PRP Records

Probable Primes Top 10000

(252402 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 ?
750146396!3-8165455Robert Price09/2014
75022^217421-11318565451Enzo Doria07/2014
7503(6883*2^217440-1)/106119329589365448Lelio R Paula04/2015
75042^217408-214565447Lelio R Paula10/2011
75052^217398-1694765444Enzo Doria05/2013
75068*5^93613+365434Lelio R Paula09/2014
750711^62828-531065429Enzo Doria01/2013
750810^65426+1365427Robert Price01/2011
75092^217341-655565427Lelio R Paula10/2011
751010^65426-5484965426Patrick De Geest05/2013
7511(21*2^217363-1)/5600362666765424Lelio R Paula01/2014
751230011^14608-10865405Enzo Doria07/2012
7513119^31504-265389Lelio R Paula10/2017
7514(43^40031-1)/4265388Robert Price04/2014
75152^217190+9439565381Henri Lifchitz02/2005
751615^55587+4665376Lelio R Paula08/2013
75172^217088-11183365350Enzo Doria05/2014
7518(13*2^217069-1)/168294565340Lelio R Paula01/2014
7519(10^65340+47)/365340Robert Price11/2017
7520(62*10^65331+1)/965332Serge Batalov11/2010
75212^216947-11135165308Enzo Doria05/2014
7522-E(18022)/77520184568268532294394923506835965307Thomas Ritschel02/2017
7523(13*10^65297+83)/365298Robert Price09/2016
75245^93400-865284Lelio R Paula06/2013
75252^216802-16565264Lelio R Paula08/2011
75262^216799-2863565264Lelio R Paula10/2011
75275*10^65255+5165256Robert Price01/2017
75282^216762-16765252Lelio R Paula08/2011
752911^62657-579065251Enzo Doria01/2013
75303^136756-11288065250Enzo Doria06/2014
75312^216752+2165249Lelio R Paula08/2011
75323*10^65247+1165248Robert Price11/2017
753311^62651-270065245Enzo Doria12/2012
753415130^15609-15609^1513065244Norbert Schneider07/2018
7536Pell-LucasQ(170413)/265230Eric W. Weisstein12/2006
7535gcd(V(790525),5*F(158105)*(F(158105)+1)+1)65230Serge Batalov04/2015
7537(2^216676-1017)/63765224Lelio R Paula04/2012
75382^216652-232765219Yves Minet10/2013
7539(9179*2^216648-1)/466765218Lelio R Paula04/2015
7540(5*10^65203-119)/365204Robert Price04/2016
75412^216555-11326965190Enzo Doria07/2014
7542(9513^16384+1)/265181Henri Lifchitz02/2007
75432^216474+1291565166Lelio R Paula02/2013
754419^50958-3265163Lelio R Paula08/2013
75452^216442-11213365156Enzo Doria06/2014
75462^216437-11221365155Enzo Doria06/2014
75472^216435-11276765154Enzo Doria06/2014
75482^216420+1270565149Lelio R Paula02/2013
75498*3^136507-765132Lelio R Paula04/2014
7550(-lucasV(1,2,432719)-2)/(5*461)65128Mike Oakes03/2017
755115132^15575-15575^1513265102Norbert Schneider07/2018
75525*10^65086-5165087Robert Price10/2017
75532^216197-11176965082Enzo Doria05/2014
75546^83631-7965078Lelio R Paula07/2013
7555572^23601+23601^57265078Norbert Schneider08/2016
7556(3^136399-7)/54422065074Lelio R Paula04/2012
75572^216154-142165069Yves Minet01/2013
75582^216145-11266365067Enzo Doria06/2014
7559(7*10^65064+53)/365065Robert Price10/2017
7560132013*10^65050+2^216091-165056Gilbert Mozzo01/2014
7561132019*10^65050+2^216091-165056Gilbert Mozzo01/2014
7562148918*10^65050+2^216091-165056Gilbert Mozzo02/2014
