PRP Records

Probable Primes Top 10000

(211563 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 ?
70016^85481+8548166518Henri Lifchitz08/2014
7002(9179*2^220913-1)/39966503Lelio R Paula04/2015
700313^59687+6666488Lelio R Paula07/2013
7004(49*10^66485-31)/966486Robert Price07/2015
7005(46*10^66469+17)/966470Robert Price06/2015
70062^220790+9766465Lelio R Paula02/2012
7007(23*2^220790+1)/80766463Lelio R Paula06/2012
700840009^14441-10266460Enzo Doria07/2012
70092^220736-14366449Lelio R Paula02/2012
7010(79*10^66447-97)/9966447Ray Chandler01/2011
70112^220675+6966430Lelio R Paula02/2012
70122^220633-11138166418Enzo Doria05/2014
7013(2^220625-509203)/400032166409Lelio R Paula05/2012
70142^220596-1581366407Enzo Doria04/2013
7015(5*10^66394-17)/366395Serge Batalov05/2009
70162^220549-185917366392Enzo Doria04/2016
70172^220478-16166371Lelio R Paula02/2012
70185^94938-1463666359Enzo Doria02/2013
7019(F(67)^4861-F(66)^4861)/F(65)66353Wayne Halsdorf03/2012
70202^220253-11487166303Enzo Doria05/2015
702112^61432+9566297Lelio R Paula07/2013
70222^220192-11156366285Enzo Doria05/2014
70232^220188-11144966284Enzo Doria05/2014
7024(4*10^66284+23)/966284Robert Price11/2014
702532501!2+266266Robert Price01/2015
7026(8*10^66261-101)/366262Robert Price10/2017
70271530*10^66254+R(66254)66258Patrick De Geest05/2016
7028(47^39623-1)/4666252Robert Price06/2014
70292^220044-9730566240Lelio R Paula04/2012
7030(77*10^66237-257)/966238Robert Price10/2017
703129^45285+266225Ray Chandler08/2011
703215^56289+3866202Lelio R Paula08/2013
70333^138749+9866201Lelio R Paula06/2013
7034(21*2^219912-1)/566201Lelio R Paula01/2014
70352^219904-1699566198Lelio R Paula10/2011
7036(3^138712-2)/529766179Lelio R Paula04/2012
7037Phi(198552,10)66177Ray Chandler07/2010
70384*6^85041+766176Lelio R Paula09/2014
70392^219812-314966171Yves Minet10/2009
70402^219795-61116766165Paul Bourdelais03/2013
704132455!2+51266162Robert Price02/2015
7042(27*2^219760-1)/22766154Lelio R Paula01/2014
7044(11^63521-4^63521)/766150Robert Price03/2013
70435*7^78274-666150Lelio R Paula09/2014
7045(-lucasV(1,2,439441)-2)/(3*11927*81359)66134Mike Oakes04/2017
70462^219679-11201566130Enzo Doria05/2014
70472^219653+15015*21965366123Henri Lifchitz04/2005
70482^219600+7656166107Enzo Doria05/2016
70492^219594+25525566105Lelio R Paula10/2011
70504*7^78210-366096Lelio R Paula09/2014
7051(15185*2^219557-1)/6366096Lelio R Paula04/2015
7052(19*2^219499-1)/1366076Lelio R Paula01/2014
70532^219496+6661566075Lelio R Paula10/2011
7054(F(79021)^5-F(79020)^5)/F(79019)66057Wayne Halsdorf03/2012
7055(2^219414+7)/44365766045Lelio R Paula04/2012
7056(115*10^66043-1)/366045Serge Batalov12/2014
705710^66033+1966034Robert Price01/2011
705810^66033-7830966033Patrick De Geest05/2013
7059(lucasV(1,2,438701)+2)/759941966025Mike Oakes04/2017
70602^219304+45424566018Henri Lifchitz03/2007
7061(27*2^219293+1)/914566012Lelio R Paula08/2012
70622^219273-11263566008Enzo Doria06/2014
