PRP Records

Probable Primes Top 10000

(172142 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 ?
62512^219812-314966171Yves Minet10/2009
62522^219795-61116766165Paul Bourdelais03/2013
625332455!2+51266162Robert Price02/2015
6254(27*2^219760-1)/22766154Lelio R Paula01/2014
6256(11^63521-4^63521)/766150Robert Price03/2013
62555*7^78274-666150Lelio R Paula09/2014
62572^219679-11201566130Enzo Doria05/2014
62582^219653+15015*21965366123Henri Lifchitz04/2005
62592^219600+7656166107Enzo Doria05/2016
62602^219594+25525566105Lelio R Paula10/2011
62614*7^78210-366096Lelio R Paula09/2014
6262(15185*2^219557-1)/6366096Lelio R Paula04/2015
6263(19*2^219499-1)/1366076Lelio R Paula01/2014
62642^219496+6661566075Lelio R Paula10/2011
6265(F(79021)^5-F(79020)^5)/F(79019)66057Wayne Halsdorf03/2012
6266(2^219414+7)/44365766045Lelio R Paula04/2012
6267(115*10^66043-1)/366045Serge Batalov12/2014
626810^66033+1966034Robert Price01/2011
626910^66033-7830966033Patrick De Geest05/2013
62702^219304+45424566018Henri Lifchitz03/2007
6271(27*2^219293+1)/914566012Lelio R Paula08/2012
62722^219273-11263566008Enzo Doria06/2014
62732^219250+2566001Lelio R Paula08/2011
6274132^31123+13165999Norbert Schneider03/2015
6275V(319871)65987Serge Batalov03/2015
62762^219189-19565983Lelio R Paula08/2011
6277(7*2^219143-1)/5565968Lelio R Paula01/2014
62782^219112-1700965960Enzo Doria05/2013
62792^219093-11120165954Enzo Doria05/2014
62802^219089-11209965953Enzo Doria06/2014
628146714!3+8165950Robert Price09/2014
6282(11*10^65944-131)/365945Robert Price02/2017
62832^219021-355365932Yves Minet03/2017
6284Pell-LucasQ(172243)/265931Eric W. Weisstein01/2007
62852^218990+7351965923Enzo Doria04/2016
628658^37378-5765914Norbert Schneider09/2014
6287(2^218945-7)/167565906Lelio R Paula04/2012
62882^218897-11188965895Enzo Doria05/2014
62892^218896+186945165895Enzo Doria05/2016
629063^36616+265885Lelio R Paula05/2013
6291(3*2^218822-1)/1165872Lelio R Paula01/2014
62922^218796-11329765865Enzo Doria07/2014
62932^218797+7372765865Enzo Doria04/2016
62943^138040-11065862Lelio R Paula06/2013
629511^63240-195065858Enzo Doria12/2012
62962^218764-11187365855Enzo Doria05/2014
6297(34*10^65839-7)/9/3765839Makoto Morimoto04/2016
62983^137988+2665838Lelio R Paula06/2013
62992^218680-71965830Yves Minet05/2012
630018^52424+1765807Lelio R Paula08/2013
6301(2*15683^15683+1)/73238442565789David Broadhurst09/2010
6302(23*2^218517+1)/1900365778Lelio R Paula07/2012
6303(5*10^65773+1)/365774Erik Branger12/2013
63042^218457-1732965763Enzo Doria05/2013
6305151703#+22338165759Nicolas PALAU10/2016
63062^218436+4075565756Lelio R Paula10/2011
6307(F(44)^7433-F(43)^7433)/F(42)65744Wayne Halsdorf03/2012
6308157^29934+29934^15765733Serge Batalov05/2014
6309211^28273-265715Lelio R Paula09/2013
6310(59*10^65712+31)/965713Robert Price09/2015
6311611^23586+23586^61165712Norbert Schneider08/2016
6312p(13991)#/2+3265712Robert Price12/2016
