PRP Records

Probable Primes Top 10000

(252675 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 ?
6501(19*2^248099-1)/2974686Lelio R Paula01/2014
6502(86*10^74676-41)/974677Robert Price11/2015
6503(p(15711)#-4)/274672Robert Price09/2017
650410^74670+3174671Robert Price01/2011
650510^74670-12246374670Patrick De Geest05/2013
65062^248036-6974667Lelio R Paula03/2012
650711^71698-600074666Enzo Doria12/2012
650858*(10^(3*24887)-1)/111-174661Robert Price10/2014
650914^65139-4574658Lelio R Paula01/2015
65106^95921-13374642Lelio R Paula01/2015
651111^71675+7874642Lelio R Paula02/2015
651218^59449-9174625Lelio R Paula01/2015
65136^95864-1604374597Enzo Doria02/2013
65145*7^88261+674590Lelio R Paula10/2014
65159*5^106710+474589Lelio R Paula10/2014
6516(777*2^247788+1)/(11*754121)74588Jens K. Andersen09/2007
6517(265*10^74579+17)/374581Robert Price05/2016
6518(2^247759-1017)/331831171774574Lelio R Paula07/2012
65195^106682-2474568Lelio R Paula08/2014
6520474^27863+27863^47474556Norbert Schneider01/2017
6521(14*10^74540+79)/374541Robert Price11/2017
6522(35365^16384+1)/274524Lelio R Paula11/2011
65233^156161+266074508Lelio R Paula01/2015
65242^247474-5869574498Lelio R Paula05/2013
652511^71519-9074480Enzo Doria07/2012
6526(19*2^247419-1)/2320298374475Lelio R Paula01/2014
6528(2^247394-7)/374473Lelio R Paula06/2012
652718^59328+1774473Lelio R Paula01/2015
65292^247379-18174469Lelio R Paula03/2012
6530(15*2^247370-1)/47974465Lelio R Paula01/2014
65312^247344+204774458Lelio R Paula05/2013
65322^247311-101774449Lelio R Paula05/2013
65332^247280+774439Lelio R Paula03/2012
6534(68*10^74434+13)/974435Ray Chandler11/2010
65353^156004-6274433Lelio R Paula01/2015
653636095!2-6474416Robert Price06/2015
65372^247165-374405M. Frind & P. Underwood07/2002
65382^247150+3276974400Lelio R Paula05/2013
653912^68911+7374368Lelio R Paula01/2015
65402^246999+7490374355Enzo Doria04/2016
65412^246989-11064374352Enzo Doria05/2014
654210^74350+27943974351Patrick De Geest07/2017
6545(10^74350+11)/374350Robert Price11/2014
654310^74350-40000000174350Robert Price07/2017
654410^74350-71624174350Patrick De Geest07/2017
654610^74335+1365974336Patrick De Geest05/2013
654710^74335-5374335Robert Price05/2011
65482^246906-121574327Lelio R Paula05/2013
65492^246848+11174309Lelio R Paula03/2012
65506^95490-1844374306Enzo Doria03/2013
655118^59188-236974298Enzo Doria03/2013
6552(1363*2^246767+1)/(3*5*7*13^2*743)74281Jens K. Andersen09/2007
65532^246744+4075574278Lelio R Paula05/2013
6554(29*10^74276+91)/374277Robert Price03/2016
65556^95441+16374268Lelio R Paula01/2015
6556V(390863)74258Serge Batalov03/2015
655710^74254+9174255Robert Price03/2011
6558(19*10^74253-1)/974254Ray Chandler02/2012
655910^74254-13056974254Patrick De Geest05/2013
6560771^25718+25718^77174250Norbert Schneider10/2016
65612^246618+42774240Henri Lifchitz02/2005
656288*10^74234+374236Robert Price11/2016
65638*10^74234-4974235Robert Price04/2016
65642^246578+1228574228Lelio R Paula05/2013
6565(3^155569-5)/274225Lelio R Paula06/2012
656613^66628+4674220Lelio R Paula01/2015
65672^246476-1729574197Lelio R Paula05/2013
6568(61*10^74189-1)/374191Robert Price11/2017
6569(15185*2^246432-1)/1374187Lelio R Paula04/2015
65705*2^246413-374179Lelio R Paula05/2014
65712^246386-2863574170Lelio R Paula05/2013
65722^246334-11124574154Enzo Doria05/2014
65733*9^77708+7^77708-2*4^77708-374153Mike Oakes12/2010
657415^63045+8274147Lelio R Paula01/2015
657519255!+19255#+174140D. Gazzoni Filho & Lucas Teixeira06/2005
65762^246268-11050774135Enzo Doria05/2014
65773^155328+266074111Lelio R Paula01/2015
65782^246148-278624974098Enzo Doria03/2016
6579(16*10^74092-19)/374093Robert Price03/2016
65802^246115-11076774088Enzo Doria05/2014
65817^87666-6874087Lelio R Paula08/2014
658210^74079+114514191974080Marisa Kirisame03/2015
658310^74079+621974080Patrick De Geest03/2016
