PRP Records

Probable Primes Top 10000

(259919 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 ?
92512^219600+7656166107Enzo Doria05/2016
92522^219594+25525566105Lelio R Paula10/2011
92534*7^78210-366096Lelio R Paula09/2014
9254(15185*2^219557-1)/6366096Lelio R Paula04/2015
9255(19*2^219499-1)/1366076Lelio R Paula01/2014
92562^219496+6661566075Lelio R Paula10/2011
9257(F(79021)^5-F(79020)^5)/F(79019)66057Wayne Halsdorf03/2012
925815871^14500+14500^1587166046Hans Havermann08/2019
9260(2^219414+7)/44365766045Lelio R Paula04/2012
9259(115*10^66043-1)/366045Serge Batalov12/2014
926110^66033+1966034Robert Price01/2011
926210^66033-7830966033Patrick De Geest05/2013
9263(2^219350+2662)/266031Stefano Morozzi12/2019
9264(lucasV(1,2,438701)+2)/759941966025Mike Oakes04/2017
92652^219304+45424566018Henri Lifchitz03/2007
9266(27*2^219293+1)/914566012Lelio R Paula08/2012
9267(2^219278+2650)/266009Stefano Morozzi12/2019
92682^219273-11263566008Enzo Doria06/2014
926917548^5771+5771^1754866003Hans Havermann08/2019
92702^219250+2566001Lelio R Paula08/2011
9271132^31123+13165999Norbert Schneider03/2015
927219327^2598+2598^1932765995Hans Havermann08/2019
927318440^3789+3789^1844065988Hans Havermann08/2019
9274V(319871)65987Serge Batalov03/2015
9275(2^219193+2166)/265984Stefano Morozzi12/2019
92762^219189-19565983Lelio R Paula08/2011
9277(2^219167+3446)/265976Stefano Morozzi12/2019
9278(7*2^219143-1)/5565968Lelio R Paula01/2014
9279(73^35401-1)/7265962Paul Bourdelais08/2017
92802^219112-1700965960Enzo Doria05/2013
92812^219093-11120165954Enzo Doria05/2014
92822^219089-11209965953Enzo Doria06/2014
928346714!3+8165950Robert Price09/2014
9284(11*10^65944-131)/365945Robert Price02/2017
9285(2^219030+2394)/265935Stefano Morozzi12/2019
92862^219021-355365932Yves Minet03/2017
9287Pell-LucasQ(172243)/265931Eric W. Weisstein01/2007
92882^218990+7351965923Enzo Doria04/2016
9289(2^218977+2634)/265919Stefano Morozzi12/2019
9290(2^218965+2354)/265915Stefano Morozzi12/2019
929158^37378-5765914Norbert Schneider09/2014
9293(2^218945-7)/167565906Lelio R Paula04/2012
92925*10^65905+8165906Robert Price08/2017
92943*10^65899-1365900Robert Price11/2017
9295(-lucasV(1,2,437845)-2)/167991765896Mike Oakes04/2017
9296127^31322-265896Lelio R Paula10/2017
92972^218897-11188965895Enzo Doria05/2014
92982^218896+186945165895Enzo Doria05/2016
9299(2^218893+3570)/265894Stefano Morozzi12/2019
930063^36616+265885Lelio R Paula05/2013
9301(3*2^218822-1)/1165872Lelio R Paula01/2014
93022^218796-11329765865Enzo Doria07/2014
93032^218797+7372765865Enzo Doria04/2016
93043^138040-11065862Lelio R Paula06/2013
930511^63240-195065858Enzo Doria12/2012
93062^218764-11187365855Enzo Doria05/2014
9307(34*10^65839-7)/9/3765839Makoto Morimoto04/2016
93083^137988+2665838Lelio R Paula06/2013
9309(2^218693+3150)/265833Stefano Morozzi12/2019
93102^218680-71965830Yves Minet05/2012
9311(2^218642+3094)/265818Stefano Morozzi12/2019
9312(2^218614+1522)/265810Stefano Morozzi12/2019
931318^52424+1765807Lelio R Paula08/2013
