PRP Records

Probable Primes Top 10000

(174961 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 ?
65013^138040-11065862Lelio R Paula06/2013
650211^63240-195065858Enzo Doria12/2012
65032^218764-11187365855Enzo Doria05/2014
6504(34*10^65839-7)/9/3765839Makoto Morimoto04/2016
65053^137988+2665838Lelio R Paula06/2013
65062^218680-71965830Yves Minet05/2012
650718^52424+1765807Lelio R Paula08/2013
6508(2*15683^15683+1)/73238442565789David Broadhurst09/2010
6509(23*2^218517+1)/1900365778Lelio R Paula07/2012
6510(5*10^65773+1)/365774Erik Branger12/2013
65112^218457-1732965763Enzo Doria05/2013
6512151703#+22338165759Nicolas PALAU10/2016
65132^218436+4075565756Lelio R Paula10/2011
6514(F(44)^7433-F(43)^7433)/F(42)65744Wayne Halsdorf03/2012
6515157^29934+29934^15765733Serge Batalov05/2014
6516211^28273-265715Lelio R Paula09/2013
6517(59*10^65712+31)/965713Robert Price09/2015
6518611^23586+23586^61165712Norbert Schneider08/2016
6519p(13991)#/2+3265712Robert Price12/2016
65202^218282-1848565710Enzo Doria05/2013
65212^218274-11125165708Enzo Doria05/2014
65222*F(314335)-165693Henri Lifchitz12/2009
65232^218200+42765685Henri Lifchitz01/2005
652446532!3+365667Robert Price10/2014
65252^218120-14765661Lelio R Paula08/2011
6526452^24729+24729^45265659Norbert Schneider09/2016
65272^218102-11489365656Enzo Doria05/2015
6528(15*2^218083-1)/1765650Lelio R Paula01/2014
6529(15*2^218081+1)/1894165646Lelio R Paula08/2012
653119^51326+3665634Lelio R Paula08/2013
6530(21*2^218045-1)/45158365634Lelio R Paula01/2014
65322^217989-3365622Lelio R Paula08/2011
6533(13*2^217961+1)/365614Lelio R Paula06/2012
65344*6^84315-565611Lelio R Paula09/2014
6535(315047^11933+1)/31504865607Faysal YAtim06/2008
65366^84303+5565601Lelio R Paula07/2013
6537(-lucasV(1,2,435857)+2)/(173*859*8017)65595Mike Oakes04/2017
6538(9787*2^217873-1)/3765589Lelio R Paula04/2015
65395*2^217858+365583Lelio R Paula04/2014
6540(19*10^65572+119)/365573Robert Price02/2017
654120^50399+5165571Lelio R Paula08/2013
654211^62946-567065552Enzo Doria01/2013
65432^217742-391165547Yves Minet08/2009
6544(19*10^65545+77)/365546Robert Price08/2016
65452^217731+13165544Lelio R Paula08/2011
65462^217720-11128765541Enzo Doria05/2014
654710^65537+2765538Robert Price01/2011
654810^65537-7685965537Patrick De Geest05/2013
6549(10223*2^217676+1)/365531Lelio R Paula06/2014
6550PadovanNumber[536485]65518Eric W. Weisstein05/2009
65517*10^65492-4765493Robert Price02/2017
65522^217547-186840765489Enzo Doria04/2016
65532^217531-11176965484Enzo Doria05/2014
65547^77484-1865482Lelio R Paula06/2013
65552^217488-11328565471Enzo Doria07/2014
6556151153#/30-3065468Henri Lifchitz12/2011
65572^217466+425765464Lelio R Paula10/2011
655846396!3-8165455Robert Price09/2014
65592^217421-11318565451Enzo Doria07/2014
6560(6883*2^217440-1)/106119329589365448Lelio R Paula04/2015
65612^217408-214565447Lelio R Paula10/2011
65622^217398-1694765444Enzo Doria05/2013