658410^74079-28270774079Patrick De Geest03/2016
6585129^35098+274078Lelio R Paula05/2013
65862^246025-11212374061Enzo Doria06/2014
6587(67*10^74045+17)/374047Robert Price02/2017
65882^245823+6683174001Marek Hubal02/2017
65895^105869+4274000Lelio R Paula08/2014
6590(21*2^245806+1)/63455573991Lelio R Paula08/2012
6591(22699*2^245762+1)/11973985Lelio R Paula06/2014
6592(3^155048-7)/26273975Lelio R Paula06/2012
65939998*2^245696+373966Donovan Johnson10/2004
659413^66400-8073966Lelio R Paula01/2015
6595(2^245704+9)/2573963Lelio R Paula07/2012
659711^71023-717073963Enzo Doria01/2013
65963*10^73962+1373963Robert Price08/2017
6598(31*2^245660-1)/11419573948Lelio R Paula01/2014
65992^245629-279781373942Eric Chen03/2016
66002^245557-15373921Lelio R Paula03/2012
6601(77*10^73917-59)/973918Robert Price11/2017
66022^245525+186988173911Enzo Doria06/2016
66032^245522+15973910Lelio R Paula03/2012
6604(13*10^73891-43)/373892Robert Price08/2017
660519^57783-5673891Lelio R Paula01/2015
66067*10^73888+7973889Robert Price02/2017
66076^94948+17428173884Mike Oakes02/2011
660811^70939-486073876Enzo Doria01/2013
66092^245372+5461573865Lelio R Paula05/2013
66102^245362-14373862Lelio R Paula03/2012
66117^87396+6^(87396-1)73859Robert Price03/2016
6612(22*10^73853-37)/373854Robert Price05/2017
66135^105646-1424673844Enzo Doria02/2013
66152^245290-4173840Lelio R Paula03/2012
66142^245290-9439573840Lelio R Paula05/2013
66168*5^105600-773813Lelio R Paula10/2014
66177*5^105573-473794Lelio R Paula10/2014
661818^58742-480573738Enzo Doria03/2013
661913^66179+6673720Lelio R Paula01/2015
6620(82*10^73714-1)/973715Robert Price12/2014
6621(29*2^244856-1)/18612173706Lelio R Paula01/2014
6622(13*2^244840-1)/279973702Lelio R Paula01/2014
6623(13*10^73701+17)/373702Robert Price06/2015
6624(2^244787-1017)/2841173684Lelio R Paula07/2012
6625(3^154421-4)/2373677Lelio R Paula06/2012
66268*7^87170+573669Lelio R Paula10/2014
6627(29*10^73659-113)/373660Robert Price11/2017
6628Phi(40100,-40100)73651Henri Lifchitz06/2013
6629(4*10^73647-19)/373648Robert Price06/2017
66302^244618-229773638Yves Minet10/2009
66313*5^105344+873633Lelio R Paula10/2014
66325^105334-1409673626Enzo Doria02/2013
6633(2^244584-7)/1323707424303373614Lelio R Paula07/2012
66342^244465-11018573592Enzo Doria05/2014
66352^244443+4075573585Lelio R Paula05/2013
66362^244404+384173573Yves Minet03/2011
66372^244372-11062773564Enzo Doria05/2014
6638(3*2^244255+1)/24573527Lelio R Paula08/2012
6639(11*2^244245+1)/2373525Lelio R Paula08/2012
6640(15185*2^244187-1)/611173509Lelio R Paula04/2015
6641(91^37507+1)/9273476Paul Bourdelais08/2017
664218^58521+6573460Lelio R Paula01/2015
664313^65940+3673454Lelio R Paula01/2015
6644(625^26267+1)/62673437Richard Fischer12/2017
66455^105050-1473427Lelio R Paula08/2014
6646(((((((((((((30201^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-273401Serge Batalov07/2016
664715^62410-4673400Lelio R Paula01/2015
66482^243733+186970773371Enzo Doria05/2016
664911^70439-543073355Enzo Doria01/2013
66502^243676-8773354Lelio R Paula03/2012
6651(101*10^73346-17)/373348Robert Price08/2016
66522^243621-11318573338Enzo Doria07/2014
6653(5*2^243610-1)/166973332Lelio R Paula01/2014
66542*5^104888-773314Lelio R Paula10/2014
6655(58695*2^243516-1)/98373308Lelio R Paula04/2015
6656(3^153648-2)/3342313809773299Lelio R Paula06/2012
665718^58376-525573278Enzo Doria03/2013
665811^70363+3273276Lelio R Paula02/2015
66592^243413+425773275Lelio R Paula05/2013
6660104824^5+5^10482473269Andrey Kulsha07/2010
66617^86689-6^8668973261Predrag Minovic09/2004
66622^243296+9019573240Lelio R Paula05/2013
6664p(15433)#/2-473218Robert Price12/2016
6663(59*10^73217-77)/973218Robert Price11/2017
66652^243127+7135573189Lelio R Paula05/2013
66662^243116-24941973186Paul Bourdelais03/2013
6667(58695*2^243085-1)/1173180Lelio R Paula04/2015
666811^70262-9873171Lelio R Paula02/2015
