PRP Records

Probable Primes Top 10000

(252538 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 ?
7501(77*10^66237-257)/966238Robert Price10/2017
750229^45285+266225Ray Chandler08/2011
750315^56289+3866202Lelio R Paula08/2013
75043^138749+9866201Lelio R Paula06/2013
7505(21*2^219912-1)/566201Lelio R Paula01/2014
75062^219904-1699566198Lelio R Paula10/2011
7507(3^138712-2)/529766179Lelio R Paula04/2012
7508Phi(198552,10)66177Ray Chandler07/2010
75094*6^85041+766176Lelio R Paula09/2014
75102^219812-314966171Yves Minet10/2009
75112^219795-61116766165Paul Bourdelais03/2013
751232455!2+51266162Robert Price02/2015
7513(27*2^219760-1)/22766154Lelio R Paula01/2014
7515(11^63521-4^63521)/766150Robert Price03/2013
75145*7^78274-666150Lelio R Paula09/2014
7516(-lucasV(1,2,439441)-2)/(3*11927*81359)66134Mike Oakes04/2017
75172^219679-11201566130Enzo Doria05/2014
75182^219653+15015*21965366123Henri Lifchitz04/2005
751915445^15782-15782^1544566108Norbert Schneider08/2018
75202^219600+7656166107Enzo Doria05/2016
75212^219594+25525566105Lelio R Paula10/2011
75224*7^78210-366096Lelio R Paula09/2014
7523(15185*2^219557-1)/6366096Lelio R Paula04/2015
7524(19*2^219499-1)/1366076Lelio R Paula01/2014
75252^219496+6661566075Lelio R Paula10/2011
7526(F(79021)^5-F(79020)^5)/F(79019)66057Wayne Halsdorf03/2012
7527(2^219414+7)/44365766045Lelio R Paula04/2012
7528(115*10^66043-1)/366045Serge Batalov12/2014
752910^66033+1966034Robert Price01/2011
753010^66033-7830966033Patrick De Geest05/2013
7531(lucasV(1,2,438701)+2)/759941966025Mike Oakes04/2017
75322^219304+45424566018Henri Lifchitz03/2007
7533(27*2^219293+1)/914566012Lelio R Paula08/2012
75342^219273-11263566008Enzo Doria06/2014
75352^219250+2566001Lelio R Paula08/2011
7536132^31123+13165999Norbert Schneider03/2015
7537V(319871)65987Serge Batalov03/2015
75382^219189-19565983Lelio R Paula08/2011
7539(7*2^219143-1)/5565968Lelio R Paula01/2014
7540(73^35401-1)/7265962Paul Bourdelais08/2017
75412^219112-1700965960Enzo Doria05/2013
75422^219093-11120165954Enzo Doria05/2014
75432^219089-11209965953Enzo Doria06/2014
754446714!3+8165950Robert Price09/2014
7545(11*10^65944-131)/365945Robert Price02/2017
75462^219021-355365932Yves Minet03/2017
7547Pell-LucasQ(172243)/265931Eric W. Weisstein01/2007
75482^218990+7351965923Enzo Doria04/2016
754958^37378-5765914Norbert Schneider09/2014
7551(2^218945-7)/167565906Lelio R Paula04/2012
75505*10^65905+8165906Robert Price08/2017
75523*10^65899-1365900Robert Price11/2017
7553(-lucasV(1,2,437845)-2)/167991765896Mike Oakes04/2017
7554127^31322-265896Lelio R Paula10/2017
75552^218897-11188965895Enzo Doria05/2014
75562^218896+186945165895Enzo Doria05/2016
755763^36616+265885Lelio R Paula05/2013
7558(3*2^218822-1)/1165872Lelio R Paula01/2014
75592^218796-11329765865Enzo Doria07/2014
75602^218797+7372765865Enzo Doria04/2016
75613^138040-11065862Lelio R Paula06/2013
756211^63240-195065858Enzo Doria12/2012
75632^218764-11187365855Enzo Doria05/2014