70632^219250+2566001Lelio R Paula08/2011
7064132^31123+13165999Norbert Schneider03/2015
7065V(319871)65987Serge Batalov03/2015
70662^219189-19565983Lelio R Paula08/2011
7067(7*2^219143-1)/5565968Lelio R Paula01/2014
7068(73^35401-1)/7265962Paul Bourdelais08/2017
70692^219112-1700965960Enzo Doria05/2013
70702^219093-11120165954Enzo Doria05/2014
70712^219089-11209965953Enzo Doria06/2014
707246714!3+8165950Robert Price09/2014
7073(11*10^65944-131)/365945Robert Price02/2017
70742^219021-355365932Yves Minet03/2017
7075Pell-LucasQ(172243)/265931Eric W. Weisstein01/2007
70762^218990+7351965923Enzo Doria04/2016
707758^37378-5765914Norbert Schneider09/2014
7079(2^218945-7)/167565906Lelio R Paula04/2012
70785*10^65905+8165906Robert Price08/2017
70803*10^65899-1365900Robert Price11/2017
7081(-lucasV(1,2,437845)-2)/167991765896Mike Oakes04/2017
7082127^31322-265896Lelio R Paula10/2017
70832^218897-11188965895Enzo Doria05/2014
70842^218896+186945165895Enzo Doria05/2016
708563^36616+265885Lelio R Paula05/2013
7086(3*2^218822-1)/1165872Lelio R Paula01/2014
70872^218796-11329765865Enzo Doria07/2014
70882^218797+7372765865Enzo Doria04/2016
70893^138040-11065862Lelio R Paula06/2013
709011^63240-195065858Enzo Doria12/2012
70912^218764-11187365855Enzo Doria05/2014
7092(34*10^65839-7)/9/3765839Makoto Morimoto04/2016
70933^137988+2665838Lelio R Paula06/2013
70942^218680-71965830Yves Minet05/2012
709518^52424+1765807Lelio R Paula08/2013
7096(2*15683^15683+1)/73238442565789David Broadhurst09/2010
7097(23*2^218517+1)/1900365778Lelio R Paula07/2012
7098(5*10^65773+1)/365774Erik Branger12/2013
70992^218457-1732965763Enzo Doria05/2013
7100151703#+22338165759Nicolas PALAU10/2016
71012^218436+4075565756Lelio R Paula10/2011
7102(F(44)^7433-F(43)^7433)/F(42)65744Wayne Halsdorf03/2012
7103157^29934+29934^15765733Serge Batalov05/2014
7104211^28273-265715Lelio R Paula09/2013
7105(59*10^65712+31)/965713Robert Price09/2015
7107611^23586+23586^61165712Norbert Schneider08/2016
7106p(13991)#/2+3265712Robert Price12/2016
71082^218282-1848565710Enzo Doria05/2013
71092^218274-11125165708Enzo Doria05/2014
71102*F(314335)-165693Henri Lifchitz12/2009
71112^218200+42765685Henri Lifchitz01/2005
7112(10199^16384+10197^16384)/265676Jeppe Stig Nielsen04/2018
7113(10199^(2^14)+(10197)^(2^14))/265676Robert Price05/2018
711446532!3+365667Robert Price10/2014
71152^218120-14765661Lelio R Paula08/2011
7116452^24729+24729^45265659Norbert Schneider09/2016
71172^218102-11489365656Enzo Doria05/2015
7118(15*2^218083-1)/1765650Lelio R Paula01/2014
7119(15*2^218081+1)/1894165646Lelio R Paula08/2012
7120(306^26407-1)/30565638Eric Chen09/2017
712219^51326+3665634Lelio R Paula08/2013
7121(21*2^218045-1)/45158365634Lelio R Paula01/2014
71232^217989-3365622Lelio R Paula08/2011
7124(13*2^217961+1)/365614Lelio R Paula06/2012
71254*6^84315-565611Lelio R Paula09/2014
7126(315047^11933+1)/31504865607Faysal YAtim06/2008
71276^84303+5565601Lelio R Paula07/2013
