PRP Records

Probable Primes Top 10000

(225451 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 ?
72512^219904-1699566198Lelio R Paula10/2011
7252(3^138712-2)/529766179Lelio R Paula04/2012
7253Phi(198552,10)66177Ray Chandler07/2010
72544*6^85041+766176Lelio R Paula09/2014
72552^219812-314966171Yves Minet10/2009
72562^219795-61116766165Paul Bourdelais03/2013
725732455!2+51266162Robert Price02/2015
7258(27*2^219760-1)/22766154Lelio R Paula01/2014
7260(11^63521-4^63521)/766150Robert Price03/2013
72595*7^78274-666150Lelio R Paula09/2014
7261(-lucasV(1,2,439441)-2)/(3*11927*81359)66134Mike Oakes04/2017
72622^219679-11201566130Enzo Doria05/2014
72632^219653+15015*21965366123Henri Lifchitz04/2005
726415445^15782-15782^1544566108Norbert Schneider08/2018
72652^219600+7656166107Enzo Doria05/2016
72662^219594+25525566105Lelio R Paula10/2011
72674*7^78210-366096Lelio R Paula09/2014
7268(15185*2^219557-1)/6366096Lelio R Paula04/2015
7269(19*2^219499-1)/1366076Lelio R Paula01/2014
72702^219496+6661566075Lelio R Paula10/2011
7271(F(79021)^5-F(79020)^5)/F(79019)66057Wayne Halsdorf03/2012
7272(2^219414+7)/44365766045Lelio R Paula04/2012
7273(115*10^66043-1)/366045Serge Batalov12/2014
727410^66033+1966034Robert Price01/2011
727510^66033-7830966033Patrick De Geest05/2013
7276(lucasV(1,2,438701)+2)/759941966025Mike Oakes04/2017
72772^219304+45424566018Henri Lifchitz03/2007
7278(27*2^219293+1)/914566012Lelio R Paula08/2012
72792^219273-11263566008Enzo Doria06/2014
72802^219250+2566001Lelio R Paula08/2011
7281132^31123+13165999Norbert Schneider03/2015
7282V(319871)65987Serge Batalov03/2015
72832^219189-19565983Lelio R Paula08/2011
7284(7*2^219143-1)/5565968Lelio R Paula01/2014
7285(73^35401-1)/7265962Paul Bourdelais08/2017
72862^219112-1700965960Enzo Doria05/2013
72872^219093-11120165954Enzo Doria05/2014
72882^219089-11209965953Enzo Doria06/2014
728946714!3+8165950Robert Price09/2014
7290(11*10^65944-131)/365945Robert Price02/2017
72912^219021-355365932Yves Minet03/2017
7292Pell-LucasQ(172243)/265931Eric W. Weisstein01/2007
72932^218990+7351965923Enzo Doria04/2016
729458^37378-5765914Norbert Schneider09/2014
7296(2^218945-7)/167565906Lelio R Paula04/2012
72955*10^65905+8165906Robert Price08/2017
72973*10^65899-1365900Robert Price11/2017
7298(-lucasV(1,2,437845)-2)/167991765896Mike Oakes04/2017
7299127^31322-265896Lelio R Paula10/2017
73002^218897-11188965895Enzo Doria05/2014
73012^218896+186945165895Enzo Doria05/2016
730263^36616+265885Lelio R Paula05/2013
7303(3*2^218822-1)/1165872Lelio R Paula01/2014
73042^218796-11329765865Enzo Doria07/2014
73052^218797+7372765865Enzo Doria04/2016
73063^138040-11065862Lelio R Paula06/2013
730711^63240-195065858Enzo Doria12/2012
73082^218764-11187365855Enzo Doria05/2014
7309(34*10^65839-7)/9/3765839Makoto Morimoto04/2016
73103^137988+2665838Lelio R Paula06/2013
73112^218680-71965830Yves Minet05/2012
731218^52424+1765807Lelio R Paula08/2013
7313(2*15683^15683+1)/73238442565789David Broadhurst09/2010