7564(34*10^65839-7)/9/3765839Makoto Morimoto04/2016
75653^137988+2665838Lelio R Paula06/2013
75662^218680-71965830Yves Minet05/2012
756718^52424+1765807Lelio R Paula08/2013
7568(2*15683^15683+1)/73238442565789David Broadhurst09/2010
7569(23*2^218517+1)/1900365778Lelio R Paula07/2012
7570(5*10^65773+1)/365774Erik Branger12/2013
7571160^29839-15965769Norbert Schneider12/2018
75722^218457-1732965763Enzo Doria05/2013
7573151703#+22338165759Nicolas PALAU10/2016
75742^218436+4075565756Lelio R Paula10/2011
7575(F(44)^7433-F(43)^7433)/F(42)65744Wayne Halsdorf03/2012
7576157^29934+29934^15765733Serge Batalov05/2014
7577211^28273-265715Lelio R Paula09/2013
7578(59*10^65712+31)/965713Robert Price09/2015
7579611^23586+23586^61165712Norbert Schneider08/2016
7580p(13991)#/2+3265712Robert Price12/2016
75812^218282-1848565710Enzo Doria05/2013
75822^218274-11125165708Enzo Doria05/2014
75832*F(314335)-165693Henri Lifchitz12/2009
75842^218200+42765685Henri Lifchitz01/2005
7585(10199^16384+10197^16384)/265676Jeppe Stig Nielsen04/2018
7586(10199^(2^14)+(10197)^(2^14))/265676Robert Price05/2018
758746532!3+365667Robert Price10/2014
75882^218120-14765661Lelio R Paula08/2011
7589452^24729+24729^45265659Norbert Schneider09/2016
75902^218102-11489365656Enzo Doria05/2015
7591(15*2^218083-1)/1765650Lelio R Paula01/2014
7592(15*2^218081+1)/1894165646Lelio R Paula08/2012
7593(306^26407-1)/30565638Eric Chen09/2017
759519^51326+3665634Lelio R Paula08/2013
7594(21*2^218045-1)/45158365634Lelio R Paula01/2014
75962^217989-3365622Lelio R Paula08/2011
7597(13*2^217961+1)/365614Lelio R Paula06/2012
75984*6^84315-565611Lelio R Paula09/2014
7599(315047^11933+1)/31504865607Faysal YAtim06/2008
76006^84303+5565601Lelio R Paula07/2013
7601(-lucasV(1,2,435857)+2)/(173*859*8017)65595Mike Oakes04/2017
7602(9787*2^217873-1)/3765589Lelio R Paula04/2015
76035*2^217858+365583Lelio R Paula04/2014
7604(19*10^65572+119)/365573Robert Price02/2017
760620^50399+5165571Lelio R Paula08/2013
76057162^17009+17009^716265571Norbert Schneider07/2018
760711^62946-567065552Enzo Doria01/2013
76082^217742-391165547Yves Minet08/2009
7609(19*10^65545+77)/365546Robert Price08/2016
76102^217731+13165544Lelio R Paula08/2011
76112^217720-11128765541Enzo Doria05/2014
7612(365^25579+1)/36665539Eric Chen10/2017
761310^65537+2765538Robert Price01/2011
761410^65537-7685965537Patrick De Geest05/2013
7615(28*10^65532+359)/965533Robert Price11/2017
7616(10223*2^217676+1)/365531Lelio R Paula06/2014
7617PadovanNumber[536485]65518Eric W. Weisstein05/2009
76185*10^65509+2365510Robert Price11/2017
7619(8*10^65507-83)/365508Robert Price10/2017
76207*10^65492-4765493Robert Price02/2017
76212^217547-186840765489Enzo Doria04/2016
76222^217531-11176965484Enzo Doria05/2014
76237^77484-1865482Lelio R Paula06/2013
76242^217488-11328565471Enzo Doria07/2014
7625151153#/30-3065468Henri Lifchitz12/2011
76262^217466+425765464Lelio R Paula10/2011
762746396!3-8165455Robert Price09/2014
