PRP Records

Probable Primes Top 10000

(252932 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 (> 50000) Who ? When ?
77522^218897-11188965895Enzo Doria05/2014
77512^218896+186945165895Enzo Doria05/2016
775363^36616+265885Lelio R Paula05/2013
7754(3*2^218822-1)/1165872Lelio R Paula01/2014
77552^218796-11329765865Enzo Doria07/2014
77562^218797+7372765865Enzo Doria04/2016
77573^138040-11065862Lelio R Paula06/2013
775811^63240-195065858Enzo Doria12/2012
77592^218764-11187365855Enzo Doria05/2014
7760(34*10^65839-7)/9/3765839Makoto Morimoto04/2016
77613^137988+2665838Lelio R Paula06/2013
77622^218680-71965830Yves Minet05/2012
776318^52424+1765807Lelio R Paula08/2013
7764(2*15683^15683+1)/73238442565789David Broadhurst09/2010
7765(23*2^218517+1)/1900365778Lelio R Paula07/2012
7766(5*10^65773+1)/365774Erik Branger12/2013
7767160^29839-15965769Norbert Schneider12/2018
77682^218457-1732965763Enzo Doria05/2013
7769151703#+22338165759Nicolas PALAU10/2016
77702^218436+4075565756Lelio R Paula10/2011
77712^218399-462765745Yves Minet05/2019
7772(F(44)^7433-F(43)^7433)/F(42)65744Wayne Halsdorf03/2012
7773157^29934+29934^15765733Serge Batalov05/2014
7774211^28273-265715Lelio R Paula09/2013
7775(59*10^65712+31)/965713Robert Price09/2015
7777611^23586+23586^61165712Norbert Schneider08/2016
7776p(13991)#/2+3265712Robert Price12/2016
77782^218282-1848565710Enzo Doria05/2013
77792^218274-11125165708Enzo Doria05/2014
77802*F(314335)-165693Henri Lifchitz12/2009
77812^218200+42765685Henri Lifchitz01/2005
7782(10199^16384+10197^16384)/265676Jeppe Stig Nielsen04/2018
7783(10199^(2^14)+(10197)^(2^14))/265676Robert Price05/2018
778446532!3+365667Robert Price10/2014
77852^218120-14765661Lelio R Paula08/2011
7786452^24729+24729^45265659Norbert Schneider09/2016
77872^218102-11489365656Enzo Doria05/2015
7788(15*2^218083-1)/1765650Lelio R Paula01/2014
7789(15*2^218081+1)/1894165646Lelio R Paula08/2012
7790(306^26407-1)/30565638Eric Chen09/2017
779219^51326+3665634Lelio R Paula08/2013
7791(21*2^218045-1)/45158365634Lelio R Paula01/2014
77932^217989-3365622Lelio R Paula08/2011
7794(13*2^217961+1)/365614Lelio R Paula06/2012
77954*6^84315-565611Lelio R Paula09/2014
7796(315047^11933+1)/31504865607Faysal YAtim06/2008
77976^84303+5565601Lelio R Paula07/2013
7798(-lucasV(1,2,435857)+2)/(173*859*8017)65595Mike Oakes04/2017
7799(9787*2^217873-1)/3765589Lelio R Paula04/2015
78005*2^217858+365583Lelio R Paula04/2014
7801(19*10^65572+119)/365573Robert Price02/2017
780220^50399+5165571Lelio R Paula08/2013
78037162^17009+17009^716265571Norbert Schneider07/2018
780411^62946-567065552Enzo Doria01/2013
78052^217742-391165547Yves Minet08/2009
7806(19*10^65545+77)/365546Robert Price08/2016
78072^217731+13165544Lelio R Paula08/2011
78082^217720-11128765541Enzo Doria05/2014
7809(365^25579+1)/36665539Eric Chen10/2017
781010^65537+2765538Robert Price01/2011
781110^65537-7685965537Patrick De Geest05/2013
7812(28*10^65532+359)/965533Robert Price11/2017