65638*5^93613+365434Lelio R Paula09/2014
656411^62828-531065429Enzo Doria01/2013
656510^65426+1365427Robert Price01/2011
65662^217341-655565427Lelio R Paula10/2011
656710^65426-5484965426Patrick De Geest05/2013
6568(21*2^217363-1)/5600362666765424Lelio R Paula01/2014
656930011^14608-10865405Enzo Doria07/2012
6570(43^40031-1)/4265388Robert Price04/2014
65712^217190+9439565381Henri Lifchitz02/2005
657215^55587+4665376Lelio R Paula08/2013
65732^217088-11183365350Enzo Doria05/2014
6574(13*2^217069-1)/168294565340Lelio R Paula01/2014
6575(62*10^65331+1)/965332Serge Batalov11/2010
65762^216947-11135165308Enzo Doria05/2014
6577-E(18022)/77520184568268532294394923506835965307Thomas Ritschel02/2017
6578(13*10^65297+83)/365298Robert Price09/2016
65795^93400-865284Lelio R Paula06/2013
65802^216802-16565264Lelio R Paula08/2011
65812^216799-2863565264Lelio R Paula10/2011
65825*10^65255+5165256Robert Price01/2017
65832^216762-16765252Lelio R Paula08/2011
658411^62657-579065251Enzo Doria01/2013
65853^136756-11288065250Enzo Doria06/2014
65862^216752+2165249Lelio R Paula08/2011
658711^62651-270065245Enzo Doria12/2012
6589Pell-LucasQ(170413)/265230Eric W. Weisstein12/2006
6588gcd(V(790525),5*F(158105)*(F(158105)+1)+1)65230Serge Batalov04/2015
6590(2^216676-1017)/63765224Lelio R Paula04/2012
65912^216652-232765219Yves Minet10/2013
6592(9179*2^216648-1)/466765218Lelio R Paula04/2015
6593(5*10^65203-119)/365204Robert Price04/2016
65942^216555-11326965190Enzo Doria07/2014
6595(9513^16384+1)/265181Henri Lifchitz02/2007
65962^216474+1291565166Lelio R Paula02/2013
659719^50958-3265163Lelio R Paula08/2013
65982^216442-11213365156Enzo Doria06/2014
65992^216437-11221365155Enzo Doria06/2014
66002^216435-11276765154Enzo Doria06/2014
66012^216420+1270565149Lelio R Paula02/2013
66028*3^136507-765132Lelio R Paula04/2014
6603(-lucasV(1,2,432719)-2)/(5*461)65128Mike Oakes03/2017
66042^216197-11176965082Enzo Doria05/2014
66066^83631-7965078Lelio R Paula07/2013
6605572^23601+23601^57265078Norbert Schneider08/2016
6607(3^136399-7)/54422065074Lelio R Paula04/2012
66082^216154-142165069Yves Minet01/2013
66092^216145-11266365067Enzo Doria06/2014
6610132013*10^65050+2^216091-165056Gilbert Mozzo01/2014
6611132019*10^65050+2^216091-165056Gilbert Mozzo01/2014
6612148918*10^65050+2^216091-165056Gilbert Mozzo02/2014
6613194014*10^65050+2^216091-165056Gilbert Mozzo02/2014
6614223864*10^65050+2^216091-165056Gilbert Mozzo04/2014
661682090*10^65050+2^216091-165055Gilbert Mozzo07/2012
661795133*10^65050+2^216091-165055Gilbert Mozzo12/2013
661598142*10^65050+2^216091-165055Gilbert Mozzo12/2013
6618((2^216091-1)*34009-48)/2565054Serge Batalov01/2012
66195977*10^65050+2^216091-165054Gilbert Mozzo03/2012
66207*2^216091+2^298-1365051Peter Lesala03/2007
66212^216091+2*29208-165050Makoto Morimoto10/2013
6622(10^(2*32521+1)-6*10^32521-1)/365043Robert Price02/2016
6623p(13861)#/2+25665039Robert Price05/2017
662411^62439-438065024Enzo Doria01/2013