76282^217421-11318565451Enzo Doria07/2014
7629(6883*2^217440-1)/106119329589365448Lelio R Paula04/2015
76302^217408-214565447Lelio R Paula10/2011
76312^217398-1694765444Enzo Doria05/2013
76328*5^93613+365434Lelio R Paula09/2014
763311^62828-531065429Enzo Doria01/2013
763410^65426+1365427Robert Price01/2011
76352^217341-655565427Lelio R Paula10/2011
763610^65426-5484965426Patrick De Geest05/2013
7637(21*2^217363-1)/5600362666765424Lelio R Paula01/2014
763830011^14608-10865405Enzo Doria07/2012
7639119^31504-265389Lelio R Paula10/2017
7640(43^40031-1)/4265388Robert Price04/2014
76412^217190+9439565381Henri Lifchitz02/2005
764215^55587+4665376Lelio R Paula08/2013
76432^217088-11183365350Enzo Doria05/2014
7644(13*2^217069-1)/168294565340Lelio R Paula01/2014
7645(10^65340+47)/365340Robert Price11/2017
7646(62*10^65331+1)/965332Serge Batalov11/2010
76472^216947-11135165308Enzo Doria05/2014
7648-E(18022)/77520184568268532294394923506835965307Thomas Ritschel02/2017
7649(13*10^65297+83)/365298Robert Price09/2016
76505^93400-865284Lelio R Paula06/2013
76512^216802-16565264Lelio R Paula08/2011
76522^216799-2863565264Lelio R Paula10/2011
76535*10^65255+5165256Robert Price01/2017
76542^216762-16765252Lelio R Paula08/2011
765511^62657-579065251Enzo Doria01/2013
76563^136756-11288065250Enzo Doria06/2014
76572^216752+2165249Lelio R Paula08/2011
76583*10^65247+1165248Robert Price11/2017
765911^62651-270065245Enzo Doria12/2012
766015130^15609-15609^1513065244Norbert Schneider07/2018
7662Pell-LucasQ(170413)/265230Eric W. Weisstein12/2006
7661gcd(V(790525),5*F(158105)*(F(158105)+1)+1)65230Serge Batalov04/2015
7663(2^216676-1017)/63765224Lelio R Paula04/2012
76642^216652-232765219Yves Minet10/2013
7665(9179*2^216648-1)/466765218Lelio R Paula04/2015
7666(5*10^65203-119)/365204Robert Price04/2016
76672^216555-11326965190Enzo Doria07/2014
7668(9513^16384+1)/265181Henri Lifchitz02/2007
76692^216474+1291565166Lelio R Paula02/2013
767019^50958-3265163Lelio R Paula08/2013
76712^216442-11213365156Enzo Doria06/2014
76722^216437-11221365155Enzo Doria06/2014
76732^216435-11276765154Enzo Doria06/2014
76742^216420+1270565149Lelio R Paula02/2013
76758*3^136507-765132Lelio R Paula04/2014
7676(-lucasV(1,2,432719)-2)/(5*461)65128Mike Oakes03/2017
767715132^15575-15575^1513265102Norbert Schneider07/2018
76785*10^65086-5165087Robert Price10/2017
76792^216197-11176965082Enzo Doria05/2014
76806^83631-7965078Lelio R Paula07/2013
7681572^23601+23601^57265078Norbert Schneider08/2016
7682(3^136399-7)/54422065074Lelio R Paula04/2012
76832^216154-142165069Yves Minet01/2013
76842^216145-11266365067Enzo Doria06/2014
7685(7*10^65064+53)/365065Robert Price10/2017
7686132013*10^65050+2^216091-165056Gilbert Mozzo01/2014
7687132019*10^65050+2^216091-165056Gilbert Mozzo01/2014
7688148918*10^65050+2^216091-165056Gilbert Mozzo02/2014
7689194014*10^65050+2^216091-165056Gilbert Mozzo02/2014
7690223864*10^65050+2^216091-165056Gilbert Mozzo04/2014
