PRP Records

Probable Primes Top 10000

(247113 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 ?
7501(43^40031-1)/4265388Robert Price04/2014
75022^217190+9439565381Henri Lifchitz02/2005
750315^55587+4665376Lelio R Paula08/2013
75042^217088-11183365350Enzo Doria05/2014
7505(13*2^217069-1)/168294565340Lelio R Paula01/2014
7506(10^65340+47)/365340Robert Price11/2017
7507(62*10^65331+1)/965332Serge Batalov11/2010
75082^216947-11135165308Enzo Doria05/2014
7509-E(18022)/77520184568268532294394923506835965307Thomas Ritschel02/2017
7510(13*10^65297+83)/365298Robert Price09/2016
75115^93400-865284Lelio R Paula06/2013
75122^216802-16565264Lelio R Paula08/2011
75132^216799-2863565264Lelio R Paula10/2011
75145*10^65255+5165256Robert Price01/2017
75152^216762-16765252Lelio R Paula08/2011
751611^62657-579065251Enzo Doria01/2013
75173^136756-11288065250Enzo Doria06/2014
75182^216752+2165249Lelio R Paula08/2011
75193*10^65247+1165248Robert Price11/2017
752011^62651-270065245Enzo Doria12/2012
752115130^15609-15609^1513065244Norbert Schneider07/2018
7522Pell-LucasQ(170413)/265230Eric W. Weisstein12/2006
7523gcd(V(790525),5*F(158105)*(F(158105)+1)+1)65230Serge Batalov04/2015
7524(2^216676-1017)/63765224Lelio R Paula04/2012
75252^216652-232765219Yves Minet10/2013
7526(9179*2^216648-1)/466765218Lelio R Paula04/2015
7527(5*10^65203-119)/365204Robert Price04/2016
75282^216555-11326965190Enzo Doria07/2014
7529(9513^16384+1)/265181Henri Lifchitz02/2007
75302^216474+1291565166Lelio R Paula02/2013
753119^50958-3265163Lelio R Paula08/2013
75322^216442-11213365156Enzo Doria06/2014
75332^216437-11221365155Enzo Doria06/2014
75342^216435-11276765154Enzo Doria06/2014
75352^216420+1270565149Lelio R Paula02/2013
75368*3^136507-765132Lelio R Paula04/2014
7537(-lucasV(1,2,432719)-2)/(5*461)65128Mike Oakes03/2017
753815132^15575-15575^1513265102Norbert Schneider07/2018
75395*10^65086-5165087Robert Price10/2017
75402^216197-11176965082Enzo Doria05/2014
75416^83631-7965078Lelio R Paula07/2013
7542572^23601+23601^57265078Norbert Schneider08/2016
7543(3^136399-7)/54422065074Lelio R Paula04/2012
75442^216154-142165069Yves Minet01/2013
75452^216145-11266365067Enzo Doria06/2014
7546(7*10^65064+53)/365065Robert Price10/2017
7547132013*10^65050+2^216091-165056Gilbert Mozzo01/2014
7548132019*10^65050+2^216091-165056Gilbert Mozzo01/2014
7549148918*10^65050+2^216091-165056Gilbert Mozzo02/2014
7550194014*10^65050+2^216091-165056Gilbert Mozzo02/2014
7551223864*10^65050+2^216091-165056Gilbert Mozzo04/2014
755382090*10^65050+2^216091-165055Gilbert Mozzo07/2012
755495133*10^65050+2^216091-165055Gilbert Mozzo12/2013
755298142*10^65050+2^216091-165055Gilbert Mozzo12/2013
7555((2^216091-1)*34009-48)/2565054Serge Batalov01/2012
75565977*10^65050+2^216091-165054Gilbert Mozzo03/2012
75577*2^216091+2^298-1365051Peter Lesala03/2007
75582^216091+2*29208-165050Makoto Morimoto10/2013
7559(10^(2*32521+1)-6*10^32521-1)/365043Robert Price02/2016
