PRP Records

Probable Primes Top 10000

(224660 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 ?
7251(27*2^219760-1)/22766154Lelio R Paula01/2014
7253(11^63521-4^63521)/766150Robert Price03/2013
72525*7^78274-666150Lelio R Paula09/2014
7254(-lucasV(1,2,439441)-2)/(3*11927*81359)66134Mike Oakes04/2017
72552^219679-11201566130Enzo Doria05/2014
72562^219653+15015*21965366123Henri Lifchitz04/2005
725715445^15782-15782^1544566108Norbert Schneider08/2018
72582^219600+7656166107Enzo Doria05/2016
72592^219594+25525566105Lelio R Paula10/2011
72604*7^78210-366096Lelio R Paula09/2014
7261(15185*2^219557-1)/6366096Lelio R Paula04/2015
7262(19*2^219499-1)/1366076Lelio R Paula01/2014
72632^219496+6661566075Lelio R Paula10/2011
7264(F(79021)^5-F(79020)^5)/F(79019)66057Wayne Halsdorf03/2012
7265(2^219414+7)/44365766045Lelio R Paula04/2012
7266(115*10^66043-1)/366045Serge Batalov12/2014
726710^66033+1966034Robert Price01/2011
726810^66033-7830966033Patrick De Geest05/2013
7269(lucasV(1,2,438701)+2)/759941966025Mike Oakes04/2017
72702^219304+45424566018Henri Lifchitz03/2007
7271(27*2^219293+1)/914566012Lelio R Paula08/2012
72722^219273-11263566008Enzo Doria06/2014
72732^219250+2566001Lelio R Paula08/2011
7274132^31123+13165999Norbert Schneider03/2015
7275V(319871)65987Serge Batalov03/2015
72762^219189-19565983Lelio R Paula08/2011
7277(7*2^219143-1)/5565968Lelio R Paula01/2014
7278(73^35401-1)/7265962Paul Bourdelais08/2017
72792^219112-1700965960Enzo Doria05/2013
72802^219093-11120165954Enzo Doria05/2014
72812^219089-11209965953Enzo Doria06/2014
728246714!3+8165950Robert Price09/2014
7283(11*10^65944-131)/365945Robert Price02/2017
72842^219021-355365932Yves Minet03/2017
7285Pell-LucasQ(172243)/265931Eric W. Weisstein01/2007
72862^218990+7351965923Enzo Doria04/2016
728758^37378-5765914Norbert Schneider09/2014
7289(2^218945-7)/167565906Lelio R Paula04/2012
72885*10^65905+8165906Robert Price08/2017
72903*10^65899-1365900Robert Price11/2017
7291(-lucasV(1,2,437845)-2)/167991765896Mike Oakes04/2017
7292127^31322-265896Lelio R Paula10/2017
72932^218897-11188965895Enzo Doria05/2014
72942^218896+186945165895Enzo Doria05/2016
729563^36616+265885Lelio R Paula05/2013
7296(3*2^218822-1)/1165872Lelio R Paula01/2014
72972^218796-11329765865Enzo Doria07/2014
72982^218797+7372765865Enzo Doria04/2016
72993^138040-11065862Lelio R Paula06/2013
730011^63240-195065858Enzo Doria12/2012
73012^218764-11187365855Enzo Doria05/2014
7302(34*10^65839-7)/9/3765839Makoto Morimoto04/2016
73033^137988+2665838Lelio R Paula06/2013
73042^218680-71965830Yves Minet05/2012
730518^52424+1765807Lelio R Paula08/2013
7306(2*15683^15683+1)/73238442565789David Broadhurst09/2010
7307(23*2^218517+1)/1900365778Lelio R Paula07/2012
7308(5*10^65773+1)/365774Erik Branger12/2013
73092^218457-1732965763Enzo Doria05/2013
7310151703#+22338165759Nicolas PALAU10/2016
73112^218436+4075565756Lelio R Paula10/2011
7312(F(44)^7433-F(43)^7433)/F(42)65744Wayne Halsdorf03/2012