931419062^2827+2827^1906265790Hans Havermann08/2019
9315(2*15683^15683+1)/73238442565789David Broadhurst09/2010
9316(23*2^218517+1)/1900365778Lelio R Paula07/2012
9317(5*10^65773+1)/365774Erik Branger12/2013
9318160^29839-15965769Norbert Schneider12/2018
93192^218457-1732965763Enzo Doria05/2013
9320151703#+22338165759Nicolas PALAU10/2016
93212^218436+4075565756Lelio R Paula10/2011
93222^218399-462765745Yves Minet05/2019
9323(F(44)^7433-F(43)^7433)/F(42)65744Wayne Halsdorf03/2012
932415952^13219+13219^1595265742Hans Havermann08/2019
9325(2^218377+2894)/265738Stefano Morozzi12/2019
9326157^29934+29934^15765733Serge Batalov05/2014
9327211^28273-265715Lelio R Paula09/2013
9328(59*10^65712+31)/965713Robert Price09/2015
9331611^23586+23586^61165712Norbert Schneider08/2016
9330p(13991)#/2+3265712Robert Price12/2016
932915865^13864+13864^1586565712Hans Havermann07/2019
93322^218282-1848565710Enzo Doria05/2013
93332^218274-11125165708Enzo Doria05/2014
93342*F(314335)-165693Henri Lifchitz12/2009
9335(2^218224+3222)/265692Stefano Morozzi12/2019
93362^218200+42765685Henri Lifchitz01/2005
9337(2^218179+2838)/265679Stefano Morozzi12/2019
9338(10199^16384+10197^16384)/265676Jeppe Stig Nielsen04/2018
9339(10199^(2^14)+(10197)^(2^14))/265676Robert Price05/2018
934046532!3+365667Robert Price10/2014
93412^218120-14765661Lelio R Paula08/2011
9342452^24729+24729^45265659Norbert Schneider09/2016
93435817^17440+17440^581765657Norbert Schneider06/2019
93442^218102-11489365656Enzo Doria05/2015
9345(2^218101+1442)/265655Stefano Morozzi12/2019
9346(15*2^218083-1)/1765650Lelio R Paula01/2014
9348(15*2^218081+1)/1894165646Lelio R Paula08/2012
9347(2^218070+3610)/265646Stefano Morozzi12/2019
934915818^14115+14115^1581865640Hans Havermann08/2019
9350(306^26407-1)/30565638Eric Chen09/2017
935219^51326+3665634Lelio R Paula08/2013
9351(21*2^218045-1)/45158365634Lelio R Paula01/2014
9353(2^218010+2194)/265628Stefano Morozzi12/2019
93542^217989-3365622Lelio R Paula08/2011
9355(13*2^217961+1)/365614Lelio R Paula06/2012
93564*6^84315-565611Lelio R Paula09/2014
9357(315047^11933+1)/31504865607Faysal YAtim06/2008
93586^84303+5565601Lelio R Paula07/2013
935916585^9024+9024^1658565601Hans Havermann08/2019
936018462^3575+3575^1846265601Hans Havermann08/2019
936115963^12862+12862^1596365597Hans Havermann08/2019
9362(-lucasV(1,2,435857)+2)/(173*859*8017)65595Mike Oakes04/2017
9363(9787*2^217873-1)/3765589Lelio R Paula04/2015
93645*2^217858+365583Lelio R Paula04/2014
9365(19*10^65572+119)/365573Robert Price02/2017
936720^50399+5165571Lelio R Paula08/2013
93667162^17009+17009^716265571Norbert Schneider07/2018
936811^62946-567065552Enzo Doria01/2013
93692^217742-391165547Yves Minet08/2009
9370(19*10^65545+77)/365546Robert Price08/2016
93712^217731+13165544Lelio R Paula08/2011
93722^217720-11128765541Enzo Doria05/2014
9373(365^25579+1)/36665539Eric Chen10/2017
937410^65537+2765538Robert Price01/2011
937510^65537-7685965537Patrick De Geest05/2013
9376(28*10^65532+359)/965533Robert Price11/2017
9377(10223*2^217676+1)/365531Lelio R Paula06/2014