7128(-lucasV(1,2,435857)+2)/(173*859*8017)65595Mike Oakes04/2017
7129(9787*2^217873-1)/3765589Lelio R Paula04/2015
71305*2^217858+365583Lelio R Paula04/2014
7131(19*10^65572+119)/365573Robert Price02/2017
713220^50399+5165571Lelio R Paula08/2013
713311^62946-567065552Enzo Doria01/2013
71342^217742-391165547Yves Minet08/2009
7135(19*10^65545+77)/365546Robert Price08/2016
71362^217731+13165544Lelio R Paula08/2011
71372^217720-11128765541Enzo Doria05/2014
7138(365^25579+1)/36665539Eric Chen10/2017
713910^65537+2765538Robert Price01/2011
714010^65537-7685965537Patrick De Geest05/2013
7141(28*10^65532+359)/965533Robert Price11/2017
7142(10223*2^217676+1)/365531Lelio R Paula06/2014
7143PadovanNumber[536485]65518Eric W. Weisstein05/2009
71445*10^65509+2365510Robert Price11/2017
7145(8*10^65507-83)/365508Robert Price10/2017
71467*10^65492-4765493Robert Price02/2017
71472^217547-186840765489Enzo Doria04/2016
71482^217531-11176965484Enzo Doria05/2014
71497^77484-1865482Lelio R Paula06/2013
71502^217488-11328565471Enzo Doria07/2014
7151151153#/30-3065468Henri Lifchitz12/2011
71522^217466+425765464Lelio R Paula10/2011
715346396!3-8165455Robert Price09/2014
71542^217421-11318565451Enzo Doria07/2014
7155(6883*2^217440-1)/106119329589365448Lelio R Paula04/2015
71562^217408-214565447Lelio R Paula10/2011
71572^217398-1694765444Enzo Doria05/2013
71588*5^93613+365434Lelio R Paula09/2014
715911^62828-531065429Enzo Doria01/2013
716010^65426+1365427Robert Price01/2011
71612^217341-655565427Lelio R Paula10/2011
716210^65426-5484965426Patrick De Geest05/2013
7163(21*2^217363-1)/5600362666765424Lelio R Paula01/2014
716430011^14608-10865405Enzo Doria07/2012
7165119^31504-265389Lelio R Paula10/2017
7166(43^40031-1)/4265388Robert Price04/2014
71672^217190+9439565381Henri Lifchitz02/2005
716815^55587+4665376Lelio R Paula08/2013
71692^217088-11183365350Enzo Doria05/2014
7170(13*2^217069-1)/168294565340Lelio R Paula01/2014
7171(10^65340+47)/365340Robert Price11/2017
7172(62*10^65331+1)/965332Serge Batalov11/2010
71732^216947-11135165308Enzo Doria05/2014
7174-E(18022)/77520184568268532294394923506835965307Thomas Ritschel02/2017
7175(13*10^65297+83)/365298Robert Price09/2016
71765^93400-865284Lelio R Paula06/2013
71772^216802-16565264Lelio R Paula08/2011
71782^216799-2863565264Lelio R Paula10/2011
71795*10^65255+5165256Robert Price01/2017
71802^216762-16765252Lelio R Paula08/2011
718111^62657-579065251Enzo Doria01/2013
71823^136756-11288065250Enzo Doria06/2014
71832^216752+2165249Lelio R Paula08/2011
71843*10^65247+1165248Robert Price11/2017
718511^62651-270065245Enzo Doria12/2012
7187Pell-LucasQ(170413)/265230Eric W. Weisstein12/2006
7186gcd(V(790525),5*F(158105)*(F(158105)+1)+1)65230Serge Batalov04/2015
7188(2^216676-1017)/63765224Lelio R Paula04/2012
71892^216652-232765219Yves Minet10/2013
7190(9179*2^216648-1)/466765218Lelio R Paula04/2015
7191(5*10^65203-119)/365204Robert Price04/2016