7560p(13861)#/2+25665039Robert Price05/2017
7561(2^216091-2096)/(2^4*3*2918437*5220283)65036Makoto Morimoto10/2017
756211^62439-438065024Enzo Doria01/2013
75633^136244+265005Mike Oakes11/2009
756413^58343-5064991Lelio R Paula07/2013
7565331^25791-1000264989Enzo Doria07/2012
75662^215877+13164986Lelio R Paula08/2011
75674*5^92959+964977Lelio R Paula09/2014
75682^215789-1882564959Lelio R Paula09/2011
7569(2^215801-509203)/4132764958Lelio R Paula05/2012
7570U(315311)64954Serge Batalov03/2015
757146072!3-5904964951Robert Price12/2015
75722^215750-595564948Lelio R Paula09/2011
757313^58281+4664922Lelio R Paula07/2013
75742^215623+18364909Lelio R Paula08/2011
7575(46*10^64904+521)/964905Robert Price08/2017
7576(3^136043-2^136043)/(19862279*33466579)64895Mike Oakes12/2016
75775*2^215554+364889Lelio R Paula04/2014
75782^215541-11207564885Enzo Doria06/2014
75792*10^64882-364883Dmitry Domanov11/2010
758010^64862+34233964863Patrick De Geest05/2013
758110^64862-4764862Robert Price05/2011
758219^50718-8464856Lelio R Paula08/2013
7583(3045*2^215471-1)/(17*1151*27067*173473)64853Jens K. Andersen09/2007
758486413!6-1264846Robert Price08/2018
758610^64843+427869783964844Robert Price05/2015
758510^64843+2196764844Patrick De Geest03/2016
758710^64843-34007364843Patrick De Geest03/2016
758811^62254+7064831Lelio R Paula07/2013
75892^215351-11192564828Enzo Doria05/2014
75902^215310-11764815Lelio R Paula08/2011
7591124^30958-12364809Norbert Schneider02/2015
7592(7*10^64807+17)/364808Erik Branger03/2014
7593(7*10^(2*32400+1)-27*10^32400-7)/964801Robert Price11/2015
75942^215243-1594964795Enzo Doria04/2013
759523^47581-22^4758164793Robert Price08/2012
7596(62*10^64783-17)/964784Robert Price09/2015
75975*3^135747-464769Lelio R Paula04/2014
7598(59*10^64767-41)/964768Robert Price09/2015
7600(2^215140+3)/1964763Lelio R Paula04/2012
75992^215135-1716964763Enzo Doria05/2013
76012^215115-11127764757Enzo Doria05/2014
76029*5^92641+264755Lelio R Paula09/2014
7603(lucasV(1,2,430086)-2)/(7*1033)64731Mike Oakes03/2017
7604(5*10^64715-23)/964715Robert Price11/2014
76052^214938-178164703Yves Minet03/2013
760611^62111-42064682Enzo Doria08/2012
76075^92525+4264673Lelio R Paula06/2013
76082^214824+7189364669Enzo Doria04/2016
76092^214799-222164661Yves Minet08/2013
76105939^17128+17128^593964637Norbert Schneider10/2018
7611(21*2^214688+1)/29364627Lelio R Paula08/2012
761292^32907+32907^9264623Serge Batalov05/2014
7613(89*10^64608-539)/964609Robert Price11/2017
76146^83013+10164597Lelio R Paula07/2013
7615p(13775)#/2+864594Robert Price01/2017
7616(7*10^64568-43)/964568Robert Price10/2014
7617Pell-LucasQ(168677)/264566Eric W. Weisstein11/2006
7618(24737*2^214476+1)/287764565Lelio R Paula06/2014
7619(47*2^214463+1)/764561Lelio R Paula04/2015
76202^214458+5461564559Lelio R Paula10/2011
7621(3^135322+7)/12291140864557Lelio R Paula04/2012
76222^214389-68311364538Paul Bourdelais03/2013
7623(76*10^64534+113)/964535Robert Price11/2017
