099Lelio R Paula12/2014
95832^159777-133348098Yves Minet05/2013
95842^159765+71748095Lelio R Paula02/2013
958535^31143-395848087Enzo Doria03/2013
95868*10^48081-948082Dmitry Domanov11/2010
958712^44553-5948081Lelio R Paula10/2012
958835086!3+218748080Robert Price12/2015
9589(11807^11807+9647)/2/548079Makoto Morimoto07/2016
95901338^15377+15377^133848076Serge Batalov05/2014
95912^159692-125948073Yves Minet08/2012
9592(lucasV(1,2,319367)+2)/(5*11)48068Mike Oakes01/2017
95932^159669+94148066Lelio R Paula02/2013
95942^159660-287948063Yves Minet09/2014
95952^159647+57348059Lelio R Paula02/2013
959619^37581+9448057Lelio R Paula11/2012
95972^159633-57706348055Paul Bourdelais11/2012
9598(11801^11801+8503)/2^4/3/17/13748048Makoto Morimoto07/2016
9599(23*2^159599+1)/2548045Lelio R Paula07/2012
96002^159597+130748044Lelio R Paula07/2008
96013^100693-3448043Lelio R Paula06/2012
9602(68*10^48032+7)/348034Robert Price03/2016
960324^34797-120748028Enzo Doria03/2013
9604(106*10^48026-1)/348028Serge Batalov12/2014
96052^159522+67948021Lelio R Paula02/2013
9606(726998^8192+1)/14745748013Lelio R Paula11/2014
9607(725753^8192+1)/13107448007Lelio R Paula12/2014
960810^48003+2148004Robert Price01/2011
960910^48003-3652148003Patrick De Geest01/2012
961020^36896-404348003Enzo Doria03/2013
961110^48000+7390948001Patrick De Geest05/2012
961210^48000-8240748000Patrick De Geest05/2012
961310^47999+7809348000Patrick De Geest05/2012
961410^47999-122747999Patrick De Geest05/2012
96152^159440-1260947997Enzo Doria10/2012
9616(11789^11789+297)/2/17/2347996Makoto Morimoto06/2016
9617(40^29959+1)/4147995Robert Price09/2013
9620(49*10^47989+41)/947990Erik Branger05/2013
961810^47989+2*47989-147990Robert Price03/2015
961910^47989+3028347990Patrick De Geest01/2016
962110^47989-1046347989Patrick De Geest01/2016
9622(11*2^159409-1)/2147987Lelio R Paula01/2014
96235^68644+9447981Lelio R Paula05/2012
96242^159386-214547980Lelio R Paula03/2009
9625Linear(0,1,1,-1,318751)47977Henri Lifchitz04/2007
9626(720710^8192+1)/966388940947977Lelio R Paula11/2014
9627(2^159392+5)/11779866947974Lelio R Paula01/2012
96286576^12565-12565^657647973Norbert Schneider11/2016
963010^47969+58504347970Robert Price03/2015
962910^47969+15329147970Patrick De Geest01/2016
963110^47969-15140747969Patrick De Geest01/2016
9632(9*2^159332+1)/547964Lelio R Paula07/2012
9633(11783^11783+65)/2^3/89/268603747963Makoto Morimoto06/2016
963420^36864+3147962Lelio R Paula11/2012
9635(2^159324+78557)/240947958Lelio R Paula05/2012
96372^159293-105147952Yves Minet05/2009
9636(355*29^32789-61)/1447952Curtis Bright05/2015
9638lucasU(1856,1,14670)-lucasU(1856,1,14669)47947Mike Oakes05/2009
9639(11779^11779+1425)/2^2/11/545679147946Makoto Morimoto07/2016
96403^100482-31047943Lelio R Paula06/2012
9641(11777^11777+5123)/2^2/5/13/225147939Makoto Morimoto07/2016
964217^38959+847938Lelio R Paula11/2012
96437*10^47936-6947937Robert Price01/2017
9644(708709^8192+1)/247927Lelio R Paula12/2014
9645(709609^8192+1)/29491447927Lelio R Paula12/2014
9647Phi(104749,3)47923Lelio R Paula02/2012
964624^34721-169147923Enzo Doria03/2013
96487*5^68554+647919Lelio R Paula09/2014
9649(16*10^47918-19)/347919Robert Price03/2016
965111836^11179+11179^1183647917Anatoly F. Selevich07/2009
9650Phi(65680,67)47917Enzo Doria04/2012
96523^100418-5247912Lelio R Paula06/2012
96532^159145-11281347908Enzo Doria06/2014
96546*F(229213)+147904Gilbert Mozzo06/2015
96556750^12509-12509^675047901Norbert Schneider10/2016
9656(5*2^159123-1)/3947900Lelio R Paula01/2014
96572^159105-11251347896Enzo Doria06/2014
9658(11*2^159097-1)/2147893Lelio R Paula01/2014
96592^159092+21147892Lelio R Paula02/2013
966010^47890+22490147891Patrick De Geest06/2016
966110^47890-2*10^4844-147890Serge Batalov01/2015
966210^47890-5791147890Patrick De Geest03/2016
96632^159078+115547888Lelio R Paula10/2011
9664(5*2^159081+1)/14347887Lelio R Paula07/2012
9665Phi(69053,5)47885Lelio R Paula01/2012
96663^100362-9847885Lelio R Paula06/2012
9667(9913*2^159034-1)/947878Lelio R Paula03/2015
96685^68484-68484^547869Donovan Johnson08/2005
96692^159001-27871347865Gary Barnes08/2009
96702^159003-1409547865Enzo Doria04/2013
