PRP Records

Probable Primes Top 10000

(218736 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 ?
725110^65426+1365427Robert Price01/2011
72522^217341-655565427Lelio R Paula10/2011
725310^65426-5484965426Patrick De Geest05/2013
7254(21*2^217363-1)/5600362666765424Lelio R Paula01/2014
725530011^14608-10865405Enzo Doria07/2012
7256119^31504-265389Lelio R Paula10/2017
7257(43^40031-1)/4265388Robert Price04/2014
72582^217190+9439565381Henri Lifchitz02/2005
725915^55587+4665376Lelio R Paula08/2013
72602^217088-11183365350Enzo Doria05/2014
7261(13*2^217069-1)/168294565340Lelio R Paula01/2014
7262(10^65340+47)/365340Robert Price11/2017
7263(62*10^65331+1)/965332Serge Batalov11/2010
72642^216947-11135165308Enzo Doria05/2014
7265-E(18022)/77520184568268532294394923506835965307Thomas Ritschel02/2017
7266(13*10^65297+83)/365298Robert Price09/2016
72675^93400-865284Lelio R Paula06/2013
72682^216802-16565264Lelio R Paula08/2011
72692^216799-2863565264Lelio R Paula10/2011
72705*10^65255+5165256Robert Price01/2017
72712^216762-16765252Lelio R Paula08/2011
727211^62657-579065251Enzo Doria01/2013
72733^136756-11288065250Enzo Doria06/2014
72742^216752+2165249Lelio R Paula08/2011
72753*10^65247+1165248Robert Price11/2017
727611^62651-270065245Enzo Doria12/2012
727715130^15609-15609^1513065244Norbert Schneider07/2018
7278Pell-LucasQ(170413)/265230Eric W. Weisstein12/2006
7279gcd(V(790525),5*F(158105)*(F(158105)+1)+1)65230Serge Batalov04/2015
7280(2^216676-1017)/63765224Lelio R Paula04/2012
72812^216652-232765219Yves Minet10/2013
7282(9179*2^216648-1)/466765218Lelio R Paula04/2015
7283(5*10^65203-119)/365204Robert Price04/2016
72842^216555-11326965190Enzo Doria07/2014
7285(9513^16384+1)/265181Henri Lifchitz02/2007
72862^216474+1291565166Lelio R Paula02/2013
728719^50958-3265163Lelio R Paula08/2013
72882^216442-11213365156Enzo Doria06/2014
72892^216437-11221365155Enzo Doria06/2014
72902^216435-11276765154Enzo Doria06/2014
72912^216420+1270565149Lelio R Paula02/2013
72928*3^136507-765132Lelio R Paula04/2014
7293(-lucasV(1,2,432719)-2)/(5*461)65128Mike Oakes03/2017
729415132^15575-15575^1513265102Norbert Schneider07/2018
72955*10^65086-5165087Robert Price10/2017
72962^216197-11176965082Enzo Doria05/2014
72976^83631-7965078Lelio R Paula07/2013
7298572^23601+23601^57265078Norbert Schneider08/2016
7299(3^136399-7)/54422065074Lelio R Paula04/2012
73002^216154-142165069Yves Minet01/2013
73012^216145-11266365067Enzo Doria06/2014
7302(7*10^65064+53)/365065Robert Price10/2017
7303132013*10^65050+2^216091-165056Gilbert Mozzo01/2014
7304132019*10^65050+2^216091-165056Gilbert Mozzo01/2014
7305148918*10^65050+2^216091-165056Gilbert Mozzo02/2014
7306194014*10^65050+2^216091-165056Gilbert Mozzo02/2014
7307223864*10^65050+2^216091-165056Gilbert Mozzo04/2014
730982090*10^65050+2^216091-165055Gilbert Mozzo07/2012
731095133*10^65050+2^216091-165055Gilbert Mozzo12/2013
730898142*10^65050+2^216091-165055Gilbert Mozzo12/2013