7313157^29934+29934^15765733Serge Batalov05/2014
7314211^28273-265715Lelio R Paula09/2013
7315(59*10^65712+31)/965713Robert Price09/2015
7316611^23586+23586^61165712Norbert Schneider08/2016
7317p(13991)#/2+3265712Robert Price12/2016
73182^218282-1848565710Enzo Doria05/2013
73192^218274-11125165708Enzo Doria05/2014
73202*F(314335)-165693Henri Lifchitz12/2009
73212^218200+42765685Henri Lifchitz01/2005
7322(10199^16384+10197^16384)/265676Jeppe Stig Nielsen04/2018
7323(10199^(2^14)+(10197)^(2^14))/265676Robert Price05/2018
732446532!3+365667Robert Price10/2014
73252^218120-14765661Lelio R Paula08/2011
7326452^24729+24729^45265659Norbert Schneider09/2016
73272^218102-11489365656Enzo Doria05/2015
7328(15*2^218083-1)/1765650Lelio R Paula01/2014
7329(15*2^218081+1)/1894165646Lelio R Paula08/2012
7330(306^26407-1)/30565638Eric Chen09/2017
733119^51326+3665634Lelio R Paula08/2013
7332(21*2^218045-1)/45158365634Lelio R Paula01/2014
73332^217989-3365622Lelio R Paula08/2011
7334(13*2^217961+1)/365614Lelio R Paula06/2012
73354*6^84315-565611Lelio R Paula09/2014
7336(315047^11933+1)/31504865607Faysal YAtim06/2008
73376^84303+5565601Lelio R Paula07/2013
7338(-lucasV(1,2,435857)+2)/(173*859*8017)65595Mike Oakes04/2017
7339(9787*2^217873-1)/3765589Lelio R Paula04/2015
73405*2^217858+365583Lelio R Paula04/2014
7341(19*10^65572+119)/365573Robert Price02/2017
734220^50399+5165571Lelio R Paula08/2013
73437162^17009+17009^716265571Norbert Schneider07/2018
734411^62946-567065552Enzo Doria01/2013
73452^217742-391165547Yves Minet08/2009
7346(19*10^65545+77)/365546Robert Price08/2016
73472^217731+13165544Lelio R Paula08/2011
73482^217720-11128765541Enzo Doria05/2014
7349(365^25579+1)/36665539Eric Chen10/2017
735010^65537+2765538Robert Price01/2011
735110^65537-7685965537Patrick De Geest05/2013
7352(28*10^65532+359)/965533Robert Price11/2017
7353(10223*2^217676+1)/365531Lelio R Paula06/2014
7354PadovanNumber[536485]65518Eric W. Weisstein05/2009
73555*10^65509+2365510Robert Price11/2017
7356(8*10^65507-83)/365508Robert Price10/2017
73577*10^65492-4765493Robert Price02/2017
73582^217547-186840765489Enzo Doria04/2016
73592^217531-11176965484Enzo Doria05/2014
73607^77484-1865482Lelio R Paula06/2013
73612^217488-11328565471Enzo Doria07/2014
7362151153#/30-3065468Henri Lifchitz12/2011
73632^217466+425765464Lelio R Paula10/2011
736446396!3-8165455Robert Price09/2014
73652^217421-11318565451Enzo Doria07/2014
7366(6883*2^217440-1)/106119329589365448Lelio R Paula04/2015
73672^217408-214565447Lelio R Paula10/2011
73682^217398-1694765444Enzo Doria05/2013
73698*5^93613+365434Lelio R Paula09/2014
737011^62828-531065429Enzo Doria01/2013
737110^65426+1365427Robert Price01/2011
73722^217341-655565427Lelio R Paula10/2011
737310^65426-5484965426Patrick De Geest05/2013
7374(21*2^217363-1)/5600362666765424Lelio R Paula01/2014
737530011^14608-10865405Enzo Doria07/2012
7376119^31504-265389Lelio R Paula10/2017
7377(43^40031-1)/4265388Robert Price04/2014