7314(23*2^218517+1)/1900365778Lelio R Paula07/2012
7315(5*10^65773+1)/365774Erik Branger12/2013
73162^218457-1732965763Enzo Doria05/2013
7317151703#+22338165759Nicolas PALAU10/2016
73182^218436+4075565756Lelio R Paula10/2011
7319(F(44)^7433-F(43)^7433)/F(42)65744Wayne Halsdorf03/2012
7320157^29934+29934^15765733Serge Batalov05/2014
7321211^28273-265715Lelio R Paula09/2013
7322(59*10^65712+31)/965713Robert Price09/2015
7324611^23586+23586^61165712Norbert Schneider08/2016
7323p(13991)#/2+3265712Robert Price12/2016
73252^218282-1848565710Enzo Doria05/2013
73262^218274-11125165708Enzo Doria05/2014
73272*F(314335)-165693Henri Lifchitz12/2009
73282^218200+42765685Henri Lifchitz01/2005
7329(10199^16384+10197^16384)/265676Jeppe Stig Nielsen04/2018
7330(10199^(2^14)+(10197)^(2^14))/265676Robert Price05/2018
733146532!3+365667Robert Price10/2014
73322^218120-14765661Lelio R Paula08/2011
7333452^24729+24729^45265659Norbert Schneider09/2016
73342^218102-11489365656Enzo Doria05/2015
7335(15*2^218083-1)/1765650Lelio R Paula01/2014
7336(15*2^218081+1)/1894165646Lelio R Paula08/2012
7337(306^26407-1)/30565638Eric Chen09/2017
733819^51326+3665634Lelio R Paula08/2013
7339(21*2^218045-1)/45158365634Lelio R Paula01/2014
73402^217989-3365622Lelio R Paula08/2011
7341(13*2^217961+1)/365614Lelio R Paula06/2012
73424*6^84315-565611Lelio R Paula09/2014
7343(315047^11933+1)/31504865607Faysal YAtim06/2008
73446^84303+5565601Lelio R Paula07/2013
7345(-lucasV(1,2,435857)+2)/(173*859*8017)65595Mike Oakes04/2017
7346(9787*2^217873-1)/3765589Lelio R Paula04/2015
73475*2^217858+365583Lelio R Paula04/2014
7348(19*10^65572+119)/365573Robert Price02/2017
735020^50399+5165571Lelio R Paula08/2013
73497162^17009+17009^716265571Norbert Schneider07/2018
735111^62946-567065552Enzo Doria01/2013
73522^217742-391165547Yves Minet08/2009
7353(19*10^65545+77)/365546Robert Price08/2016
73542^217731+13165544Lelio R Paula08/2011
73552^217720-11128765541Enzo Doria05/2014
7356(365^25579+1)/36665539Eric Chen10/2017
735710^65537+2765538Robert Price01/2011
735810^65537-7685965537Patrick De Geest05/2013
7359(28*10^65532+359)/965533Robert Price11/2017
7360(10223*2^217676+1)/365531Lelio R Paula06/2014
7361PadovanNumber[536485]65518Eric W. Weisstein05/2009
73625*10^65509+2365510Robert Price11/2017
7363(8*10^65507-83)/365508Robert Price10/2017
73647*10^65492-4765493Robert Price02/2017
73652^217547-186840765489Enzo Doria04/2016
73662^217531-11176965484Enzo Doria05/2014
73677^77484-1865482Lelio R Paula06/2013
73682^217488-11328565471Enzo Doria07/2014
7369151153#/30-3065468Henri Lifchitz12/2011
73702^217466+425765464Lelio R Paula10/2011
737146396!3-8165455Robert Price09/2014
73722^217421-11318565451Enzo Doria07/2014
7373(6883*2^217440-1)/106119329589365448Lelio R Paula04/2015
73742^217408-214565447Lelio R Paula10/2011
73752^217398-1694765444Enzo Doria05/2013
73768*5^93613+365434Lelio R Paula09/2014
737711^62828-531065429Enzo Doria01/2013