9378PadovanNumber[536485]65518Eric W. Weisstein05/2009
93795*10^65509+2365510Robert Price11/2017
9380(8*10^65507-83)/365508Robert Price10/2017
93817*10^65492-4765493Robert Price02/2017
93822^217547-186840765489Enzo Doria04/2016
93832^217531-11176965484Enzo Doria05/2014
93847^77484-1865482Lelio R Paula06/2013
93855754^17413+17413^575465473Norbert Schneider05/2019
93862^217488-11328565471Enzo Doria07/2014
9387(2^217488+2622)/265471Stefano Morozzi12/2019
9388151153#/30-3065468Henri Lifchitz12/2011
93892^217466+425765464Lelio R Paula10/2011
9390(2^217455+1190)/265461Stefano Morozzi12/2019
939146396!3-8165455Robert Price09/2014
93922^217421-11318565451Enzo Doria07/2014
9393(6883*2^217440-1)/106119329589365448Lelio R Paula04/2015
93942^217408-214565447Lelio R Paula10/2011
93952^217398-1694765444Enzo Doria05/2013
939616097^11628+11628^1609765443Hans Havermann07/2019
9397(2^217387+2838)/265440Stefano Morozzi12/2019
93988*5^93613+365434Lelio R Paula09/2014
939915929^12810+12810^1592965430Hans Havermann07/2019
940011^62828-531065429Enzo Doria01/2013
940110^65426+1365427Robert Price01/2011
94022^217341-655565427Lelio R Paula10/2011
940310^65426-5484965426Patrick De Geest05/2013
9404(21*2^217363-1)/5600362666765424Lelio R Paula01/2014
940530011^14608-10865405Enzo Doria07/2012
9406(2^217250+2602)/265399Stefano Morozzi12/2019
9407119^31504-265389Lelio R Paula10/2017
9408(43^40031-1)/4265388Robert Price04/2014
94092^217190+9439565381Henri Lifchitz02/2005
941015^55587+4665376Lelio R Paula08/2013
941118443^3502+3502^1844365368Hans Havermann07/2019
9412(2^217112+2386)/265357Stefano Morozzi12/2019
94132^217088-11183365350Enzo Doria05/2014
9414(2^217075+2478)/265346Stefano Morozzi12/2019
9415(2^217075+618)/265346Stefano Morozzi12/2019
9416(13*2^217069-1)/168294565340Lelio R Paula01/2014
9417(10^65340+47)/365340Robert Price11/2017
9418(62*10^65331+1)/965332Serge Batalov11/2010
9419(2^217001+2162)/265324Stefano Morozzi12/2019
94202^216947-11135165308Enzo Doria05/2014
9421-E(18022)/77520184568268532294394923506835965307Thomas Ritschel02/2017
9422(13*10^65297+83)/365298Robert Price09/2016
942316413^9502+9502^1641365288Hans Havermann07/2019
9424(2^216878+2938)/265287Stefano Morozzi12/2019
9425(2^216877+1074)/265287Stefano Morozzi12/2019
94265^93400-865284Lelio R Paula06/2013
94272^216802-16565264Lelio R Paula08/2011
94282^216799-2863565264Lelio R Paula10/2011
94295*10^65255+5165256Robert Price01/2017
94302^216762-16765252Lelio R Paula08/2011
943111^62657-579065251Enzo Doria01/2013
94323^136756-11288065250Enzo Doria06/2014
94332^216752+2165249Lelio R Paula08/2011
94343*10^65247+1165248Robert Price11/2017
943511^62651-270065245Enzo Doria12/2012
943615130^15609-15609^1513065244Norbert Schneider07/2018
9438Pell-LucasQ(170413)/265230Eric W. Weisstein12/2006
9437gcd(V(790525),5*F(158105)*(F(158105)+1)+1)65230Serge Batalov04/2015
9439(2^216684+1330)/265229Stefano Morozzi12/2019
9440(2^216676-1017)/63765224Lelio R Paula04/2012
94412^216652-232765219Yves Minet10/2013