73782^217190+9439565381Henri Lifchitz02/2005
737915^55587+4665376Lelio R Paula08/2013
73802^217088-11183365350Enzo Doria05/2014
7381(13*2^217069-1)/168294565340Lelio R Paula01/2014
7382(10^65340+47)/365340Robert Price11/2017
7383(62*10^65331+1)/965332Serge Batalov11/2010
73842^216947-11135165308Enzo Doria05/2014
7385-E(18022)/77520184568268532294394923506835965307Thomas Ritschel02/2017
7386(13*10^65297+83)/365298Robert Price09/2016
73875^93400-865284Lelio R Paula06/2013
73882^216802-16565264Lelio R Paula08/2011
73892^216799-2863565264Lelio R Paula10/2011
73905*10^65255+5165256Robert Price01/2017
73912^216762-16765252Lelio R Paula08/2011
739211^62657-579065251Enzo Doria01/2013
73933^136756-11288065250Enzo Doria06/2014
73942^216752+2165249Lelio R Paula08/2011
73953*10^65247+1165248Robert Price11/2017
739611^62651-270065245Enzo Doria12/2012
739715130^15609-15609^1513065244Norbert Schneider07/2018
7399Pell-LucasQ(170413)/265230Eric W. Weisstein12/2006
7398gcd(V(790525),5*F(158105)*(F(158105)+1)+1)65230Serge Batalov04/2015
7400(2^216676-1017)/63765224Lelio R Paula04/2012
74012^216652-232765219Yves Minet10/2013
7402(9179*2^216648-1)/466765218Lelio R Paula04/2015
7403(5*10^65203-119)/365204Robert Price04/2016
74042^216555-11326965190Enzo Doria07/2014
7405(9513^16384+1)/265181Henri Lifchitz02/2007
74062^216474+1291565166Lelio R Paula02/2013
740719^50958-3265163Lelio R Paula08/2013
74082^216442-11213365156Enzo Doria06/2014
74092^216437-11221365155Enzo Doria06/2014
74102^216435-11276765154Enzo Doria06/2014
74112^216420+1270565149Lelio R Paula02/2013
74128*3^136507-765132Lelio R Paula04/2014
7413(-lucasV(1,2,432719)-2)/(5*461)65128Mike Oakes03/2017
741415132^15575-15575^1513265102Norbert Schneider07/2018
74155*10^65086-5165087Robert Price10/2017
74162^216197-11176965082Enzo Doria05/2014
74186^83631-7965078Lelio R Paula07/2013
7417572^23601+23601^57265078Norbert Schneider08/2016
7419(3^136399-7)/54422065074Lelio R Paula04/2012
74202^216154-142165069Yves Minet01/2013
74212^216145-11266365067Enzo Doria06/2014
7422(7*10^65064+53)/365065Robert Price10/2017
7423132013*10^65050+2^216091-165056Gilbert Mozzo01/2014
7424132019*10^65050+2^216091-165056Gilbert Mozzo01/2014
7425148918*10^65050+2^216091-165056Gilbert Mozzo02/2014
7426194014*10^65050+2^216091-165056Gilbert Mozzo02/2014
7427223864*10^65050+2^216091-165056Gilbert Mozzo04/2014
743082090*10^65050+2^216091-165055Gilbert Mozzo07/2012
742995133*10^65050+2^216091-165055Gilbert Mozzo12/2013
742898142*10^65050+2^216091-165055Gilbert Mozzo12/2013
7431((2^216091-1)*34009-48)/2565054Serge Batalov01/2012
74325977*10^65050+2^216091-165054Gilbert Mozzo03/2012
74337*2^216091+2^298-1365051Peter Lesala03/2007
74342^216091+2*29208-165050Makoto Morimoto10/2013
7435(10^(2*32521+1)-6*10^32521-1)/365043Robert Price02/2016
7436p(13861)#/2+25665039Robert Price05/2017
7437(2^216091-2096)/(2^4*3*2918437*5220283)65036Makoto Morimoto10/2017
743811^62439-438065024Enzo Doria01/2013