7311((2^216091-1)*34009-48)/2565054Serge Batalov01/2012
73125977*10^65050+2^216091-165054Gilbert Mozzo03/2012
73137*2^216091+2^298-1365051Peter Lesala03/2007
73142^216091+2*29208-165050Makoto Morimoto10/2013
7315(10^(2*32521+1)-6*10^32521-1)/365043Robert Price02/2016
7316p(13861)#/2+25665039Robert Price05/2017
7317(2^216091-2096)/(2^4*3*2918437*5220283)65036Makoto Morimoto10/2017
731811^62439-438065024Enzo Doria01/2013
73193^136244+265005Mike Oakes11/2009
732013^58343-5064991Lelio R Paula07/2013
7321331^25791-1000264989Enzo Doria07/2012
73222^215877+13164986Lelio R Paula08/2011
73234*5^92959+964977Lelio R Paula09/2014
73242^215789-1882564959Lelio R Paula09/2011
7325(2^215801-509203)/4132764958Lelio R Paula05/2012
7326U(315311)64954Serge Batalov03/2015
732746072!3-5904964951Robert Price12/2015
73282^215750-595564948Lelio R Paula09/2011
732913^58281+4664922Lelio R Paula07/2013
73302^215623+18364909Lelio R Paula08/2011
7331(46*10^64904+521)/964905Robert Price08/2017
7332(3^136043-2^136043)/(19862279*33466579)64895Mike Oakes12/2016
73335*2^215554+364889Lelio R Paula04/2014
73342^215541-11207564885Enzo Doria06/2014
73352*10^64882-364883Dmitry Domanov11/2010
733610^64862+34233964863Patrick De Geest05/2013
733710^64862-4764862Robert Price05/2011
733819^50718-8464856Lelio R Paula08/2013
7339(3045*2^215471-1)/(17*1151*27067*173473)64853Jens K. Andersen09/2007
734086413!6-1264846Robert Price08/2018
734110^64843+427869783964844Robert Price05/2015
734210^64843+2196764844Patrick De Geest03/2016
734310^64843-34007364843Patrick De Geest03/2016
734411^62254+7064831Lelio R Paula07/2013
73452^215351-11192564828Enzo Doria05/2014
73462^215310-11764815Lelio R Paula08/2011
7347124^30958-12364809Norbert Schneider02/2015
7348(7*10^64807+17)/364808Erik Branger03/2014
7349(7*10^(2*32400+1)-27*10^32400-7)/964801Robert Price11/2015
73502^215243-1594964795Enzo Doria04/2013
735123^47581-22^4758164793Robert Price08/2012
7352(62*10^64783-17)/964784Robert Price09/2015
73535*3^135747-464769Lelio R Paula04/2014
7354(59*10^64767-41)/964768Robert Price09/2015
7356(2^215140+3)/1964763Lelio R Paula04/2012
73552^215135-1716964763Enzo Doria05/2013
73572^215115-11127764757Enzo Doria05/2014
73589*5^92641+264755Lelio R Paula09/2014
7359(lucasV(1,2,430086)-2)/(7*1033)64731Mike Oakes03/2017
7360(5*10^64715-23)/964715Robert Price11/2014
73612^214938-178164703Yves Minet03/2013
736211^62111-42064682Enzo Doria08/2012
73635^92525+4264673Lelio R Paula06/2013
73642^214824+7189364669Enzo Doria04/2016
73652^214799-222164661Yves Minet08/2013
7366(21*2^214688+1)/29364627Lelio R Paula08/2012
736792^32907+32907^9264623Serge Batalov05/2014
7368(89*10^64608-539)/964609Robert Price11/2017
73696^83013+10164597Lelio R Paula07/2013
7370p(13775)#/2+864594Robert Price01/2017
7371(7*10^64568-43)/964568Robert Price10/2014
7372Pell-LucasQ(168677)/264566Eric W. Weisstein11/2006
7373(24737*2^214476+1)/287764565Lelio R Paula06/2014
7374(47*2^214463+1)/764561Lelio R Paula04/2015