769382090*10^65050+2^216091-165055Gilbert Mozzo07/2012
769295133*10^65050+2^216091-165055Gilbert Mozzo12/2013
769198142*10^65050+2^216091-165055Gilbert Mozzo12/2013
7694((2^216091-1)*34009-48)/2565054Serge Batalov01/2012
76955977*10^65050+2^216091-165054Gilbert Mozzo03/2012
76967*2^216091+2^298-1365051Peter Lesala03/2007
76972^216091+2*29208-165050Makoto Morimoto10/2013
7698(10^(2*32521+1)-6*10^32521-1)/365043Robert Price02/2016
7699p(13861)#/2+25665039Robert Price05/2017
7700(2^216091-2096)/(2^4*3*2918437*5220283)65036Makoto Morimoto10/2017
770111^62439-438065024Enzo Doria01/2013
77023^136244+265005Mike Oakes11/2009
770313^58343-5064991Lelio R Paula07/2013
7704331^25791-1000264989Enzo Doria07/2012
77052^215877+13164986Lelio R Paula08/2011
77064*5^92959+964977Lelio R Paula09/2014
77072^215789-1882564959Lelio R Paula09/2011
7708(2^215801-509203)/4132764958Lelio R Paula05/2012
7709U(315311)64954Serge Batalov03/2015
771046072!3-5904964951Robert Price12/2015
77112^215750-595564948Lelio R Paula09/2011
771213^58281+4664922Lelio R Paula07/2013
77132^215623+18364909Lelio R Paula08/2011
7714(46*10^64904+521)/964905Robert Price08/2017
7715(3^136043-2^136043)/(19862279*33466579)64895Mike Oakes12/2016
77165*2^215554+364889Lelio R Paula04/2014
77172^215541-11207564885Enzo Doria06/2014
77182*10^64882-364883Dmitry Domanov11/2010
771910^64862+34233964863Patrick De Geest05/2013
772010^64862-4764862Robert Price05/2011
772119^50718-8464856Lelio R Paula08/2013
7722(3045*2^215471-1)/(17*1151*27067*173473)64853Jens K. Andersen09/2007
772386413!6-1264846Robert Price08/2018
772510^64843+427869783964844Robert Price05/2015
772410^64843+2196764844Patrick De Geest03/2016
772610^64843-34007364843Patrick De Geest03/2016
772711^62254+7064831Lelio R Paula07/2013
77282^215351-11192564828Enzo Doria05/2014
77292^215310-11764815Lelio R Paula08/2011
7730124^30958-12364809Norbert Schneider02/2015
7731(7*10^64807+17)/364808Erik Branger03/2014
7732(7*10^(2*32400+1)-27*10^32400-7)/964801Robert Price11/2015
77332^215243-1594964795Enzo Doria04/2013
773423^47581-22^4758164793Robert Price08/2012
7735(62*10^64783-17)/964784Robert Price09/2015
77365*3^135747-464769Lelio R Paula04/2014
7737(59*10^64767-41)/964768Robert Price09/2015
7738(2^215140+3)/1964763Lelio R Paula04/2012
77392^215135-1716964763Enzo Doria05/2013
77402^215115-11127764757Enzo Doria05/2014
77419*5^92641+264755Lelio R Paula09/2014
7742(lucasV(1,2,430086)-2)/(7*1033)64731Mike Oakes03/2017
77435791^17200+17200^579164720Norbert Schneider12/2018
7744(5*10^64715-23)/964715Robert Price11/2014
77452^214938-178164703Yves Minet03/2013
774611^62111-42064682Enzo Doria08/2012
77475^92525+4264673Lelio R Paula06/2013
77482^214824+7189364669Enzo Doria04/2016
77492^214799-222164661Yves Minet08/2013
77505939^17128+17128^593964637Norbert Schneider10/2018


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: February, 14 2019 10:37 (Time in France)

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