74393^136244+265005Mike Oakes11/2009
744013^58343-5064991Lelio R Paula07/2013
7441331^25791-1000264989Enzo Doria07/2012
74422^215877+13164986Lelio R Paula08/2011
74434*5^92959+964977Lelio R Paula09/2014
74442^215789-1882564959Lelio R Paula09/2011
7445(2^215801-509203)/4132764958Lelio R Paula05/2012
7446U(315311)64954Serge Batalov03/2015
744746072!3-5904964951Robert Price12/2015
74482^215750-595564948Lelio R Paula09/2011
744913^58281+4664922Lelio R Paula07/2013
74502^215623+18364909Lelio R Paula08/2011
7451(46*10^64904+521)/964905Robert Price08/2017
7452(3^136043-2^136043)/(19862279*33466579)64895Mike Oakes12/2016
74535*2^215554+364889Lelio R Paula04/2014
74542^215541-11207564885Enzo Doria06/2014
74552*10^64882-364883Dmitry Domanov11/2010
745610^64862+34233964863Patrick De Geest05/2013
745710^64862-4764862Robert Price05/2011
745819^50718-8464856Lelio R Paula08/2013
7459(3045*2^215471-1)/(17*1151*27067*173473)64853Jens K. Andersen09/2007
746086413!6-1264846Robert Price08/2018
746110^64843+427869783964844Robert Price05/2015
746210^64843+2196764844Patrick De Geest03/2016
746310^64843-34007364843Patrick De Geest03/2016
746411^62254+7064831Lelio R Paula07/2013
74652^215351-11192564828Enzo Doria05/2014
74662^215310-11764815Lelio R Paula08/2011
7467124^30958-12364809Norbert Schneider02/2015
7468(7*10^64807+17)/364808Erik Branger03/2014
7469(7*10^(2*32400+1)-27*10^32400-7)/964801Robert Price11/2015
74702^215243-1594964795Enzo Doria04/2013
747123^47581-22^4758164793Robert Price08/2012
7472(62*10^64783-17)/964784Robert Price09/2015
74735*3^135747-464769Lelio R Paula04/2014
7474(59*10^64767-41)/964768Robert Price09/2015
7476(2^215140+3)/1964763Lelio R Paula04/2012
74752^215135-1716964763Enzo Doria05/2013
74772^215115-11127764757Enzo Doria05/2014
74789*5^92641+264755Lelio R Paula09/2014
7479(lucasV(1,2,430086)-2)/(7*1033)64731Mike Oakes03/2017
7480(5*10^64715-23)/964715Robert Price11/2014
74812^214938-178164703Yves Minet03/2013
748211^62111-42064682Enzo Doria08/2012
74835^92525+4264673Lelio R Paula06/2013
74842^214824+7189364669Enzo Doria04/2016
74852^214799-222164661Yves Minet08/2013
7486(21*2^214688+1)/29364627Lelio R Paula08/2012
748792^32907+32907^9264623Serge Batalov05/2014
7488(89*10^64608-539)/964609Robert Price11/2017
74896^83013+10164597Lelio R Paula07/2013
7490p(13775)#/2+864594Robert Price01/2017
7491(7*10^64568-43)/964568Robert Price10/2014
7492Pell-LucasQ(168677)/264566Eric W. Weisstein11/2006
7493(24737*2^214476+1)/287764565Lelio R Paula06/2014
7494(47*2^214463+1)/764561Lelio R Paula04/2015
74952^214458+5461564559Lelio R Paula10/2011
7496(3^135322+7)/12291140864557Lelio R Paula04/2012
74972^214389-68311364538Paul Bourdelais03/2013
7498(76*10^64534+113)/964535Robert Price11/2017
74992^214369-11124164532Enzo Doria05/2014
7500(19^50461+3^50461)/2264526Robert Price07/2013


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: October, 15 2018 21:33 (Time in France)

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