76242^214369-11124164532Enzo Doria05/2014
7625(19^50461+3^50461)/2264526Robert Price07/2013
762611^61954-366064519Enzo Doria12/2012
7627(23*2^214319-1)/2164517Lelio R Paula01/2014
7628(58695*2^214310-1)/57164516Lelio R Paula04/2015
762935^41779-3464510Norbert Schneider04/2014
7630(159^29303+1)/16064506Eric Chen12/2017
7631(89*10^64504-179)/964505Robert Price11/2017
763211^61939-522064503Enzo Doria01/2013
7633(2^214271+78557)/3564501Lelio R Paula05/2012
7634L(308604)+P(308604)64495Robert Price12/2017
7635126^30706-12564494Norbert Schneider02/2015
7636gcd(V(1157265),5*F(231453)*(F(231453)-1)+1)64492Serge Batalov04/2015
76372^214215+1290964486Lelio R Paula10/2011
76385^92225+6664463Lelio R Paula06/2013
76392^214126-24055164459Paul Bourdelais03/2013
76408*6^82827+564453Lelio R Paula09/2014
7641(31*2^214120-1)/217048564452Lelio R Paula01/2014
7642(31*2^214088-1)/595564445Lelio R Paula01/2014
764314^56227+8964444Lelio R Paula08/2013
76462^214055-15964437Lelio R Paula08/2011
764410^64436+266764437Patrick De Geest05/2013
764565^35543-64^3554364437Robert Price08/2013
764710^64436-5364436Robert Price05/2011
7648(3^135043-lucasV(1,3,135043)+1)/364432Paul Vanderveen11/2017
7649Phi(128878,10)/3950329792764428Maksym Voznyy11/2015
76503^135027+10064425Lelio R Paula05/2013
7651(3^134972-7)/264398Lelio R Paula04/2012
76526*10^64387+764388Dmitry Domanov11/2010
76532^213864-1837764380Enzo Doria05/2013
7654(2^213821+9)/20964365Lelio R Paula04/2012
76552^213788+13564357Lelio R Paula08/2011
7656(3^134883+2)/4831364351Lelio R Paula04/2012
7657(49^38069-46^38069)/364344Serge Batalov12/2016
7658(11^61781+2^61781)/1364338Robert Price02/2013
76596^82670+3764330Lelio R Paula07/2013
7660(3^134839+4)/3231295964328Lelio R Paula04/2012
7661(22*10^64326+161)/364327Robert Price02/2017
766211^61767-405064324Enzo Doria12/2012
76632^213645-11485364314Enzo Doria05/2015
766413^57733+1864312Lelio R Paula07/2013
76652^213621+7270764307Enzo Doria04/2016
766610^64305+13679164306Patrick De Geest05/2011
766710^64305-964305Alexander Gramolin01/2011
7668V(307652)64295Serge Batalov03/2015
76694*10^64286-8964287Robert Price08/2017
7670(2^213546-5)/222164281Lelio R Paula04/2012
76712^213438-5869564252Lelio R Paula10/2011
76722^213367-10564230Lelio R Paula08/2011
7673595^23148+23148^59564225Norbert Schneider07/2016
76743^134601+868064221Lelio R Paula05/2013
7675(26*10^64220+61)/364221Robert Price06/2017
7676500^23793+23793^50064217Norbert Schneider08/2016
7677179^28504-264216Lelio R Paula10/2017
76792^213314-45564214Yves Minet02/2012
767839^40359-3864214Norbert Schneider05/2014
76802^213292-1608564208Enzo Doria04/2013
7681(72524!5+1)/2564203Joe McLean10/2018
76822^213274-7764202Lelio R Paula08/2011
768319^50203+7864198Lelio R Paula08/2013
7684(44*10^64192-233)/964193Robert Price10/2017
76852^213240-11286564192Enzo Doria06/2014
76862^213190-11239164177Enzo Doria06/2014
7687(9913*2^213184-1)/965764175Lelio R Paula04/2015
768814^55991+2764173Lelio R Paula07/2013
