PRP Records

Probable Primes Top 10000

(180278 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 ?
6501(4*10^66284+23)/966284Robert Price11/2014
650232501!2+266266Robert Price01/2015
65031530*10^66254+R(66254)66258Patrick De Geest05/2016
6504(47^39623-1)/4666252Robert Price06/2014
65052^220044-9730566240Lelio R Paula04/2012
650629^45285+266225Ray Chandler08/2011
650715^56289+3866202Lelio R Paula08/2013
65083^138749+9866201Lelio R Paula06/2013
6509(21*2^219912-1)/566201Lelio R Paula01/2014
65102^219904-1699566198Lelio R Paula10/2011
6511(3^138712-2)/529766179Lelio R Paula04/2012
6512Phi(198552,10)66177Ray Chandler07/2010
65134*6^85041+766176Lelio R Paula09/2014
65142^219812-314966171Yves Minet10/2009
65152^219795-61116766165Paul Bourdelais03/2013
651632455!2+51266162Robert Price02/2015
6517(27*2^219760-1)/22766154Lelio R Paula01/2014
6519(11^63521-4^63521)/766150Robert Price03/2013
65185*7^78274-666150Lelio R Paula09/2014
6520(-lucasV(1,2,439441)-2)/(3*11927*81359)66134Mike Oakes04/2017
65212^219679-11201566130Enzo Doria05/2014
65222^219653+15015*21965366123Henri Lifchitz04/2005
65232^219600+7656166107Enzo Doria05/2016
65242^219594+25525566105Lelio R Paula10/2011
65254*7^78210-366096Lelio R Paula09/2014
6526(15185*2^219557-1)/6366096Lelio R Paula04/2015
6527(19*2^219499-1)/1366076Lelio R Paula01/2014
65282^219496+6661566075Lelio R Paula10/2011
6529(F(79021)^5-F(79020)^5)/F(79019)66057Wayne Halsdorf03/2012
6530(2^219414+7)/44365766045Lelio R Paula04/2012
6531(115*10^66043-1)/366045Serge Batalov12/2014
653210^66033+1966034Robert Price01/2011
653310^66033-7830966033Patrick De Geest05/2013
6534(lucasV(1,2,438701)+2)/759941966025Mike Oakes04/2017
65352^219304+45424566018Henri Lifchitz03/2007
6536(27*2^219293+1)/914566012Lelio R Paula08/2012
65372^219273-11263566008Enzo Doria06/2014
65382^219250+2566001Lelio R Paula08/2011
6539132^31123+13165999Norbert Schneider03/2015
6540V(319871)65987Serge Batalov03/2015
65412^219189-19565983Lelio R Paula08/2011
6542(7*2^219143-1)/5565968Lelio R Paula01/2014
65432^219112-1700965960Enzo Doria05/2013
65442^219093-11120165954Enzo Doria05/2014
65452^219089-11209965953Enzo Doria06/2014
654646714!3+8165950Robert Price09/2014
6547(11*10^65944-131)/365945Robert Price02/2017
65482^219021-355365932Yves Minet03/2017
6549Pell-LucasQ(172243)/265931Eric W. Weisstein01/2007
65502^218990+7351965923Enzo Doria04/2016
655158^37378-5765914Norbert Schneider09/2014
6552(2^218945-7)/167565906Lelio R Paula04/2012
6553(-lucasV(1,2,437845)-2)/167991765896Mike Oakes04/2017
65552^218897-11188965895Enzo Doria05/2014
65542^218896+186945165895Enzo Doria05/2016
655663^36616+265885Lelio R Paula05/2013
6557(3*2^218822-1)/1165872Lelio R Paula01/2014
65582^218796-11329765865Enzo Doria07/2014
65592^218797+7372765865Enzo Doria04/2016
65603^138040-11065862Lelio R Paula06/2013
656111^63240-195065858Enzo Doria12/2012
65622^218764-11187365855Enzo Doria05/2014
6563(34*10^65839-7)/9/3765839Makoto Morimoto04/2016