737810^65426+1365427Robert Price01/2011
73792^217341-655565427Lelio R Paula10/2011
738010^65426-5484965426Patrick De Geest05/2013
7381(21*2^217363-1)/5600362666765424Lelio R Paula01/2014
738230011^14608-10865405Enzo Doria07/2012
7383119^31504-265389Lelio R Paula10/2017
7384(43^40031-1)/4265388Robert Price04/2014
73852^217190+9439565381Henri Lifchitz02/2005
738615^55587+4665376Lelio R Paula08/2013
73872^217088-11183365350Enzo Doria05/2014
7388(13*2^217069-1)/168294565340Lelio R Paula01/2014
7389(10^65340+47)/365340Robert Price11/2017
7390(62*10^65331+1)/965332Serge Batalov11/2010
73912^216947-11135165308Enzo Doria05/2014
7392-E(18022)/77520184568268532294394923506835965307Thomas Ritschel02/2017
7393(13*10^65297+83)/365298Robert Price09/2016
73945^93400-865284Lelio R Paula06/2013
73952^216802-16565264Lelio R Paula08/2011
73962^216799-2863565264Lelio R Paula10/2011
73975*10^65255+5165256Robert Price01/2017
73982^216762-16765252Lelio R Paula08/2011
739911^62657-579065251Enzo Doria01/2013
74003^136756-11288065250Enzo Doria06/2014
74012^216752+2165249Lelio R Paula08/2011
74023*10^65247+1165248Robert Price11/2017
740311^62651-270065245Enzo Doria12/2012
740415130^15609-15609^1513065244Norbert Schneider07/2018
7405Pell-LucasQ(170413)/265230Eric W. Weisstein12/2006
7406gcd(V(790525),5*F(158105)*(F(158105)+1)+1)65230Serge Batalov04/2015
7407(2^216676-1017)/63765224Lelio R Paula04/2012
74082^216652-232765219Yves Minet10/2013
7409(9179*2^216648-1)/466765218Lelio R Paula04/2015
7410(5*10^65203-119)/365204Robert Price04/2016
74112^216555-11326965190Enzo Doria07/2014
7412(9513^16384+1)/265181Henri Lifchitz02/2007
74132^216474+1291565166Lelio R Paula02/2013
741419^50958-3265163Lelio R Paula08/2013
74152^216442-11213365156Enzo Doria06/2014
74162^216437-11221365155Enzo Doria06/2014
74172^216435-11276765154Enzo Doria06/2014
74182^216420+1270565149Lelio R Paula02/2013
74198*3^136507-765132Lelio R Paula04/2014
7420(-lucasV(1,2,432719)-2)/(5*461)65128Mike Oakes03/2017
742115132^15575-15575^1513265102Norbert Schneider07/2018
74225*10^65086-5165087Robert Price10/2017
74232^216197-11176965082Enzo Doria05/2014
74256^83631-7965078Lelio R Paula07/2013
7424572^23601+23601^57265078Norbert Schneider08/2016
7426(3^136399-7)/54422065074Lelio R Paula04/2012
74272^216154-142165069Yves Minet01/2013
74282^216145-11266365067Enzo Doria06/2014
7429(7*10^65064+53)/365065Robert Price10/2017
7430132013*10^65050+2^216091-165056Gilbert Mozzo01/2014
7431132019*10^65050+2^216091-165056Gilbert Mozzo01/2014
7432148918*10^65050+2^216091-165056Gilbert Mozzo02/2014
7433194014*10^65050+2^216091-165056Gilbert Mozzo02/2014
7434223864*10^65050+2^216091-165056Gilbert Mozzo04/2014
743682090*10^65050+2^216091-165055Gilbert Mozzo07/2012
743795133*10^65050+2^216091-165055Gilbert Mozzo12/2013
743598142*10^65050+2^216091-165055Gilbert Mozzo12/2013
7438((2^216091-1)*34009-48)/2565054Serge Batalov01/2012
74395977*10^65050+2^216091-165054Gilbert Mozzo03/2012
