PRP Records

Probable Primes Top 10000

(205869 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) !!!


Submit your PRPs


See the Top discoverers
See the Latest PRPs
Search by form



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 ?
70012^219021-355365932Yves Minet03/2017
7002Pell-LucasQ(172243)/265931Eric W. Weisstein01/2007
70032^218990+7351965923Enzo Doria04/2016
700458^37378-5765914Norbert Schneider09/2014
7006(2^218945-7)/167565906Lelio R Paula04/2012
70055*10^65905+8165906Robert Price08/2017
70073*10^65899-1365900Robert Price11/2017
7008(-lucasV(1,2,437845)-2)/167991765896Mike Oakes04/2017
7009127^31322-265896Lelio R Paula10/2017
70102^218897-11188965895Enzo Doria05/2014
70112^218896+186945165895Enzo Doria05/2016
701263^36616+265885Lelio R Paula05/2013
7013(3*2^218822-1)/1165872Lelio R Paula01/2014
70142^218796-11329765865Enzo Doria07/2014
70152^218797+7372765865Enzo Doria04/2016
70163^138040-11065862Lelio R Paula06/2013
701711^63240-195065858Enzo Doria12/2012
70182^218764-11187365855Enzo Doria05/2014
7019(34*10^65839-7)/9/3765839Makoto Morimoto04/2016
70203^137988+2665838Lelio R Paula06/2013
70212^218680-71965830Yves Minet05/2012
702218^52424+1765807Lelio R Paula08/2013
7023(2*15683^15683+1)/73238442565789David Broadhurst09/2010
7024(23*2^218517+1)/1900365778Lelio R Paula07/2012
7025(5*10^65773+1)/365774Erik Branger12/2013
70262^218457-1732965763Enzo Doria05/2013
7027151703#+22338165759Nicolas PALAU10/2016
70282^218436+4075565756Lelio R Paula10/2011
7029(F(44)^7433-F(43)^7433)/F(42)65744Wayne Halsdorf03/2012
7030157^29934+29934^15765733Serge Batalov05/2014
7031211^28273-265715Lelio R Paula09/2013
7032(59*10^65712+31)/965713Robert Price09/2015
7034611^23586+23586^61165712Norbert Schneider08/2016
7033p(13991)#/2+3265712Robert Price12/2016
70352^218282-1848565710Enzo Doria05/2013
70362^218274-11125165708Enzo Doria05/2014
70372*F(314335)-165693Henri Lifchitz12/2009
70382^218200+42765685Henri Lifchitz01/2005
7039(10199^16384+10197^16384)/265676Jeppe Stig Nielsen04/2018
704046532!3+365667Robert Price10/2014
70412^218120-14765661Lelio R Paula08/2011
7042452^24729+24729^45265659Norbert Schneider09/2016
70432^218102-11489365656Enzo Doria05/2015
7044(15*2^218083-1)/1765650Lelio R Paula01/2014
7045(15*2^218081+1)/1894165646Lelio R Paula08/2012
7046(306^26407-1)/30565638Eric Chen09/2017
704819^51326+3665634Lelio R Paula08/2013
7047(21*2^218045-1)/45158365634Lelio R Paula01/2014
70492^217989-3365622Lelio R Paula08/2011
7050(13*2^217961+1)/365614Lelio R Paula06/2012
70514*6^84315-565611Lelio R Paula09/2014
7052(315047^11933+1)/31504865607Faysal YAtim06/2008
70536^84303+5565601Lelio R Paula07/2013
7054(-lucasV(1,2,435857)+2)/(173*859*8017)65595Mike Oakes04/2017
7055(9787*2^217873-1)/3765589Lelio R Paula04/2015
70565*2^217858+365583Lelio R Paula04/2014
7057(19*10^65572+119)/365573Robert Price02/2017
705820^50399+5165571Lelio R Paula08/2013
705911^62946-567065552Enzo Doria01/2013
70602^217742-391165547Yves Minet08/2009