65643^137988+2665838Lelio R Paula06/2013
65652^218680-71965830Yves Minet05/2012
656618^52424+1765807Lelio R Paula08/2013
6567(2*15683^15683+1)/73238442565789David Broadhurst09/2010
6568(23*2^218517+1)/1900365778Lelio R Paula07/2012
6569(5*10^65773+1)/365774Erik Branger12/2013
65702^218457-1732965763Enzo Doria05/2013
6571151703#+22338165759Nicolas PALAU10/2016
65722^218436+4075565756Lelio R Paula10/2011
6573(F(44)^7433-F(43)^7433)/F(42)65744Wayne Halsdorf03/2012
6574157^29934+29934^15765733Serge Batalov05/2014
6575211^28273-265715Lelio R Paula09/2013
6576(59*10^65712+31)/965713Robert Price09/2015
6578611^23586+23586^61165712Norbert Schneider08/2016
6577p(13991)#/2+3265712Robert Price12/2016
65792^218282-1848565710Enzo Doria05/2013
65802^218274-11125165708Enzo Doria05/2014
65812*F(314335)-165693Henri Lifchitz12/2009
65822^218200+42765685Henri Lifchitz01/2005
658346532!3+365667Robert Price10/2014
65842^218120-14765661Lelio R Paula08/2011
6585452^24729+24729^45265659Norbert Schneider09/2016
65862^218102-11489365656Enzo Doria05/2015
6587(15*2^218083-1)/1765650Lelio R Paula01/2014
6588(15*2^218081+1)/1894165646Lelio R Paula08/2012
658919^51326+3665634Lelio R Paula08/2013
6590(21*2^218045-1)/45158365634Lelio R Paula01/2014
65912^217989-3365622Lelio R Paula08/2011
6592(13*2^217961+1)/365614Lelio R Paula06/2012
65934*6^84315-565611Lelio R Paula09/2014
6594(315047^11933+1)/31504865607Faysal YAtim06/2008
65956^84303+5565601Lelio R Paula07/2013
6596(-lucasV(1,2,435857)+2)/(173*859*8017)65595Mike Oakes04/2017
6597(9787*2^217873-1)/3765589Lelio R Paula04/2015
65985*2^217858+365583Lelio R Paula04/2014
6599(19*10^65572+119)/365573Robert Price02/2017
660020^50399+5165571Lelio R Paula08/2013
660111^62946-567065552Enzo Doria01/2013
66022^217742-391165547Yves Minet08/2009
6603(19*10^65545+77)/365546Robert Price08/2016
66042^217731+13165544Lelio R Paula08/2011
66052^217720-11128765541Enzo Doria05/2014
660610^65537+2765538Robert Price01/2011
660710^65537-7685965537Patrick De Geest05/2013
6608(10223*2^217676+1)/365531Lelio R Paula06/2014
6609PadovanNumber[536485]65518Eric W. Weisstein05/2009
66107*10^65492-4765493Robert Price02/2017
66112^217547-186840765489Enzo Doria04/2016
66122^217531-11176965484Enzo Doria05/2014
66137^77484-1865482Lelio R Paula06/2013
66142^217488-11328565471Enzo Doria07/2014
6615151153#/30-3065468Henri Lifchitz12/2011
66162^217466+425765464Lelio R Paula10/2011
661746396!3-8165455Robert Price09/2014
66182^217421-11318565451Enzo Doria07/2014
6619(6883*2^217440-1)/106119329589365448Lelio R Paula04/2015
66202^217408-214565447Lelio R Paula10/2011
66212^217398-1694765444Enzo Doria05/2013
66228*5^93613+365434Lelio R Paula09/2014
662311^62828-531065429Enzo Doria01/2013
662410^65426+1365427Robert Price01/2011
66252^217341-655565427Lelio R Paula10/2011
662610^65426-5484965426Patrick De Geest05/2013
6627(21*2^217363-1)/5600362666765424Lelio R Paula01/2014
662830011^14608-10865405Enzo Doria07/2012