96715^68476-2103647863Enzo Doria03/2013
9672(695277^8192+1)/247859Lelio R Paula12/2014
96732^158977+7471747857Yves Minet12/2009
96743*5^68464-847855Lelio R Paula09/2014
967513855^2844+2844^1385547855Hans Havermann08/2015
967612030^9503+9503^1203047854Jens K. Andersen01/2009
9677110597#+13131747853Nicolas PALAU09/2016
9678(3*2^158960+1)/49947850Lelio R Paula07/2012
96792^158948+1968347849Lelio R Paula10/2011
9680lucasU(1873,1,14622)-lucasU(1873,1,14621)47848Mike Oakes05/2009
9681(266*10^47844-17)/347846Robert Price06/2016
96826411^12568-12568^641147846Norbert Schneider11/2016
9683lucasU(1656,1,14862)-lucasU(1656,1,14861)47839Mike Oakes05/2009
9684(2^158894-3)/3747831Lelio R Paula01/2012
968534918!3-2747826Robert Price09/2014
96862*10^47823+8947824Robert Price07/2016
96876950^12447-12447^695047822Norbert Schneider03/2013
96882^158838-1385347816Enzo Doria04/2013
968918^38087+3747810Lelio R Paula11/2012
9690(685559^8192+1)/247809Lelio R Paula12/2014
9691(684701^8192+1)/247805Lelio R Paula12/2014
9693(11*2^158796+1)/347803Lelio R Paula01/2012
9692(684463^8192+1)/247803Lelio R Paula12/2014
9694110503#+20839147798Makoto Morimoto12/2015
9695(11^45893-4^45893)/747792Robert Price03/2013
9696(58*10^47791+23)/947792Erik Branger05/2013
9697(11743^11743+5271)/247792Makoto Morimoto07/2016
96982^158757+2947791Henri Lifchitz05/2005
96992^158758+20547791Lelio R Paula02/2013
970035^30951-3647791Enzo Doria03/2013
970110^47784+14147785Patrick De Geest06/2016
970210^47784-2*10^10720-147784Serge Batalov01/2015
970310^47784-13192747784Patrick De Geest03/2016
97042^158710-11260747777Enzo Doria06/2014
9705(677621^8192+1)/247768Lelio R Paula12/2014
97062^158656+66147761Lelio R Paula02/2013
9707(14^41669+13^41669)/2747757Robert Price04/2013
9708(676199^8192+1)/13107447755Lelio R Paula12/2014
9709(675075^8192+1)/247754Lelio R Paula12/2014
97107^56505-2647753Lelio R Paula06/2012
9711(lucasV(1,2,317394)-2)/(7^2*23*43*67*127*463*9619*35267*45343)47749Mike Oakes01/2017
97122^158603+75547745Lelio R Paula02/2013
97133*2^158583+547739Lelio R Paula02/2014
971410^47738+2508347739Patrick De Geest06/2016
971510^47738-2*10^408-147738Serge Batalov01/2015
971610^47738-7817747738Patrick De Geest03/2016
97172^158564+8785547733Lelio R Paula11/2008
97182^158559-150747732Yves Minet08/2012
971910^47728+7947729Robert Price01/2011
97202^158552-11261947729Enzo Doria06/2014
972110^47728-7187947728Patrick De Geest10/2011
97227^56474+6447727Lelio R Paula06/2012
9723(2^158557+47)/2893147726Lelio R Paula01/2012
97242^158535-70647747724Paul Bourdelais11/2012
972510^47722-2*10^7928-147722Serge Batalov01/2015
9726(7*10^47719+71)/347720Robert Price03/2016
97312^158497+2147713Donovan Johnson02/2006
9727((19541*3^50000)^2+(3^100000-19541*3^50000)^2)/3^10000047713Robert Price07/2014
9728((148735*3^50000)^2+(3^100000-148735*3^50000)^2)/3^10000047713Robert Price08/2014
9729((155921*3^50000)^2+(3^100000-155921*3^50000)^2)/3^10000047713Robert Price08/2014
9730((228248*3^50000)^2+(3^100000-228248*3^50000)^2)/3^10000047713Robert Price08/2014
9732(666459^8192+1)/13107447704Lelio R Paula12/2014
9733(22*10^47701-19)/347702Robert Price02/2017
97362^158451+10547699Lelio R Paula03/2009
97353^99972-11047699Lelio R Paula04/2012
9734(664661^8192+1)/247699Lelio R Paula12/2014
9737(664063^8192+1)/247696Lelio R Paula12/2014
97387800^12253+12253^780047690Norbert Schneider02/2014
9740(2^158420+3)/4209147685Lelio R Paula01/2012
9739(662996^8192+1)/63897747685Lelio R Paula11/2014
97415755^12682+12682^575547685Norbert Schneider01/2016
97433^99932+3^49967+547680Mike Oakes12/2010
9742(661141^8192+1)/247680Lelio R Paula12/2014
9744(11719^11719+2293)/2^2/31/220347678Makoto Morimoto07/2016
974513^42800-8047677Lelio R Paula10/2012
9746F(228223)/12285369586644810752947676Donovan Johnson05/2007
97472^158361-11269347672Enzo Doria06/2014
97482^158351-215547669Yves Minet08/2013
9749(11717^11717+4778)/5/11/4123347668Makoto Morimoto07/2016
97502^158345+67747667Lelio R Paula02/2013


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: March, 26 2017 17:51 (Time in France)

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