7061(19*10^65545+77)/365546Robert Price08/2016
70622^217731+13165544Lelio R Paula08/2011
70632^217720-11128765541Enzo Doria05/2014
7064(365^25579+1)/36665539Eric Chen10/2017
706510^65537+2765538Robert Price01/2011
706610^65537-7685965537Patrick De Geest05/2013
7067(28*10^65532+359)/965533Robert Price11/2017
7068(10223*2^217676+1)/365531Lelio R Paula06/2014
7069PadovanNumber[536485]65518Eric W. Weisstein05/2009
70705*10^65509+2365510Robert Price11/2017
7071(8*10^65507-83)/365508Robert Price10/2017
70727*10^65492-4765493Robert Price02/2017
70732^217547-186840765489Enzo Doria04/2016
70742^217531-11176965484Enzo Doria05/2014
70757^77484-1865482Lelio R Paula06/2013
70762^217488-11328565471Enzo Doria07/2014
7077151153#/30-3065468Henri Lifchitz12/2011
70782^217466+425765464Lelio R Paula10/2011
707946396!3-8165455Robert Price09/2014
70802^217421-11318565451Enzo Doria07/2014
7081(6883*2^217440-1)/106119329589365448Lelio R Paula04/2015
70822^217408-214565447Lelio R Paula10/2011
70832^217398-1694765444Enzo Doria05/2013
70848*5^93613+365434Lelio R Paula09/2014
708511^62828-531065429Enzo Doria01/2013
708610^65426+1365427Robert Price01/2011
70872^217341-655565427Lelio R Paula10/2011
708810^65426-5484965426Patrick De Geest05/2013
7089(21*2^217363-1)/5600362666765424Lelio R Paula01/2014
709030011^14608-10865405Enzo Doria07/2012
7091119^31504-265389Lelio R Paula10/2017
7092(43^40031-1)/4265388Robert Price04/2014
70932^217190+9439565381Henri Lifchitz02/2005
709415^55587+4665376Lelio R Paula08/2013
70952^217088-11183365350Enzo Doria05/2014
7096(13*2^217069-1)/168294565340Lelio R Paula01/2014
7097(10^65340+47)/365340Robert Price11/2017
7098(62*10^65331+1)/965332Serge Batalov11/2010
70992^216947-11135165308Enzo Doria05/2014
7100-E(18022)/77520184568268532294394923506835965307Thomas Ritschel02/2017
7101(13*10^65297+83)/365298Robert Price09/2016
71025^93400-865284Lelio R Paula06/2013
71032^216802-16565264Lelio R Paula08/2011
71042^216799-2863565264Lelio R Paula10/2011
71055*10^65255+5165256Robert Price01/2017
71062^216762-16765252Lelio R Paula08/2011
710711^62657-579065251Enzo Doria01/2013
71083^136756-11288065250Enzo Doria06/2014
71092^216752+2165249Lelio R Paula08/2011
71103*10^65247+1165248Robert Price11/2017
711111^62651-270065245Enzo Doria12/2012
7113Pell-LucasQ(170413)/265230Eric W. Weisstein12/2006
7112gcd(V(790525),5*F(158105)*(F(158105)+1)+1)65230Serge Batalov04/2015
7114(2^216676-1017)/63765224Lelio R Paula04/2012
71152^216652-232765219Yves Minet10/2013
7116(9179*2^216648-1)/466765218Lelio R Paula04/2015
7117(5*10^65203-119)/365204Robert Price04/2016
71182^216555-11326965190Enzo Doria07/2014
7119(9513^16384+1)/265181Henri Lifchitz02/2007
71202^216474+1291565166Lelio R Paula02/2013
712119^50958-3265163Lelio R Paula08/2013
71222^216442-11213365156Enzo Doria06/2014
71232^216437-11221365155Enzo Doria06/2014
71242^216435-11276765154Enzo Doria06/2014
71252^216420+1270565149Lelio R Paula02/2013
71268*3^136507-765132Lelio R Paula04/2014