66253^136244+265005Mike Oakes11/2009
662613^58343-5064991Lelio R Paula07/2013
6627331^25791-1000264989Enzo Doria07/2012
66282^215877+13164986Lelio R Paula08/2011
66294*5^92959+964977Lelio R Paula09/2014
66302^215789-1882564959Lelio R Paula09/2011
6631(2^215801-509203)/4132764958Lelio R Paula05/2012
6632U(315311)64954Serge Batalov03/2015
663346072!3-5904964951Robert Price12/2015
66342^215750-595564948Lelio R Paula09/2011
663513^58281+4664922Lelio R Paula07/2013
66362^215623+18364909Lelio R Paula08/2011
6637(3^136043-2^136043)/(19862279*33466579)64895Mike Oakes12/2016
66385*2^215554+364889Lelio R Paula04/2014
66392^215541-11207564885Enzo Doria06/2014
66402*10^64882-364883Dmitry Domanov11/2010
664110^64862+34233964863Patrick De Geest05/2013
664210^64862-4764862Robert Price05/2011
664319^50718-8464856Lelio R Paula08/2013
6644(3045*2^215471-1)/(17*1151*27067*173473)64853Jens K. Andersen09/2007
664610^64843+427869783964844Robert Price05/2015
664510^64843+2196764844Patrick De Geest03/2016
664710^64843-34007364843Patrick De Geest03/2016
664811^62254+7064831Lelio R Paula07/2013
66492^215351-11192564828Enzo Doria05/2014
66502^215310-11764815Lelio R Paula08/2011
6651124^30958-12364809Norbert Schneider02/2015
6652(7*10^64807+17)/364808Erik Branger03/2014
6653(7*10^(2*32400+1)-27*10^32400-7)/964801Robert Price11/2015
66542^215243-1594964795Enzo Doria04/2013
665523^47581-22^4758164793Robert Price08/2012
6656(62*10^64783-17)/964784Robert Price09/2015
66575*3^135747-464769Lelio R Paula04/2014
6658(59*10^64767-41)/964768Robert Price09/2015
6660(2^215140+3)/1964763Lelio R Paula04/2012
66592^215135-1716964763Enzo Doria05/2013
66612^215115-11127764757Enzo Doria05/2014
66629*5^92641+264755Lelio R Paula09/2014
6663(lucasV(1,2,430086)-2)/(7*1033)64731Mike Oakes03/2017
6664(5*10^64715-23)/964715Robert Price11/2014
66652^214938-178164703Yves Minet03/2013
666611^62111-42064682Enzo Doria08/2012
66675^92525+4264673Lelio R Paula06/2013
66682^214824+7189364669Enzo Doria04/2016
66692^214799-222164661Yves Minet08/2013
6670(21*2^214688+1)/29364627Lelio R Paula08/2012
667192^32907+32907^9264623Serge Batalov05/2014
66726^83013+10164597Lelio R Paula07/2013
6673p(13775)#/2+864594Robert Price01/2017
6674(7*10^64568-43)/964568Robert Price10/2014
6675Pell-LucasQ(168677)/264566Eric W. Weisstein11/2006
6676(24737*2^214476+1)/287764565Lelio R Paula06/2014
6677(47*2^214463+1)/764561Lelio R Paula04/2015
66782^214458+5461564559Lelio R Paula10/2011
6679(3^135322+7)/12291140864557Lelio R Paula04/2012
66802^214389-68311364538Paul Bourdelais03/2013
66812^214369-11124164532Enzo Doria05/2014
6682(19^50461+3^50461)/2264526Robert Price07/2013
668311^61954-366064519Enzo Doria12/2012
6684(23*2^214319-1)/2164517Lelio R Paula01/2014
6685(58695*2^214310-1)/57164516Lelio R Paula04/2015
668635^41779-3464510Norbert Schneider04/2014
668711^61939-522064503Enzo Doria01/2013
6688(2^214271+78557)/3564501Lelio R Paula05/2012