63132^218282-1848565710Enzo Doria05/2013
63142^218274-11125165708Enzo Doria05/2014
63152*F(314335)-165693Henri Lifchitz12/2009
63162^218200+42765685Henri Lifchitz01/2005
631746532!3+365667Robert Price10/2014
63182^218120-14765661Lelio R Paula08/2011
6319452^24729+24729^45265659Norbert Schneider09/2016
63202^218102-11489365656Enzo Doria05/2015
6321(15*2^218083-1)/1765650Lelio R Paula01/2014
6322(15*2^218081+1)/1894165646Lelio R Paula08/2012
632419^51326+3665634Lelio R Paula08/2013
6323(21*2^218045-1)/45158365634Lelio R Paula01/2014
63252^217989-3365622Lelio R Paula08/2011
6326(13*2^217961+1)/365614Lelio R Paula06/2012
63274*6^84315-565611Lelio R Paula09/2014
6328(315047^11933+1)/31504865607Faysal YAtim06/2008
63296^84303+5565601Lelio R Paula07/2013
6330(9787*2^217873-1)/3765589Lelio R Paula04/2015
63315*2^217858+365583Lelio R Paula04/2014
6332(19*10^65572+119)/365573Robert Price02/2017
633320^50399+5165571Lelio R Paula08/2013
633411^62946-567065552Enzo Doria01/2013
63352^217742-391165547Yves Minet08/2009
6336(19*10^65545+77)/365546Robert Price08/2016
63372^217731+13165544Lelio R Paula08/2011
63382^217720-11128765541Enzo Doria05/2014
633910^65537+2765538Robert Price01/2011
634010^65537-7685965537Patrick De Geest05/2013
6341(10223*2^217676+1)/365531Lelio R Paula06/2014
6342PadovanNumber[536485]65518Eric W. Weisstein05/2009
63437*10^65492-4765493Robert Price02/2017
63442^217547-186840765489Enzo Doria04/2016
63452^217531-11176965484Enzo Doria05/2014
63467^77484-1865482Lelio R Paula06/2013
63472^217488-11328565471Enzo Doria07/2014
6348151153#/30-3065468Henri Lifchitz12/2011
63492^217466+425765464Lelio R Paula10/2011
635046396!3-8165455Robert Price09/2014
63512^217421-11318565451Enzo Doria07/2014
6352(6883*2^217440-1)/106119329589365448Lelio R Paula04/2015
63532^217408-214565447Lelio R Paula10/2011
63542^217398-1694765444Enzo Doria05/2013
63558*5^93613+365434Lelio R Paula09/2014
635611^62828-531065429Enzo Doria01/2013
635710^65426+1365427Robert Price01/2011
63582^217341-655565427Lelio R Paula10/2011
635910^65426-5484965426Patrick De Geest05/2013
6360(21*2^217363-1)/5600362666765424Lelio R Paula01/2014
636130011^14608-10865405Enzo Doria07/2012
6362(43^40031-1)/4265388Robert Price04/2014
63632^217190+9439565381Henri Lifchitz02/2005
636415^55587+4665376Lelio R Paula08/2013
63652^217088-11183365350Enzo Doria05/2014
6366(13*2^217069-1)/168294565340Lelio R Paula01/2014
6367(62*10^65331+1)/965332Serge Batalov11/2010
63682^216947-11135165308Enzo Doria05/2014
6369-E(18022)/77520184568268532294394923506835965307Thomas Ritschel02/2017
6370(13*10^65297+83)/365298Robert Price09/2016
63715^93400-865284Lelio R Paula06/2013
63722^216802-16565264Lelio R Paula08/2011
63732^216799-2863565264Lelio R Paula10/2011
63745*10^65255+5165256Robert Price01/2017
63752^216762-16765252Lelio R Paula08/2011
637611^62657-579065251Enzo Doria01/2013
63773^136756-11288065250Enzo Doria06/2014
63782^216752+2165249Lelio R Paula08/2011