7563194014*10^65050+2^216091-165056Gilbert Mozzo02/2014
7564223864*10^65050+2^216091-165056Gilbert Mozzo04/2014
756782090*10^65050+2^216091-165055Gilbert Mozzo07/2012
756695133*10^65050+2^216091-165055Gilbert Mozzo12/2013
756598142*10^65050+2^216091-165055Gilbert Mozzo12/2013
7568((2^216091-1)*34009-48)/2565054Serge Batalov01/2012
75695977*10^65050+2^216091-165054Gilbert Mozzo03/2012
75707*2^216091+2^298-1365051Peter Lesala03/2007
75712^216091+2*29208-165050Makoto Morimoto10/2013
7572(10^(2*32521+1)-6*10^32521-1)/365043Robert Price02/2016
7573p(13861)#/2+25665039Robert Price05/2017
7574(2^216091-2096)/(2^4*3*2918437*5220283)65036Makoto Morimoto10/2017
757511^62439-438065024Enzo Doria01/2013
75763^136244+265005Mike Oakes11/2009
757713^58343-5064991Lelio R Paula07/2013
7578331^25791-1000264989Enzo Doria07/2012
75792^215877+13164986Lelio R Paula08/2011
75804*5^92959+964977Lelio R Paula09/2014
75812^215789-1882564959Lelio R Paula09/2011
7582(2^215801-509203)/4132764958Lelio R Paula05/2012
7583U(315311)64954Serge Batalov03/2015
758446072!3-5904964951Robert Price12/2015
75852^215750-595564948Lelio R Paula09/2011
758613^58281+4664922Lelio R Paula07/2013
75872^215623+18364909Lelio R Paula08/2011
7588(46*10^64904+521)/964905Robert Price08/2017
7589(3^136043-2^136043)/(19862279*33466579)64895Mike Oakes12/2016
75905*2^215554+364889Lelio R Paula04/2014
75912^215541-11207564885Enzo Doria06/2014
75922*10^64882-364883Dmitry Domanov11/2010
759310^64862+34233964863Patrick De Geest05/2013
759410^64862-4764862Robert Price05/2011
759519^50718-8464856Lelio R Paula08/2013
7596(3045*2^215471-1)/(17*1151*27067*173473)64853Jens K. Andersen09/2007
759786413!6-1264846Robert Price08/2018
759810^64843+427869783964844Robert Price05/2015
759910^64843+2196764844Patrick De Geest03/2016
760010^64843-34007364843Patrick De Geest03/2016
760111^62254+7064831Lelio R Paula07/2013
76022^215351-11192564828Enzo Doria05/2014
76032^215310-11764815Lelio R Paula08/2011
7604124^30958-12364809Norbert Schneider02/2015
7605(7*10^64807+17)/364808Erik Branger03/2014
7606(7*10^(2*32400+1)-27*10^32400-7)/964801Robert Price11/2015
76072^215243-1594964795Enzo Doria04/2013
760823^47581-22^4758164793Robert Price08/2012
7609(62*10^64783-17)/964784Robert Price09/2015
76105*3^135747-464769Lelio R Paula04/2014
7611(59*10^64767-41)/964768Robert Price09/2015
7613(2^215140+3)/1964763Lelio R Paula04/2012
76122^215135-1716964763Enzo Doria05/2013
76142^215115-11127764757Enzo Doria05/2014
76159*5^92641+264755Lelio R Paula09/2014
7616(lucasV(1,2,430086)-2)/(7*1033)64731Mike Oakes03/2017
76175791^17200+17200^579164720Norbert Schneider12/2018
7618(5*10^64715-23)/964715Robert Price11/2014
76192^214938-178164703Yves Minet03/2013
762011^62111-42064682Enzo Doria08/2012
76215^92525+4264673Lelio R Paula06/2013
76222^214824+7189364669Enzo Doria04/2016
76232^214799-222164661Yves Minet08/2013
76245939^17128+17128^593964637Norbert Schneider10/2018