7813(10223*2^217676+1)/365531Lelio R Paula06/2014
7814PadovanNumber[536485]65518Eric W. Weisstein05/2009
78155*10^65509+2365510Robert Price11/2017
7816(8*10^65507-83)/365508Robert Price10/2017
78177*10^65492-4765493Robert Price02/2017
78182^217547-186840765489Enzo Doria04/2016
78192^217531-11176965484Enzo Doria05/2014
78207^77484-1865482Lelio R Paula06/2013
78215754^17413+17413^575465473Norbert Schneider05/2019
78222^217488-11328565471Enzo Doria07/2014
7823151153#/30-3065468Henri Lifchitz12/2011
78242^217466+425765464Lelio R Paula10/2011
782546396!3-8165455Robert Price09/2014
78262^217421-11318565451Enzo Doria07/2014
7827(6883*2^217440-1)/106119329589365448Lelio R Paula04/2015
78282^217408-214565447Lelio R Paula10/2011
78292^217398-1694765444Enzo Doria05/2013
78308*5^93613+365434Lelio R Paula09/2014
783111^62828-531065429Enzo Doria01/2013
783210^65426+1365427Robert Price01/2011
78332^217341-655565427Lelio R Paula10/2011
783410^65426-5484965426Patrick De Geest05/2013
7835(21*2^217363-1)/5600362666765424Lelio R Paula01/2014
783630011^14608-10865405Enzo Doria07/2012
7837119^31504-265389Lelio R Paula10/2017
7838(43^40031-1)/4265388Robert Price04/2014
78392^217190+9439565381Henri Lifchitz02/2005
784015^55587+4665376Lelio R Paula08/2013
78412^217088-11183365350Enzo Doria05/2014
7842(13*2^217069-1)/168294565340Lelio R Paula01/2014
7843(10^65340+47)/365340Robert Price11/2017
7844(62*10^65331+1)/965332Serge Batalov11/2010
78452^216947-11135165308Enzo Doria05/2014
7846-E(18022)/77520184568268532294394923506835965307Thomas Ritschel02/2017
7847(13*10^65297+83)/365298Robert Price09/2016
78485^93400-865284Lelio R Paula06/2013
78492^216802-16565264Lelio R Paula08/2011
78502^216799-2863565264Lelio R Paula10/2011
78515*10^65255+5165256Robert Price01/2017
78522^216762-16765252Lelio R Paula08/2011
785311^62657-579065251Enzo Doria01/2013
78543^136756-11288065250Enzo Doria06/2014
78552^216752+2165249Lelio R Paula08/2011
78563*10^65247+1165248Robert Price11/2017
785711^62651-270065245Enzo Doria12/2012
785815130^15609-15609^1513065244Norbert Schneider07/2018
7860Pell-LucasQ(170413)/265230Eric W. Weisstein12/2006
7859gcd(V(790525),5*F(158105)*(F(158105)+1)+1)65230Serge Batalov04/2015
7861(2^216676-1017)/63765224Lelio R Paula04/2012
78622^216652-232765219Yves Minet10/2013
7863(9179*2^216648-1)/466765218Lelio R Paula04/2015
7864(5*10^65203-119)/365204Robert Price04/2016
78652^216555-11326965190Enzo Doria07/2014
7866(9513^16384+1)/265181Henri Lifchitz02/2007
78672^216474+1291565166Lelio R Paula02/2013
786819^50958-3265163Lelio R Paula08/2013
78692^216442-11213365156Enzo Doria06/2014
78702^216437-11221365155Enzo Doria06/2014
78712^216435-11276765154Enzo Doria06/2014
78722^216420+1270565149Lelio R Paula02/2013
78738*3^136507-765132Lelio R Paula04/2014
7874(-lucasV(1,2,432719)-2)/(5*461)65128Mike Oakes03/2017
787515132^15575-15575^1513265102Norbert Schneider07/2018
78765*10^65086-5165087Robert Price10/2017
78772^216197-11176965082Enzo Doria05/2014