637911^62651-270065245Enzo Doria12/2012
6381Pell-LucasQ(170413)/265230Eric W. Weisstein12/2006
6380gcd(V(790525),5*F(158105)*(F(158105)+1)+1)65230Serge Batalov04/2015
6382(2^216676-1017)/63765224Lelio R Paula04/2012
63832^216652-232765219Yves Minet10/2013
6384(9179*2^216648-1)/466765218Lelio R Paula04/2015
6385(5*10^65203-119)/365204Robert Price04/2016
63862^216555-11326965190Enzo Doria07/2014
6387(9513^16384+1)/265181Henri Lifchitz02/2007
63882^216474+1291565166Lelio R Paula02/2013
638919^50958-3265163Lelio R Paula08/2013
63902^216442-11213365156Enzo Doria06/2014
63912^216437-11221365155Enzo Doria06/2014
63922^216435-11276765154Enzo Doria06/2014
63932^216420+1270565149Lelio R Paula02/2013
63948*3^136507-765132Lelio R Paula04/2014
63952^216197-11176965082Enzo Doria05/2014
63976^83631-7965078Lelio R Paula07/2013
6396572^23601+23601^57265078Norbert Schneider08/2016
6398(3^136399-7)/54422065074Lelio R Paula04/2012
63992^216154-142165069Yves Minet01/2013
64002^216145-11266365067Enzo Doria06/2014
6401132013*10^65050+2^216091-165056Gilbert Mozzo01/2014
6402132019*10^65050+2^216091-165056Gilbert Mozzo01/2014
6403148918*10^65050+2^216091-165056Gilbert Mozzo02/2014
6404194014*10^65050+2^216091-165056Gilbert Mozzo02/2014
6405223864*10^65050+2^216091-165056Gilbert Mozzo04/2014
640782090*10^65050+2^216091-165055Gilbert Mozzo07/2012
640895133*10^65050+2^216091-165055Gilbert Mozzo12/2013
640698142*10^65050+2^216091-165055Gilbert Mozzo12/2013
6409((2^216091-1)*34009-48)/2565054Serge Batalov01/2012
64105977*10^65050+2^216091-165054Gilbert Mozzo03/2012
64117*2^216091+2^298-1365051Peter Lesala03/2007
64122^216091+2*29208-165050Makoto Morimoto10/2013
6413(10^(2*32521+1)-6*10^32521-1)/365043Robert Price02/2016
641411^62439-438065024Enzo Doria01/2013
64153^136244+265005Mike Oakes11/2009
641613^58343-5064991Lelio R Paula07/2013
6417331^25791-1000264989Enzo Doria07/2012
64182^215877+13164986Lelio R Paula08/2011
64194*5^92959+964977Lelio R Paula09/2014
64202^215789-1882564959Lelio R Paula09/2011
6421(2^215801-509203)/4132764958Lelio R Paula05/2012
6422U(315311)64954Serge Batalov03/2015
642346072!3-5904964951Robert Price12/2015
64242^215750-595564948Lelio R Paula09/2011
642513^58281+4664922Lelio R Paula07/2013
64262^215623+18364909Lelio R Paula08/2011
6427(3^136043-2^136043)/(19862279*33466579)64895Mike Oakes12/2016
64285*2^215554+364889Lelio R Paula04/2014
64292^215541-11207564885Enzo Doria06/2014
64302*10^64882-364883Dmitry Domanov11/2010
643110^64862+34233964863Patrick De Geest05/2013
643210^64862-4764862Robert Price05/2011
643319^50718-8464856Lelio R Paula08/2013
6434(3045*2^215471-1)/(17*1151*27067*173473)64853Jens K. Andersen09/2007
643510^64843+427869783964844Robert Price05/2015
643610^64843+2196764844Patrick De Geest03/2016
643710^64843-34007364843Patrick De Geest03/2016
643811^62254+7064831Lelio R Paula07/2013
64392^215351-11192564828Enzo Doria05/2014
64402^215310-11764815Lelio R Paula08/2011