73752^214458+5461564559Lelio R Paula10/2011
7376(3^135322+7)/12291140864557Lelio R Paula04/2012
73772^214389-68311364538Paul Bourdelais03/2013
7378(76*10^64534+113)/964535Robert Price11/2017
73792^214369-11124164532Enzo Doria05/2014
7380(19^50461+3^50461)/2264526Robert Price07/2013
738111^61954-366064519Enzo Doria12/2012
7382(23*2^214319-1)/2164517Lelio R Paula01/2014
7383(58695*2^214310-1)/57164516Lelio R Paula04/2015
738435^41779-3464510Norbert Schneider04/2014
7385(159^29303+1)/16064506Eric Chen12/2017
7386(89*10^64504-179)/964505Robert Price11/2017
738711^61939-522064503Enzo Doria01/2013
7388(2^214271+78557)/3564501Lelio R Paula05/2012
7389L(308604)+P(308604)64495Robert Price12/2017
7390126^30706-12564494Norbert Schneider02/2015
7391gcd(V(1157265),5*F(231453)*(F(231453)-1)+1)64492Serge Batalov04/2015
73922^214215+1290964486Lelio R Paula10/2011
73935^92225+6664463Lelio R Paula06/2013
73942^214126-24055164459Paul Bourdelais03/2013
73958*6^82827+564453Lelio R Paula09/2014
7396(31*2^214120-1)/217048564452Lelio R Paula01/2014
7397(31*2^214088-1)/595564445Lelio R Paula01/2014
739814^56227+8964444Lelio R Paula08/2013
74012^214055-15964437Lelio R Paula08/2011
739910^64436+266764437Patrick De Geest05/2013
740065^35543-64^3554364437Robert Price08/2013
740210^64436-5364436Robert Price05/2011
7403(3^135043-lucasV(1,3,135043)+1)/364432Paul Vanderveen11/2017
7404Phi(128878,10)/3950329792764428Maksym Voznyy11/2015
74053^135027+10064425Lelio R Paula05/2013
7406(3^134972-7)/264398Lelio R Paula04/2012
74076*10^64387+764388Dmitry Domanov11/2010
74082^213864-1837764380Enzo Doria05/2013
7409(2^213821+9)/20964365Lelio R Paula04/2012
74102^213788+13564357Lelio R Paula08/2011
7411(3^134883+2)/4831364351Lelio R Paula04/2012
7412(49^38069-46^38069)/364344Serge Batalov12/2016
7413(11^61781+2^61781)/1364338Robert Price02/2013
74146^82670+3764330Lelio R Paula07/2013
7415(3^134839+4)/3231295964328Lelio R Paula04/2012
7416(22*10^64326+161)/364327Robert Price02/2017
741711^61767-405064324Enzo Doria12/2012
74182^213645-11485364314Enzo Doria05/2015
741913^57733+1864312Lelio R Paula07/2013
74202^213621+7270764307Enzo Doria04/2016
742110^64305+13679164306Patrick De Geest05/2011
742210^64305-964305Alexander Gramolin01/2011
7423V(307652)64295Serge Batalov03/2015
74244*10^64286-8964287Robert Price08/2017
7425(2^213546-5)/222164281Lelio R Paula04/2012
74262^213438-5869564252Lelio R Paula10/2011
74272^213367-10564230Lelio R Paula08/2011
7428595^23148+23148^59564225Norbert Schneider07/2016
74303^134601+868064221Lelio R Paula05/2013
7429(26*10^64220+61)/364221Robert Price06/2017
7431500^23793+23793^50064217Norbert Schneider08/2016
7432179^28504-264216Lelio R Paula10/2017
74342^213314-45564214Yves Minet02/2012
743339^40359-3864214Norbert Schneider05/2014
74352^213292-1608564208Enzo Doria04/2013
74362^213274-7764202Lelio R Paula08/2011
743719^50203+7864198Lelio R Paula08/2013
7438(44*10^64192-233)/964193Robert Price10/2017