78786^83631-7965078Lelio R Paula07/2013
7879572^23601+23601^57265078Norbert Schneider08/2016
7880(3^136399-7)/54422065074Lelio R Paula04/2012
78812^216154-142165069Yves Minet01/2013
78822^216145-11266365067Enzo Doria06/2014
7883(7*10^65064+53)/365065Robert Price10/2017
7884132013*10^65050+2^216091-165056Gilbert Mozzo01/2014
7885132019*10^65050+2^216091-165056Gilbert Mozzo01/2014
7886148918*10^65050+2^216091-165056Gilbert Mozzo02/2014
7887194014*10^65050+2^216091-165056Gilbert Mozzo02/2014
7888223864*10^65050+2^216091-165056Gilbert Mozzo04/2014
789182090*10^65050+2^216091-165055Gilbert Mozzo07/2012
789095133*10^65050+2^216091-165055Gilbert Mozzo12/2013
788998142*10^65050+2^216091-165055Gilbert Mozzo12/2013
7892((2^216091-1)*34009-48)/2565054Serge Batalov01/2012
78935977*10^65050+2^216091-165054Gilbert Mozzo03/2012
78947*2^216091+2^298-1365051Peter Lesala03/2007
78952^216091+2*29208-165050Makoto Morimoto10/2013
7896(10^(2*32521+1)-6*10^32521-1)/365043Robert Price02/2016
7897p(13861)#/2+25665039Robert Price05/2017
7898(2^216091-2096)/(2^4*3*2918437*5220283)65036Makoto Morimoto10/2017
789911^62439-438065024Enzo Doria01/2013
79003^136244+265005Mike Oakes11/2009
790113^58343-5064991Lelio R Paula07/2013
7902331^25791-1000264989Enzo Doria07/2012
79032^215877+13164986Lelio R Paula08/2011
79044*5^92959+964977Lelio R Paula09/2014
79052^215789-1882564959Lelio R Paula09/2011
7906(2^215801-509203)/4132764958Lelio R Paula05/2012
7907U(315311)64954Serge Batalov03/2015
790846072!3-5904964951Robert Price12/2015
79092^215750-595564948Lelio R Paula09/2011
791013^58281+4664922Lelio R Paula07/2013
79112^215623+18364909Lelio R Paula08/2011
7912(46*10^64904+521)/964905Robert Price08/2017
7913(3^136043-2^136043)/(19862279*33466579)64895Mike Oakes12/2016
79145*2^215554+364889Lelio R Paula04/2014
79152^215541-11207564885Enzo Doria06/2014
79162*10^64882-364883Dmitry Domanov11/2010
791710^64862+34233964863Patrick De Geest05/2013
791810^64862-4764862Robert Price05/2011
791919^50718-8464856Lelio R Paula08/2013
7920(3045*2^215471-1)/(17*1151*27067*173473)64853Jens K. Andersen09/2007
792186413!6-1264846Robert Price08/2018
792310^64843+427869783964844Robert Price05/2015
792210^64843+2196764844Patrick De Geest03/2016
792410^64843-34007364843Patrick De Geest03/2016
792511^62254+7064831Lelio R Paula07/2013
79262^215351-11192564828Enzo Doria05/2014
79272^215310-11764815Lelio R Paula08/2011
7928124^30958-12364809Norbert Schneider02/2015
7929(7*10^64807+17)/364808Erik Branger03/2014
7930(7*10^(2*32400+1)-27*10^32400-7)/964801Robert Price11/2015
79312^215243-1594964795Enzo Doria04/2013
793223^47581-22^4758164793Robert Price08/2012
7933(62*10^64783-17)/964784Robert Price09/2015
79345*3^135747-464769Lelio R Paula04/2014
7935(59*10^64767-41)/964768Robert Price09/2015
7936(2^215140+3)/1964763Lelio R Paula04/2012
79372^215135-1716964763Enzo Doria05/2013
79382^215115-11127764757Enzo Doria05/2014
79399*5^92641+264755Lelio R Paula09/2014
7940(lucasV(1,2,430086)-2)/(7*1033)64731Mike Oakes03/2017