7625(21*2^214688+1)/29364627Lelio R Paula08/2012
762692^32907+32907^9264623Serge Batalov05/2014
7627(89*10^64608-539)/964609Robert Price11/2017
76286^83013+10164597Lelio R Paula07/2013
7629p(13775)#/2+864594Robert Price01/2017
7630(7*10^64568-43)/964568Robert Price10/2014
7631Pell-LucasQ(168677)/264566Eric W. Weisstein11/2006
7632(24737*2^214476+1)/287764565Lelio R Paula06/2014
7633(47*2^214463+1)/764561Lelio R Paula04/2015
76342^214458+5461564559Lelio R Paula10/2011
7635(3^135322+7)/12291140864557Lelio R Paula04/2012
76362^214389-68311364538Paul Bourdelais03/2013
7637(76*10^64534+113)/964535Robert Price11/2017
76382^214369-11124164532Enzo Doria05/2014
7639(19^50461+3^50461)/2264526Robert Price07/2013
764011^61954-366064519Enzo Doria12/2012
7641(23*2^214319-1)/2164517Lelio R Paula01/2014
7642(58695*2^214310-1)/57164516Lelio R Paula04/2015
764335^41779-3464510Norbert Schneider04/2014
7644(159^29303+1)/16064506Eric Chen12/2017
7645(89*10^64504-179)/964505Robert Price11/2017
764611^61939-522064503Enzo Doria01/2013
7647(2^214271+78557)/3564501Lelio R Paula05/2012
7648L(308604)+P(308604)64495Robert Price12/2017
7649126^30706-12564494Norbert Schneider02/2015
7650gcd(V(1157265),5*F(231453)*(F(231453)-1)+1)64492Serge Batalov04/2015
76512^214215+1290964486Lelio R Paula10/2011
76525^92225+6664463Lelio R Paula06/2013
76532^214126-24055164459Paul Bourdelais03/2013
76548*6^82827+564453Lelio R Paula09/2014
7655(31*2^214120-1)/217048564452Lelio R Paula01/2014
7656(31*2^214088-1)/595564445Lelio R Paula01/2014
765714^56227+8964444Lelio R Paula08/2013
76602^214055-15964437Lelio R Paula08/2011
765810^64436+266764437Patrick De Geest05/2013
765965^35543-64^3554364437Robert Price08/2013
766110^64436-5364436Robert Price05/2011
7662(3^135043-lucasV(1,3,135043)+1)/364432Paul Vanderveen11/2017
7663Phi(128878,10)/3950329792764428Maksym Voznyy11/2015
76643^135027+10064425Lelio R Paula05/2013
7665(3^134972-7)/264398Lelio R Paula04/2012
76666*10^64387+764388Dmitry Domanov11/2010
76672^213864-1837764380Enzo Doria05/2013
7668(2^213821+9)/20964365Lelio R Paula04/2012
76692^213788+13564357Lelio R Paula08/2011
7670(3^134883+2)/4831364351Lelio R Paula04/2012
7671(49^38069-46^38069)/364344Serge Batalov12/2016
7672(11^61781+2^61781)/1364338Robert Price02/2013
76736^82670+3764330Lelio R Paula07/2013
7674(3^134839+4)/3231295964328Lelio R Paula04/2012
7675(22*10^64326+161)/364327Robert Price02/2017
767611^61767-405064324Enzo Doria12/2012
76772^213645-11485364314Enzo Doria05/2015
767813^57733+1864312Lelio R Paula07/2013
76792^213621+7270764307Enzo Doria04/2016
768010^64305+13679164306Patrick De Geest05/2011
768110^64305-964305Alexander Gramolin01/2011
7682V(307652)64295Serge Batalov03/2015
76834*10^64286-8964287Robert Price08/2017
7684(2^213546-5)/222164281Lelio R Paula04/2012
76852^213438-5869564252Lelio R Paula10/2011
76862^213367-10564230Lelio R Paula08/2011
7687595^23148+23148^59564225Norbert Schneider07/2016
76893^134601+868064221Lelio R Paula05/2013