6689126^30706-12564494Norbert Schneider02/2015
6690gcd(V(1157265),5*F(231453)*(F(231453)-1)+1)64492Serge Batalov04/2015
66912^214215+1290964486Lelio R Paula10/2011
66925^92225+6664463Lelio R Paula06/2013
66932^214126-24055164459Paul Bourdelais03/2013
66948*6^82827+564453Lelio R Paula09/2014
6695(31*2^214120-1)/217048564452Lelio R Paula01/2014
6696(31*2^214088-1)/595564445Lelio R Paula01/2014
669714^56227+8964444Lelio R Paula08/2013
67002^214055-15964437Lelio R Paula08/2011
669810^64436+266764437Patrick De Geest05/2013
669965^35543-64^3554364437Robert Price08/2013
670110^64436-5364436Robert Price05/2011
6702Phi(128878,10)/3950329792764428Maksym Voznyy11/2015
67033^135027+10064425Lelio R Paula05/2013
6704(3^134972-7)/264398Lelio R Paula04/2012
67056*10^64387+764388Dmitry Domanov11/2010
67062^213864-1837764380Enzo Doria05/2013
6707(2^213821+9)/20964365Lelio R Paula04/2012
67082^213788+13564357Lelio R Paula08/2011
6709(3^134883+2)/4831364351Lelio R Paula04/2012
6710(49^38069-46^38069)/364344Serge Batalov12/2016
6711(11^61781+2^61781)/1364338Robert Price02/2013
67126^82670+3764330Lelio R Paula07/2013
6713(3^134839+4)/3231295964328Lelio R Paula04/2012
6714(22*10^64326+161)/364327Robert Price02/2017
671511^61767-405064324Enzo Doria12/2012
67162^213645-11485364314Enzo Doria05/2015
671713^57733+1864312Lelio R Paula07/2013
67182^213621+7270764307Enzo Doria04/2016
671910^64305+13679164306Patrick De Geest05/2011
672010^64305-964305Alexander Gramolin01/2011
6721V(307652)64295Serge Batalov03/2015
6722(2^213546-5)/222164281Lelio R Paula04/2012
67232^213438-5869564252Lelio R Paula10/2011
67242^213367-10564230Lelio R Paula08/2011
6725595^23148+23148^59564225Norbert Schneider07/2016
67263^134601+868064221Lelio R Paula05/2013
6727(26*10^64220+61)/364221Robert Price06/2017
6728500^23793+23793^50064217Norbert Schneider08/2016
67302^213314-45564214Yves Minet02/2012
672939^40359-3864214Norbert Schneider05/2014
67312^213292-1608564208Enzo Doria04/2013
67322^213274-7764202Lelio R Paula08/2011
673319^50203+7864198Lelio R Paula08/2013
67342^213240-11286564192Enzo Doria06/2014
67352^213190-11239164177Enzo Doria06/2014
6736(9913*2^213184-1)/965764175Lelio R Paula04/2015
673714^55991+2764173Lelio R Paula07/2013
67382^213158-11258164167Enzo Doria06/2014
67392^213148+9164164Lelio R Paula08/2011
67416^82439+12564151Lelio R Paula07/2013
67407*2^213102+964151Lelio R Paula04/2014
6742L(306854)+F(306855)64129Henri Lifchitz01/2007
6743610^23017+23017^61064110Norbert Schneider07/2016
67442^212950-6487564105Lelio R Paula10/2011
6745(266*10^64102-17)/364104Robert Price06/2016
6746p(13679)#/2+6464097Robert Price03/2017
674719^50119+9464090Lelio R Paula08/2013
67482^212880-14764084Lelio R Paula08/2011
674911^61523-459064070Enzo Doria01/2013
67505^91663+3864070Lelio R Paula05/2013


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: June, 22 2017 08:34 (Time in France)

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