7127(-lucasV(1,2,432719)-2)/(5*461)65128Mike Oakes03/2017
71285*10^65086-5165087Robert Price10/2017
71292^216197-11176965082Enzo Doria05/2014
71306^83631-7965078Lelio R Paula07/2013
7131572^23601+23601^57265078Norbert Schneider08/2016
7132(3^136399-7)/54422065074Lelio R Paula04/2012
71332^216154-142165069Yves Minet01/2013
71342^216145-11266365067Enzo Doria06/2014
7135(7*10^65064+53)/365065Robert Price10/2017
7136132013*10^65050+2^216091-165056Gilbert Mozzo01/2014
7137132019*10^65050+2^216091-165056Gilbert Mozzo01/2014
7138148918*10^65050+2^216091-165056Gilbert Mozzo02/2014
7139194014*10^65050+2^216091-165056Gilbert Mozzo02/2014
7140223864*10^65050+2^216091-165056Gilbert Mozzo04/2014
714282090*10^65050+2^216091-165055Gilbert Mozzo07/2012
714395133*10^65050+2^216091-165055Gilbert Mozzo12/2013
714198142*10^65050+2^216091-165055Gilbert Mozzo12/2013
7144((2^216091-1)*34009-48)/2565054Serge Batalov01/2012
71455977*10^65050+2^216091-165054Gilbert Mozzo03/2012
71467*2^216091+2^298-1365051Peter Lesala03/2007
71472^216091+2*29208-165050Makoto Morimoto10/2013
7148(10^(2*32521+1)-6*10^32521-1)/365043Robert Price02/2016
7149p(13861)#/2+25665039Robert Price05/2017
7150(2^216091-2096)/(2^4*3*2918437*5220283)65036Makoto Morimoto10/2017
715111^62439-438065024Enzo Doria01/2013
71523^136244+265005Mike Oakes11/2009
715313^58343-5064991Lelio R Paula07/2013
7154331^25791-1000264989Enzo Doria07/2012
71552^215877+13164986Lelio R Paula08/2011
71564*5^92959+964977Lelio R Paula09/2014
71572^215789-1882564959Lelio R Paula09/2011
7158(2^215801-509203)/4132764958Lelio R Paula05/2012
7159U(315311)64954Serge Batalov03/2015
716046072!3-5904964951Robert Price12/2015
71612^215750-595564948Lelio R Paula09/2011
716213^58281+4664922Lelio R Paula07/2013
71632^215623+18364909Lelio R Paula08/2011
7164(46*10^64904+521)/964905Robert Price08/2017
7165(3^136043-2^136043)/(19862279*33466579)64895Mike Oakes12/2016
71665*2^215554+364889Lelio R Paula04/2014
71672^215541-11207564885Enzo Doria06/2014
71682*10^64882-364883Dmitry Domanov11/2010
716910^64862+34233964863Patrick De Geest05/2013
717010^64862-4764862Robert Price05/2011
717119^50718-8464856Lelio R Paula08/2013
7172(3045*2^215471-1)/(17*1151*27067*173473)64853Jens K. Andersen09/2007
717410^64843+427869783964844Robert Price05/2015
717310^64843+2196764844Patrick De Geest03/2016
717510^64843-34007364843Patrick De Geest03/2016
717611^62254+7064831Lelio R Paula07/2013
71772^215351-11192564828Enzo Doria05/2014
71782^215310-11764815Lelio R Paula08/2011
7179124^30958-12364809Norbert Schneider02/2015
7180(7*10^64807+17)/364808Erik Branger03/2014
7181(7*10^(2*32400+1)-27*10^32400-7)/964801Robert Price11/2015
71822^215243-1594964795Enzo Doria04/2013
718323^47581-22^4758164793Robert Price08/2012
7184(62*10^64783-17)/964784Robert Price09/2015
71855*3^135747-464769Lelio R Paula04/2014
7186(59*10^64767-41)/964768Robert Price09/2015
7188(2^215140+3)/1964763Lelio R Paula04/2012
71872^215135-1716964763Enzo Doria05/2013
71892^215115-11127764757Enzo Doria05/2014