74407*2^216091+2^298-1365051Peter Lesala03/2007
74412^216091+2*29208-165050Makoto Morimoto10/2013
7442(10^(2*32521+1)-6*10^32521-1)/365043Robert Price02/2016
7443p(13861)#/2+25665039Robert Price05/2017
7444(2^216091-2096)/(2^4*3*2918437*5220283)65036Makoto Morimoto10/2017
744511^62439-438065024Enzo Doria01/2013
74463^136244+265005Mike Oakes11/2009
744713^58343-5064991Lelio R Paula07/2013
7448331^25791-1000264989Enzo Doria07/2012
74492^215877+13164986Lelio R Paula08/2011
74504*5^92959+964977Lelio R Paula09/2014
74512^215789-1882564959Lelio R Paula09/2011
7452(2^215801-509203)/4132764958Lelio R Paula05/2012
7453U(315311)64954Serge Batalov03/2015
745446072!3-5904964951Robert Price12/2015
74552^215750-595564948Lelio R Paula09/2011
745613^58281+4664922Lelio R Paula07/2013
74572^215623+18364909Lelio R Paula08/2011
7458(46*10^64904+521)/964905Robert Price08/2017
7459(3^136043-2^136043)/(19862279*33466579)64895Mike Oakes12/2016
74605*2^215554+364889Lelio R Paula04/2014
74612^215541-11207564885Enzo Doria06/2014
74622*10^64882-364883Dmitry Domanov11/2010
746310^64862+34233964863Patrick De Geest05/2013
746410^64862-4764862Robert Price05/2011
746519^50718-8464856Lelio R Paula08/2013
7466(3045*2^215471-1)/(17*1151*27067*173473)64853Jens K. Andersen09/2007
746786413!6-1264846Robert Price08/2018
746910^64843+427869783964844Robert Price05/2015
746810^64843+2196764844Patrick De Geest03/2016
747010^64843-34007364843Patrick De Geest03/2016
747111^62254+7064831Lelio R Paula07/2013
74722^215351-11192564828Enzo Doria05/2014
74732^215310-11764815Lelio R Paula08/2011
7474124^30958-12364809Norbert Schneider02/2015
7475(7*10^64807+17)/364808Erik Branger03/2014
7476(7*10^(2*32400+1)-27*10^32400-7)/964801Robert Price11/2015
74772^215243-1594964795Enzo Doria04/2013
747823^47581-22^4758164793Robert Price08/2012
7479(62*10^64783-17)/964784Robert Price09/2015
74805*3^135747-464769Lelio R Paula04/2014
7481(59*10^64767-41)/964768Robert Price09/2015
7483(2^215140+3)/1964763Lelio R Paula04/2012
74822^215135-1716964763Enzo Doria05/2013
74842^215115-11127764757Enzo Doria05/2014
74859*5^92641+264755Lelio R Paula09/2014
7486(lucasV(1,2,430086)-2)/(7*1033)64731Mike Oakes03/2017
7487(5*10^64715-23)/964715Robert Price11/2014
74882^214938-178164703Yves Minet03/2013
748911^62111-42064682Enzo Doria08/2012
74905^92525+4264673Lelio R Paula06/2013
74912^214824+7189364669Enzo Doria04/2016
74922^214799-222164661Yves Minet08/2013
7493(21*2^214688+1)/29364627Lelio R Paula08/2012
749492^32907+32907^9264623Serge Batalov05/2014
7495(89*10^64608-539)/964609Robert Price11/2017
74966^83013+10164597Lelio R Paula07/2013
7497p(13775)#/2+864594Robert Price01/2017
7498(7*10^64568-43)/964568Robert Price10/2014
7499Pell-LucasQ(168677)/264566Eric W. Weisstein11/2006
7500(24737*2^214476+1)/287764565Lelio R Paula06/2014


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: October, 20 2018 23:15 (Time in France)

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