6441124^30958-12364809Norbert Schneider02/2015
6442(7*10^64807+17)/364808Erik Branger03/2014
6443(7*10^(2*32400+1)-27*10^32400-7)/964801Robert Price11/2015
64442^215243-1594964795Enzo Doria04/2013
644523^47581-22^4758164793Robert Price08/2012
6446(62*10^64783-17)/964784Robert Price09/2015
64475*3^135747-464769Lelio R Paula04/2014
6448(59*10^64767-41)/964768Robert Price09/2015
6450(2^215140+3)/1964763Lelio R Paula04/2012
64492^215135-1716964763Enzo Doria05/2013
64512^215115-11127764757Enzo Doria05/2014
64529*5^92641+264755Lelio R Paula09/2014
6453(5*10^64715-23)/964715Robert Price11/2014
64542^214938-178164703Yves Minet03/2013
645511^62111-42064682Enzo Doria08/2012
64565^92525+4264673Lelio R Paula06/2013
64572^214824+7189364669Enzo Doria04/2016
64582^214799-222164661Yves Minet08/2013
6459(21*2^214688+1)/29364627Lelio R Paula08/2012
646092^32907+32907^9264623Serge Batalov05/2014
64616^83013+10164597Lelio R Paula07/2013
6462p(13775)#/2+864594Robert Price01/2017
6463(7*10^64568-43)/964568Robert Price10/2014
6464Pell-LucasQ(168677)/264566Eric W. Weisstein11/2006
6465(24737*2^214476+1)/287764565Lelio R Paula06/2014
6466(47*2^214463+1)/764561Lelio R Paula04/2015
64672^214458+5461564559Lelio R Paula10/2011
6468(3^135322+7)/12291140864557Lelio R Paula04/2012
64692^214389-68311364538Paul Bourdelais03/2013
64702^214369-11124164532Enzo Doria05/2014
6471(19^50461+3^50461)/2264526Robert Price07/2013
647211^61954-366064519Enzo Doria12/2012
6473(23*2^214319-1)/2164517Lelio R Paula01/2014
6474(58695*2^214310-1)/57164516Lelio R Paula04/2015
647535^41779-3464510Norbert Schneider04/2014
647611^61939-522064503Enzo Doria01/2013
6477(2^214271+78557)/3564501Lelio R Paula05/2012
6478126^30706-12564494Norbert Schneider02/2015
6479gcd(V(1157265),5*F(231453)*(F(231453)-1)+1)64492Serge Batalov04/2015
64802^214215+1290964486Lelio R Paula10/2011
64815^92225+6664463Lelio R Paula06/2013
64822^214126-24055164459Paul Bourdelais03/2013
64838*6^82827+564453Lelio R Paula09/2014
6484(31*2^214120-1)/217048564452Lelio R Paula01/2014
6485(31*2^214088-1)/595564445Lelio R Paula01/2014
648614^56227+8964444Lelio R Paula08/2013
64892^214055-15964437Lelio R Paula08/2011
648710^64436+266764437Patrick De Geest05/2013
648865^35543-64^3554364437Robert Price08/2013
649010^64436-5364436Robert Price05/2011
6491Phi(128878,10)/3950329792764428Maksym Voznyy11/2015
64923^135027+10064425Lelio R Paula05/2013
6493(3^134972-7)/264398Lelio R Paula04/2012
64946*10^64387+764388Dmitry Domanov11/2010
64952^213864-1837764380Enzo Doria05/2013
6496(2^213821+9)/20964365Lelio R Paula04/2012
64972^213788+13564357Lelio R Paula08/2011
6498(3^134883+2)/4831364351Lelio R Paula04/2012
6499(49^38069-46^38069)/364344Serge Batalov12/2016
6500(11^61781+2^61781)/1364338Robert Price02/2013


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: March, 18 2017 12:02 (Time in France)

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