71909*5^92641+264755Lelio R Paula09/2014
7191(lucasV(1,2,430086)-2)/(7*1033)64731Mike Oakes03/2017
7192(5*10^64715-23)/964715Robert Price11/2014
71932^214938-178164703Yves Minet03/2013
719411^62111-42064682Enzo Doria08/2012
71955^92525+4264673Lelio R Paula06/2013
71962^214824+7189364669Enzo Doria04/2016
71972^214799-222164661Yves Minet08/2013
7198(21*2^214688+1)/29364627Lelio R Paula08/2012
719992^32907+32907^9264623Serge Batalov05/2014
7200(89*10^64608-539)/964609Robert Price11/2017
72016^83013+10164597Lelio R Paula07/2013
7202p(13775)#/2+864594Robert Price01/2017
7203(7*10^64568-43)/964568Robert Price10/2014
7204Pell-LucasQ(168677)/264566Eric W. Weisstein11/2006
7205(24737*2^214476+1)/287764565Lelio R Paula06/2014
7206(47*2^214463+1)/764561Lelio R Paula04/2015
72072^214458+5461564559Lelio R Paula10/2011
7208(3^135322+7)/12291140864557Lelio R Paula04/2012
72092^214389-68311364538Paul Bourdelais03/2013
7210(76*10^64534+113)/964535Robert Price11/2017
72112^214369-11124164532Enzo Doria05/2014
7212(19^50461+3^50461)/2264526Robert Price07/2013
721311^61954-366064519Enzo Doria12/2012
7214(23*2^214319-1)/2164517Lelio R Paula01/2014
7215(58695*2^214310-1)/57164516Lelio R Paula04/2015
721635^41779-3464510Norbert Schneider04/2014
7217(159^29303+1)/16064506Eric Chen12/2017
7218(89*10^64504-179)/964505Robert Price11/2017
721911^61939-522064503Enzo Doria01/2013
7220(2^214271+78557)/3564501Lelio R Paula05/2012
7221L(308604)+P(308604)64495Robert Price12/2017
7222126^30706-12564494Norbert Schneider02/2015
7223gcd(V(1157265),5*F(231453)*(F(231453)-1)+1)64492Serge Batalov04/2015
72242^214215+1290964486Lelio R Paula10/2011
72255^92225+6664463Lelio R Paula06/2013
72262^214126-24055164459Paul Bourdelais03/2013
72278*6^82827+564453Lelio R Paula09/2014
7228(31*2^214120-1)/217048564452Lelio R Paula01/2014
7229(31*2^214088-1)/595564445Lelio R Paula01/2014
723014^56227+8964444Lelio R Paula08/2013
72332^214055-15964437Lelio R Paula08/2011
723110^64436+266764437Patrick De Geest05/2013
723265^35543-64^3554364437Robert Price08/2013
723410^64436-5364436Robert Price05/2011
7235(3^135043-lucasV(1,3,135043)+1)/364432Paul Vanderveen11/2017
7236Phi(128878,10)/3950329792764428Maksym Voznyy11/2015
72373^135027+10064425Lelio R Paula05/2013
7238(3^134972-7)/264398Lelio R Paula04/2012
72396*10^64387+764388Dmitry Domanov11/2010
72402^213864-1837764380Enzo Doria05/2013
7241(2^213821+9)/20964365Lelio R Paula04/2012
72422^213788+13564357Lelio R Paula08/2011
7243(3^134883+2)/4831364351Lelio R Paula04/2012
7244(49^38069-46^38069)/364344Serge Batalov12/2016
7245(11^61781+2^61781)/1364338Robert Price02/2013
72466^82670+3764330Lelio R Paula07/2013
7247(3^134839+4)/3231295964328Lelio R Paula04/2012
7248(22*10^64326+161)/364327Robert Price02/2017
724911^61767-405064324Enzo Doria12/2012
72502^213645-11485364314Enzo Doria05/2015


Find by discoverer :


Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: April, 22 2018 09:48 (Time in France)

Go back
Valid XHTML 1.0!    Valid CSS!