6669(2^243034+47)/72270330373152Lelio R Paula07/2012
6670(2^242966+47)/4688773136Lelio R Paula07/2012
6671(43^44773-1)/4273134Robert Price04/2014
66726^93980-15835973131Mike Oakes02/2011
66736^93915+5373081Lelio R Paula01/2015
6674(5*10^73079+211)/973079Robert Price12/2017
6675(74*10^73076+43)/973077Robert Price10/2015
6676(3^153125+2)/114495573054Lelio R Paula06/2012
66772^242632-11219973040Enzo Doria06/2014
6678V(351646)73029Serge Batalov03/2015
667918^58175-8573026Lelio R Paula01/2015
6680p(15395)#/2-473019Robert Price12/2016
6681(4^121271+3^121271)/773012Jean-Louis Charton03/2011
66828*6^93825-573011Lelio R Paula10/2014
6683(F(220)^1601-F(219)^1601)/F(218)73005Wayne Halsdorf08/2013
6684(73^39181+1)/7473005Paul Bourdelais08/2017
66856^93815+14373003Lelio R Paula01/2015
66866^93812+573000Wojciech Florek03/2006
668719^57078-6272989Lelio R Paula01/2015
6688(29*10^72985+91)/372986Robert Price03/2016
668911^70082-252072983Enzo Doria12/2012
66906^93773+13372970Lelio R Paula01/2015
66912^242328-5972948Lelio R Paula03/2012
66925^104358-1301672944Enzo Doria02/2013
6693(75*10^72941-57)/9972941Ray Chandler03/2011
669412^67585-9572937Lelio R Paula02/2015
66952^242230-11328572919Enzo Doria07/2014
6696(5*10^72916-11)/372917Erik Branger12/2013
66972^242220-11039972916Enzo Doria05/2014
66982^242205-11341372911Enzo Doria07/2014
6699(3^152809+3^76405+1)/772908Serge Batalov03/2014
67002^242175+7424372902Yves Minet03/2011
67012^242150+1765972895Lelio R Paula11/2009
670211^69982-234072879Enzo Doria12/2012
6703(23*2^242093+1)/1011772875Lelio R Paula08/2012
6704(67607*2^242043+1)/3326372863Lelio R Paula06/2014
67052^242032+8772859Lelio R Paula03/2012
67062^241968-11059572840Enzo Doria05/2014
6707(10^72821+71)/972821Robert Price11/2014
67082^241852-6487572805Lelio R Paula05/2013
6709F(348307)/2056289086590809372776Donovan Johnson07/2007
6710(67*10^72772+23)/972773Ray Chandler11/2010
6711(8*10^72759+67)/372760Robert Price01/2017
67122^241670+14572750Lelio R Paula03/2012
67135^104074+5272745Lelio R Paula08/2014
6714(3^152466-5)/72472742Lelio R Paula06/2012
671520^55908-4172738Lelio R Paula01/2015
6716(73*10^72735+53)/972736Robert Price10/2015
671710^72730+22401172731Patrick De Geest05/2013
671810^72730-9972730Robert Price05/2011
67193*10^72723+6772724Robert Price11/2017
6720(11^69833+3^69833)/1472723Robert Price03/2013
6721(10^72723-79)/372723Robert Price10/2017
6722(88*10^72711-43)/972712Robert Price11/2015
67233^152379+28072704Lelio R Paula01/2015
6724(25*10^72703-241)/972704Robert Price01/2017
6725(47*10^72696+133)/972697Robert Price04/2017
672617^59077-9072692Lelio R Paula01/2015
672765^40096+5872691Lelio R Paula01/2016
6728(29*2^241446-1)/24572682Lelio R Paula01/2014
673011^69783-3840000072672Enzo Doria01/2013
67292^241409-11290372672Enzo Doria06/2014
6731(3^152287+1)/472659Paul Bourdelais04/2008
67323^152249-5672642Lelio R Paula01/2015
673310^72631+3772632Robert Price01/2011
673410^72631-881372631Patrick De Geest05/2013
6735(19*2^241254+1)/10172624Lelio R Paula08/2012
6736(9^76103+8^76103)/1772620Robert Price12/2012
67372^241220-11233772615Enzo Doria06/2014
6738(82*10^72612+449)/972613Robert Price02/2017
67392^241169-1579372600Enzo Doria04/2013
67409*10^72595+1172596Robert Kinser01/2017
6741(25*2^241048+1)/8972563Lelio R Paula08/2012
6742(22*10^72560+17)/372561Robert Price09/2015
67432^241032-2372558Lelio R Paula02/2012
674434485*10^72550+2^241004-372555Gilbert Mozzo12/2012
67452^241004-372550M. Frind & P. Underwood07/2002
674697*10^72522-372524Robert Price01/2017
6747(68*10^72516+7)/372518Robert Price03/2016
6748(78557*2^240844+1)/6372505Lelio R Paula06/2014
674967^39701-6672497Norbert Schneider11/2014
6750(185*10^72484+7)/372486Robert Price02/2017


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: April, 20 2019 09:21 (Time in France)

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