7688(26*10^64220+61)/364221Robert Price06/2017
7690500^23793+23793^50064217Norbert Schneider08/2016
7691179^28504-264216Lelio R Paula10/2017
76932^213314-45564214Yves Minet02/2012
769239^40359-3864214Norbert Schneider05/2014
76942^213292-1608564208Enzo Doria04/2013
7695(72524!5+1)/2564203Joe McLean10/2018
76962^213274-7764202Lelio R Paula08/2011
769719^50203+7864198Lelio R Paula08/2013
7698(44*10^64192-233)/964193Robert Price10/2017
76992^213240-11286564192Enzo Doria06/2014
77002^213190-11239164177Enzo Doria06/2014
7701(9913*2^213184-1)/965764175Lelio R Paula04/2015
770214^55991+2764173Lelio R Paula07/2013
77032^213158-11258164167Enzo Doria06/2014
77042^213148+9164164Lelio R Paula08/2011
7705(96^32369+1)/9764163Paul Bourdelais08/2017
77076^82439+12564151Lelio R Paula07/2013
77067*2^213102+964151Lelio R Paula04/2014
7708L(306854)+F(306855)64129Henri Lifchitz01/2007
7709610^23017+23017^61064110Norbert Schneider07/2016
77102^212950-6487564105Lelio R Paula10/2011
7711(266*10^64102-17)/364104Robert Price06/2016
7712p(13679)#/2+6464097Robert Price03/2017
771319^50119+9464090Lelio R Paula08/2013
77142^212880-14764084Lelio R Paula08/2011
771511^61523-459064070Enzo Doria01/2013
77165^91663+3864070Lelio R Paula05/2013
77175^91650+5264061Lelio R Paula05/2013
77182^212770+6964051Lelio R Paula08/2011
7719(3^134227+1)/464042Paul Bourdelais11/2007
7720(2*10^64041-17)/364041Robert Price08/2014
7721(15^54449+1)/1664036Paul Bourdelais03/2010
7722(29*10^64027+91)/364028Robert Price03/2016
7723(lucasV(1,2,425405)+2)/(17*89)64027Mike Oakes03/2017
772416878!+16878#-164022D. Gazzoni Filho & Lucas Teixeira05/2005
77252^212663+5364018Lelio R Paula08/2011
7726(4*10^64014+197)/364015Robert Price03/2017
772785402!6-364014Robert Price08/2018
7728(140^29819+1)/14163994Richard Fischer05/2018
772910^63986+6363987Robert Price01/2011
773010^63986-3155763986Patrick De Geest05/2013
773131487!2-2^3148763982Robert Price09/2015
7732(21*2^212522-1)/141632363971Lelio R Paula01/2014
77335^91517+9863968Lelio R Paula04/2013
7734(19*10^63960-43)/363961Robert Price10/2017
7735(62*10^63954-17)/963955Robert Price09/2015
77375^91493-4^9149363951Predrag Minovic04/2004
7736V(364793)63951Serge Batalov03/2015
774019^50004+5863943Lelio R Paula05/2013
77385*6^82172-763943Lelio R Paula09/2014
7739(56*10^63942+223)/963943Robert Price07/2016
774119^50000-2463938Lelio R Paula05/2013
7742(23*2^212374-1)/2701963928Lelio R Paula01/2014
7743(9*2^212355-1)/76163924Lelio R Paula01/2014
77452^212344-18363922Lelio R Paula08/2011
7744(58695*2^212336-1)/37963922Lelio R Paula04/2015
774610^63916+7963917Robert Price01/2011
774710^63916-7682363916Patrick De Geest05/2013
77482^212295-2563908Lelio R Paula08/2011
77502^212285-238363905Yves Minet10/2013
7749267^26336+26336^26763905Norbert Schneider09/2014


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: December, 17 2018 20:37 (Time in France)

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