74392^213240-11286564192Enzo Doria06/2014
74402^213190-11239164177Enzo Doria06/2014
7441(9913*2^213184-1)/965764175Lelio R Paula04/2015
744214^55991+2764173Lelio R Paula07/2013
74432^213158-11258164167Enzo Doria06/2014
74442^213148+9164164Lelio R Paula08/2011
7445(96^32369+1)/9764163Paul Bourdelais08/2017
74476^82439+12564151Lelio R Paula07/2013
74467*2^213102+964151Lelio R Paula04/2014
7448L(306854)+F(306855)64129Henri Lifchitz01/2007
7449610^23017+23017^61064110Norbert Schneider07/2016
74502^212950-6487564105Lelio R Paula10/2011
7451(266*10^64102-17)/364104Robert Price06/2016
7452p(13679)#/2+6464097Robert Price03/2017
745319^50119+9464090Lelio R Paula08/2013
74542^212880-14764084Lelio R Paula08/2011
745511^61523-459064070Enzo Doria01/2013
74565^91663+3864070Lelio R Paula05/2013
74575^91650+5264061Lelio R Paula05/2013
74582^212770+6964051Lelio R Paula08/2011
7459(3^134227+1)/464042Paul Bourdelais11/2007
7460(2*10^64041-17)/364041Robert Price08/2014
7461(15^54449+1)/1664036Paul Bourdelais03/2010
7462(29*10^64027+91)/364028Robert Price03/2016
7463(lucasV(1,2,425405)+2)/(17*89)64027Mike Oakes03/2017
746416878!+16878#-164022D. Gazzoni Filho & Lucas Teixeira05/2005
74652^212663+5364018Lelio R Paula08/2011
7466(4*10^64014+197)/364015Robert Price03/2017
746785402!6-364014Robert Price08/2018
7468(140^29819+1)/14163994Richard Fischer05/2018
746910^63986+6363987Robert Price01/2011
747010^63986-3155763986Patrick De Geest05/2013
747131487!2-2^3148763982Robert Price09/2015
7472(21*2^212522-1)/141632363971Lelio R Paula01/2014
74735^91517+9863968Lelio R Paula04/2013
7474(19*10^63960-43)/363961Robert Price10/2017
7475(62*10^63954-17)/963955Robert Price09/2015
74775^91493-4^9149363951Predrag Minovic04/2004
7476V(364793)63951Serge Batalov03/2015
747919^50004+5863943Lelio R Paula05/2013
74785*6^82172-763943Lelio R Paula09/2014
7480(56*10^63942+223)/963943Robert Price07/2016
748119^50000-2463938Lelio R Paula05/2013
7482(23*2^212374-1)/2701963928Lelio R Paula01/2014
7483(9*2^212355-1)/76163924Lelio R Paula01/2014
74852^212344-18363922Lelio R Paula08/2011
7484(58695*2^212336-1)/37963922Lelio R Paula04/2015
748610^63916+7963917Robert Price01/2011
748710^63916-7682363916Patrick De Geest05/2013
74882^212295-2563908Lelio R Paula08/2011
74902^212285-238363905Yves Minet10/2013
7489267^26336+26336^26763905Norbert Schneider09/2014
7491(-lucasV(1,2,424552)-2)/160163899Mike Oakes03/2017
749219^49962+6063890Lelio R Paula05/2013
74933^133906-11305663890Enzo Doria07/2014
7494(lucasV(1,2,424451)+2)/363886Mike Oakes03/2017
74953*6^82092+563881Lelio R Paula09/2014
749615441^13706+13706^1544163879Hans Havermann02/2017
74972^212154-77635163865Paul Bourdelais03/2013
749835^41359+263862Lelio R Paula05/2013
7499(61*10^63857-43)/963858Robert Price09/2015
7500(2^212131-3)/48563856Lelio R Paula04/2012


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: August, 14 2018 21:45 (Time in France)

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