6629(43^40031-1)/4265388Robert Price04/2014
66302^217190+9439565381Henri Lifchitz02/2005
663115^55587+4665376Lelio R Paula08/2013
66322^217088-11183365350Enzo Doria05/2014
6633(13*2^217069-1)/168294565340Lelio R Paula01/2014
6634(62*10^65331+1)/965332Serge Batalov11/2010
66352^216947-11135165308Enzo Doria05/2014
6636-E(18022)/77520184568268532294394923506835965307Thomas Ritschel02/2017
6637(13*10^65297+83)/365298Robert Price09/2016
66385^93400-865284Lelio R Paula06/2013
66392^216802-16565264Lelio R Paula08/2011
66402^216799-2863565264Lelio R Paula10/2011
66415*10^65255+5165256Robert Price01/2017
66422^216762-16765252Lelio R Paula08/2011
664311^62657-579065251Enzo Doria01/2013
66443^136756-11288065250Enzo Doria06/2014
66452^216752+2165249Lelio R Paula08/2011
664611^62651-270065245Enzo Doria12/2012
6648Pell-LucasQ(170413)/265230Eric W. Weisstein12/2006
6647gcd(V(790525),5*F(158105)*(F(158105)+1)+1)65230Serge Batalov04/2015
6649(2^216676-1017)/63765224Lelio R Paula04/2012
66502^216652-232765219Yves Minet10/2013
6651(9179*2^216648-1)/466765218Lelio R Paula04/2015
6652(5*10^65203-119)/365204Robert Price04/2016
66532^216555-11326965190Enzo Doria07/2014
6654(9513^16384+1)/265181Henri Lifchitz02/2007
66552^216474+1291565166Lelio R Paula02/2013
665619^50958-3265163Lelio R Paula08/2013
66572^216442-11213365156Enzo Doria06/2014
66582^216437-11221365155Enzo Doria06/2014
66592^216435-11276765154Enzo Doria06/2014
66602^216420+1270565149Lelio R Paula02/2013
66618*3^136507-765132Lelio R Paula04/2014
6662(-lucasV(1,2,432719)-2)/(5*461)65128Mike Oakes03/2017
66632^216197-11176965082Enzo Doria05/2014
66646^83631-7965078Lelio R Paula07/2013
6665572^23601+23601^57265078Norbert Schneider08/2016
6666(3^136399-7)/54422065074Lelio R Paula04/2012
66672^216154-142165069Yves Minet01/2013
66682^216145-11266365067Enzo Doria06/2014
6669132013*10^65050+2^216091-165056Gilbert Mozzo01/2014
6670132019*10^65050+2^216091-165056Gilbert Mozzo01/2014
6671148918*10^65050+2^216091-165056Gilbert Mozzo02/2014
6672194014*10^65050+2^216091-165056Gilbert Mozzo02/2014
6673223864*10^65050+2^216091-165056Gilbert Mozzo04/2014
667682090*10^65050+2^216091-165055Gilbert Mozzo07/2012
667595133*10^65050+2^216091-165055Gilbert Mozzo12/2013
667498142*10^65050+2^216091-165055Gilbert Mozzo12/2013
6677((2^216091-1)*34009-48)/2565054Serge Batalov01/2012
66785977*10^65050+2^216091-165054Gilbert Mozzo03/2012
66797*2^216091+2^298-1365051Peter Lesala03/2007
66802^216091+2*29208-165050Makoto Morimoto10/2013
6681(10^(2*32521+1)-6*10^32521-1)/365043Robert Price02/2016
6682p(13861)#/2+25665039Robert Price05/2017
668311^62439-438065024Enzo Doria01/2013
66843^136244+265005Mike Oakes11/2009
668513^58343-5064991Lelio R Paula07/2013
6686331^25791-1000264989Enzo Doria07/2012
66872^215877+13164986Lelio R Paula08/2011
66884*5^92959+964977Lelio R Paula09/2014
66892^215789-1882564959Lelio R Paula09/2011
6690(2^215801-509203)/4132764958Lelio R Paula05/2012