79415791^17200+17200^579164720Norbert Schneider12/2018
7942(5*10^64715-23)/964715Robert Price11/2014
79432^214938-178164703Yves Minet03/2013
794411^62111-42064682Enzo Doria08/2012
79455^92525+4264673Lelio R Paula06/2013
79462^214824+7189364669Enzo Doria04/2016
79472^214799-222164661Yves Minet08/2013
79485939^17128+17128^593964637Norbert Schneider10/2018
7949(21*2^214688+1)/29364627Lelio R Paula08/2012
795092^32907+32907^9264623Serge Batalov05/2014
7951(89*10^64608-539)/964609Robert Price11/2017
79526^83013+10164597Lelio R Paula07/2013
7953p(13775)#/2+864594Robert Price01/2017
7954(7*10^64568-43)/964568Robert Price10/2014
7955Pell-LucasQ(168677)/264566Eric W. Weisstein11/2006
7956(24737*2^214476+1)/287764565Lelio R Paula06/2014
7957(47*2^214463+1)/764561Lelio R Paula04/2015
79582^214458+5461564559Lelio R Paula10/2011
7959(3^135322+7)/12291140864557Lelio R Paula04/2012
79602^214389-68311364538Paul Bourdelais03/2013
7961(76*10^64534+113)/964535Robert Price11/2017
79622^214369-11124164532Enzo Doria05/2014
7963(19^50461+3^50461)/2264526Robert Price07/2013
796411^61954-366064519Enzo Doria12/2012
7965(23*2^214319-1)/2164517Lelio R Paula01/2014
7966(58695*2^214310-1)/57164516Lelio R Paula04/2015
79672^214300-454764511Yves Minet03/2019
796835^41779-3464510Norbert Schneider04/2014
7969(159^29303+1)/16064506Eric Chen12/2017
7970(89*10^64504-179)/964505Robert Price11/2017
797111^61939-522064503Enzo Doria01/2013
7972(2^214271+78557)/3564501Lelio R Paula05/2012
7973L(308604)+P(308604)64495Robert Price12/2017
7974126^30706-12564494Norbert Schneider02/2015
7975gcd(V(1157265),5*F(231453)*(F(231453)-1)+1)64492Serge Batalov04/2015
79762^214215+1290964486Lelio R Paula10/2011
79775^92225+6664463Lelio R Paula06/2013
79782^214126-24055164459Paul Bourdelais03/2013
79798*6^82827+564453Lelio R Paula09/2014
7980(31*2^214120-1)/217048564452Lelio R Paula01/2014
7981(31*2^214088-1)/595564445Lelio R Paula01/2014
798214^56227+8964444Lelio R Paula08/2013
79852^214055-15964437Lelio R Paula08/2011
798310^64436+266764437Patrick De Geest05/2013
798465^35543-64^3554364437Robert Price08/2013
798610^64436-5364436Robert Price05/2011
7987(3^135043-lucasV(1,3,135043)+1)/364432Paul Vanderveen11/2017
7988Phi(128878,10)/3950329792764428Maksym Voznyy11/2015
79893^135027+10064425Lelio R Paula05/2013
7990(3^134972-7)/264398Lelio R Paula04/2012
79916*10^64387+764388Dmitry Domanov11/2010
79922^213864-1837764380Enzo Doria05/2013
7993(2^213821+9)/20964365Lelio R Paula04/2012
79942^213788+13564357Lelio R Paula08/2011
799517703^4316+4316^1770364352Hans Havermann06/2019
7996(3^134883+2)/4831364351Lelio R Paula04/2012
7997(49^38069-46^38069)/364344Serge Batalov12/2016
7998(11^61781+2^61781)/1364338Robert Price02/2013
79996^82670+3764330Lelio R Paula07/2013
8000(3^134839+4)/3231295964328Lelio R Paula04/2012


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: June, 18 2019 07:14 (Time in France)

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