9442(9179*2^216648-1)/466765218Lelio R Paula04/2015
9443(5*10^65203-119)/365204Robert Price04/2016
944415977^12034+12034^1597765193Hans Havermann07/2019
94452^216555-11326965190Enzo Doria07/2014
9446(2^216550+3510)/265188Stefano Morozzi12/2019
9447(2^216539+1986)/265185Stefano Morozzi12/2019
9448(2^216537+3426)/265184Stefano Morozzi12/2019
9450(9513^16384+1)/265181Henri Lifchitz02/2007
944915753^13730+13730^1575365181Hans Havermann07/2019
9451(2^216507+1274)/265175Stefano Morozzi12/2019
94522^216474+1291565166Lelio R Paula02/2013
945319^50958-3265163Lelio R Paula08/2013
94542^216442-11213365156Enzo Doria06/2014
94552^216437-11221365155Enzo Doria06/2014
94562^216435-11276765154Enzo Doria06/2014
94572^216420+1270565149Lelio R Paula02/2013
9458(2^216383+3114)/265138Stefano Morozzi12/2019
94598*3^136507-765132Lelio R Paula04/2014
9460(-lucasV(1,2,432719)-2)/(5*461)65128Mike Oakes03/2017
946116803^7496+7496^1680365109Hans Havermann07/2019
946215132^15575-15575^1513265102Norbert Schneider07/2018
9463(2^216244+1530)/265096Stefano Morozzi12/2019
94645*10^65086-5165087Robert Price10/2017
94652^216197-11176965082Enzo Doria05/2014
94676^83631-7965078Lelio R Paula07/2013
9466572^23601+23601^57265078Norbert Schneider08/2016
9468(3^136399-7)/54422065074Lelio R Paula04/2012
946915592^14911+14911^1559265074Hans Havermann07/2019
94702^216154-142165069Yves Minet01/2013
94712^216145-11266365067Enzo Doria06/2014
9472(7*10^65064+53)/365065Robert Price10/2017
9473132013*10^65050+2^216091-165056Gilbert Mozzo01/2014
9474132019*10^65050+2^216091-165056Gilbert Mozzo01/2014
9475148918*10^65050+2^216091-165056Gilbert Mozzo02/2014
9476194014*10^65050+2^216091-165056Gilbert Mozzo02/2014
9477223864*10^65050+2^216091-165056Gilbert Mozzo04/2014
947982090*10^65050+2^216091-165055Gilbert Mozzo07/2012
948095133*10^65050+2^216091-165055Gilbert Mozzo12/2013
947898142*10^65050+2^216091-165055Gilbert Mozzo12/2013
9481((2^216091-1)*34009-48)/2565054Serge Batalov01/2012
94825977*10^65050+2^216091-165054Gilbert Mozzo03/2012
9483(2^216102+2074)/265053Stefano Morozzi12/2019
94847*2^216091+2^298-1365051Peter Lesala03/2007
94852^216091+2*29208-165050Makoto Morimoto10/2013
948615845^12736+12736^1584565045Hans Havermann07/2019
9487(10^(2*32521+1)-6*10^32521-1)/365043Robert Price02/2016
9488p(13861)#/2+25665039Robert Price05/2017
9489(2^216091-2096)/(2^4*3*2918437*5220283)65036Makoto Morimoto10/2017
949011^62439-438065024Enzo Doria01/2013
949116489^8776+8776^1648965022Hans Havermann07/2019
9492(2^215959+1994)/265010Stefano Morozzi12/2019
94933^136244+265005Mike Oakes11/2009
949413^58343-5064991Lelio R Paula07/2013
9495331^25791-1000264989Enzo Doria07/2012
9496(2^215887+2090)/264989Stefano Morozzi12/2019
94972^215877+13164986Lelio R Paula08/2011
94984*5^92959+964977Lelio R Paula09/2014
9499(2^215839+2478)/264974Stefano Morozzi12/2019
9500(2^215822+702)/264969Stefano Morozzi12/2019


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: March, 29 2020 17:41 (Time in France)

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