6691U(315311)64954Serge Batalov03/2015
669246072!3-5904964951Robert Price12/2015
66932^215750-595564948Lelio R Paula09/2011
669413^58281+4664922Lelio R Paula07/2013
66952^215623+18364909Lelio R Paula08/2011
6696(3^136043-2^136043)/(19862279*33466579)64895Mike Oakes12/2016
66975*2^215554+364889Lelio R Paula04/2014
66982^215541-11207564885Enzo Doria06/2014
66992*10^64882-364883Dmitry Domanov11/2010
670010^64862+34233964863Patrick De Geest05/2013
670110^64862-4764862Robert Price05/2011
670219^50718-8464856Lelio R Paula08/2013
6703(3045*2^215471-1)/(17*1151*27067*173473)64853Jens K. Andersen09/2007
670510^64843+427869783964844Robert Price05/2015
670410^64843+2196764844Patrick De Geest03/2016
670610^64843-34007364843Patrick De Geest03/2016
670711^62254+7064831Lelio R Paula07/2013
67082^215351-11192564828Enzo Doria05/2014
67092^215310-11764815Lelio R Paula08/2011
6710124^30958-12364809Norbert Schneider02/2015
6711(7*10^64807+17)/364808Erik Branger03/2014
6712(7*10^(2*32400+1)-27*10^32400-7)/964801Robert Price11/2015
67132^215243-1594964795Enzo Doria04/2013
671423^47581-22^4758164793Robert Price08/2012
6715(62*10^64783-17)/964784Robert Price09/2015
67165*3^135747-464769Lelio R Paula04/2014
6717(59*10^64767-41)/964768Robert Price09/2015
6719(2^215140+3)/1964763Lelio R Paula04/2012
67182^215135-1716964763Enzo Doria05/2013
67202^215115-11127764757Enzo Doria05/2014
67219*5^92641+264755Lelio R Paula09/2014
6722(lucasV(1,2,430086)-2)/(7*1033)64731Mike Oakes03/2017
6723(5*10^64715-23)/964715Robert Price11/2014
67242^214938-178164703Yves Minet03/2013
672511^62111-42064682Enzo Doria08/2012
67265^92525+4264673Lelio R Paula06/2013
67272^214824+7189364669Enzo Doria04/2016
67282^214799-222164661Yves Minet08/2013
6729(21*2^214688+1)/29364627Lelio R Paula08/2012
673092^32907+32907^9264623Serge Batalov05/2014
67316^83013+10164597Lelio R Paula07/2013
6732p(13775)#/2+864594Robert Price01/2017
6733(7*10^64568-43)/964568Robert Price10/2014
6734Pell-LucasQ(168677)/264566Eric W. Weisstein11/2006
6735(24737*2^214476+1)/287764565Lelio R Paula06/2014
6736(47*2^214463+1)/764561Lelio R Paula04/2015
67372^214458+5461564559Lelio R Paula10/2011
6738(3^135322+7)/12291140864557Lelio R Paula04/2012
67392^214389-68311364538Paul Bourdelais03/2013
67402^214369-11124164532Enzo Doria05/2014
6741(19^50461+3^50461)/2264526Robert Price07/2013
674211^61954-366064519Enzo Doria12/2012
6743(23*2^214319-1)/2164517Lelio R Paula01/2014
6744(58695*2^214310-1)/57164516Lelio R Paula04/2015
674535^41779-3464510Norbert Schneider04/2014
674611^61939-522064503Enzo Doria01/2013
6747(2^214271+78557)/3564501Lelio R Paula05/2012
6748126^30706-12564494Norbert Schneider02/2015
6749gcd(V(1157265),5*F(231453)*(F(231453)-1)+1)64492Serge Batalov04/2015
67502^214215+1290964486Lelio R Paula10/2011


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: August, 20 2017 08:36 (Time in France)

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