71922^216555-11326965190Enzo Doria07/2014
7193(9513^16384+1)/265181Henri Lifchitz02/2007
71942^216474+1291565166Lelio R Paula02/2013
719519^50958-3265163Lelio R Paula08/2013
71962^216442-11213365156Enzo Doria06/2014
71972^216437-11221365155Enzo Doria06/2014
71982^216435-11276765154Enzo Doria06/2014
71992^216420+1270565149Lelio R Paula02/2013
72008*3^136507-765132Lelio R Paula04/2014
7201(-lucasV(1,2,432719)-2)/(5*461)65128Mike Oakes03/2017
72025*10^65086-5165087Robert Price10/2017
72032^216197-11176965082Enzo Doria05/2014
72046^83631-7965078Lelio R Paula07/2013
7205572^23601+23601^57265078Norbert Schneider08/2016
7206(3^136399-7)/54422065074Lelio R Paula04/2012
72072^216154-142165069Yves Minet01/2013
72082^216145-11266365067Enzo Doria06/2014
7209(7*10^65064+53)/365065Robert Price10/2017
7210132013*10^65050+2^216091-165056Gilbert Mozzo01/2014
7211132019*10^65050+2^216091-165056Gilbert Mozzo01/2014
7212148918*10^65050+2^216091-165056Gilbert Mozzo02/2014
7213194014*10^65050+2^216091-165056Gilbert Mozzo02/2014
7214223864*10^65050+2^216091-165056Gilbert Mozzo04/2014
721782090*10^65050+2^216091-165055Gilbert Mozzo07/2012
721695133*10^65050+2^216091-165055Gilbert Mozzo12/2013
721598142*10^65050+2^216091-165055Gilbert Mozzo12/2013
7218((2^216091-1)*34009-48)/2565054Serge Batalov01/2012
72195977*10^65050+2^216091-165054Gilbert Mozzo03/2012
72207*2^216091+2^298-1365051Peter Lesala03/2007
72212^216091+2*29208-165050Makoto Morimoto10/2013
7222(10^(2*32521+1)-6*10^32521-1)/365043Robert Price02/2016
7223p(13861)#/2+25665039Robert Price05/2017
7224(2^216091-2096)/(2^4*3*2918437*5220283)65036Makoto Morimoto10/2017
722511^62439-438065024Enzo Doria01/2013
72263^136244+265005Mike Oakes11/2009
722713^58343-5064991Lelio R Paula07/2013
7228331^25791-1000264989Enzo Doria07/2012
72292^215877+13164986Lelio R Paula08/2011
72304*5^92959+964977Lelio R Paula09/2014
72312^215789-1882564959Lelio R Paula09/2011
7232(2^215801-509203)/4132764958Lelio R Paula05/2012
7233U(315311)64954Serge Batalov03/2015
723446072!3-5904964951Robert Price12/2015
72352^215750-595564948Lelio R Paula09/2011
723613^58281+4664922Lelio R Paula07/2013
72372^215623+18364909Lelio R Paula08/2011
7238(46*10^64904+521)/964905Robert Price08/2017
7239(3^136043-2^136043)/(19862279*33466579)64895Mike Oakes12/2016
72405*2^215554+364889Lelio R Paula04/2014
72412^215541-11207564885Enzo Doria06/2014
72422*10^64882-364883Dmitry Domanov11/2010
724310^64862+34233964863Patrick De Geest05/2013
724410^64862-4764862Robert Price05/2011
724519^50718-8464856Lelio R Paula08/2013
7246(3045*2^215471-1)/(17*1151*27067*173473)64853Jens K. Andersen09/2007
724810^64843+427869783964844Robert Price05/2015
724710^64843+2196764844Patrick De Geest03/2016
724910^64843-34007364843Patrick De Geest03/2016
725011^62254+7064831Lelio R Paula07/2013


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: June, 18 2018 23:06 (Time in France)

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