76892^213158-11258164167Enzo Doria06/2014
76902^213148+9164164Lelio R Paula08/2011
7691(96^32369+1)/9764163Paul Bourdelais08/2017
76936^82439+12564151Lelio R Paula07/2013
76927*2^213102+964151Lelio R Paula04/2014
7694L(306854)+F(306855)64129Henri Lifchitz01/2007
7695610^23017+23017^61064110Norbert Schneider07/2016
76962^212950-6487564105Lelio R Paula10/2011
7697(266*10^64102-17)/364104Robert Price06/2016
7698p(13679)#/2+6464097Robert Price03/2017
769919^50119+9464090Lelio R Paula08/2013
77002^212880-14764084Lelio R Paula08/2011
770111^61523-459064070Enzo Doria01/2013
77025^91663+3864070Lelio R Paula05/2013
77035^91650+5264061Lelio R Paula05/2013
77042^212770+6964051Lelio R Paula08/2011
7705(3^134227+1)/464042Paul Bourdelais11/2007
7706(2*10^64041-17)/364041Robert Price08/2014
7707(15^54449+1)/1664036Paul Bourdelais03/2010
7708(29*10^64027+91)/364028Robert Price03/2016
7709(lucasV(1,2,425405)+2)/(17*89)64027Mike Oakes03/2017
771016878!+16878#-164022D. Gazzoni Filho & Lucas Teixeira05/2005
77112^212663+5364018Lelio R Paula08/2011
7712(4*10^64014+197)/364015Robert Price03/2017
771385402!6-364014Robert Price08/2018
7714(140^29819+1)/14163994Richard Fischer05/2018
771510^63986+6363987Robert Price01/2011
771610^63986-3155763986Patrick De Geest05/2013
771731487!2-2^3148763982Robert Price09/2015
7718(21*2^212522-1)/141632363971Lelio R Paula01/2014
77195^91517+9863968Lelio R Paula04/2013
7720(19*10^63960-43)/363961Robert Price10/2017
7721(62*10^63954-17)/963955Robert Price09/2015
77235^91493-4^9149363951Predrag Minovic04/2004
7722V(364793)63951Serge Batalov03/2015
772619^50004+5863943Lelio R Paula05/2013
77245*6^82172-763943Lelio R Paula09/2014
7725(56*10^63942+223)/963943Robert Price07/2016
772719^50000-2463938Lelio R Paula05/2013
7728(23*2^212374-1)/2701963928Lelio R Paula01/2014
7729(9*2^212355-1)/76163924Lelio R Paula01/2014
77312^212344-18363922Lelio R Paula08/2011
7730(58695*2^212336-1)/37963922Lelio R Paula04/2015
773210^63916+7963917Robert Price01/2011
773310^63916-7682363916Patrick De Geest05/2013
77342^212295-2563908Lelio R Paula08/2011
77362^212285-238363905Yves Minet10/2013
7735267^26336+26336^26763905Norbert Schneider09/2014
7737(-lucasV(1,2,424552)-2)/160163899Mike Oakes03/2017
773819^49962+6063890Lelio R Paula05/2013
77393^133906-11305663890Enzo Doria07/2014
7740(lucasV(1,2,424451)+2)/363886Mike Oakes03/2017
77413*6^82092+563881Lelio R Paula09/2014
774215441^13706+13706^1544163879Hans Havermann02/2017
77432^212154-77635163865Paul Bourdelais03/2013
774435^41359+263862Lelio R Paula05/2013
7745(61*10^63857-43)/963858Robert Price09/2015
7746(2^212131-3)/48563856Lelio R Paula04/2012
77472^212112-45999563853Enzo Doria06/2015
774815^54290+5863850Lelio R Paula05/2013
77493*2^212097-763849Lelio R Paula04/2014
775055^36683-5463842Norbert Schneider08/2014


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: December, 11 2018 05:54 (Time in France)

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