PRP Records

Probable Primes Top 10000

(252932 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 ?
65015*7^89231-675410Lelio R Paula10/2014
65032^250503-1699575409Lelio R Paula05/2013
650211^72411-2875409Lelio R Paula02/2015
65043*5^107860-875392Lelio R Paula10/2014
6505(34*10^75387-403)/975388Robert Price10/2017
65072^250426+2983575386Lelio R Paula05/2013
65068*3^157999-775386Lelio R Paula05/2014
6508(88*10^75381-43)/975382Robert Price11/2015
65092^250382-11175575373Enzo Doria05/2014
65102^250374-279805175371Eric Chen03/2016
6511(22*10^75368-1)/375369Robert Price12/2014
65122^250369-454375369Yves Minet03/2019
6513(19*10^75338+119)/375339Robert Price02/2017
65142^250223-185916775325Enzo Doria03/2016
6515(3^157854-7)/6602528275308Lelio R Paula06/2012
65163^157831-9875305Lelio R Paula01/2015
6517(46^45281+11^45281)/5775290Serge Batalov12/2016
651892^38335-9175282Norbert Schneider01/2016
65192^250020+1891575264Lelio R Paula05/2013
65202^250002+819375259Lelio R Paula05/2013
6521(11*2^249977-7)/1575251Renaud Lifchitz02/2011
6522(2^249968+78557)/6375247Lelio R Paula07/2012
6523(5*10^75244+91)/375245Robert Price11/2016
6524(10489!)^2+Prime(10489)75242Robert Price08/2014
652514^65644+6775237Lelio R Paula01/2015
6526(2^249928-5)/1185905975229Lelio R Paula06/2012
6527129^35638+275218Lelio R Paula05/2013
65282^249853-11047575214Enzo Doria05/2014
65292^249762+7540975186Enzo Doria04/2016
6530565^27318+27318^56575181Norbert Schneider12/2016
6531(2^249741-7)/68575177Lelio R Paula06/2012
65322^249726-11218175176Enzo Doria06/2014
65332^249721+1171575174Lelio R Paula05/2013
6534(38661^16384+1)/275158Lelio R Paula11/2011
65352^249658-4735575155Lelio R Paula05/2013
6536155^34311+275153Lelio R Paula05/2013
6537(10^87682+1)/(10^12526+1)/99009900990175145Maksym Voznyy06/2015
6538(23*2^249602+1)/9375138Lelio R Paula08/2012
65392^249522+841575114Lelio R Paula05/2013
65402^249489-11091175104Enzo Doria05/2014
6541(28*10^75078+131)/375079Robert Price02/2017
6542(206*10^75073-17)/975075Robert Price03/2017
65432^249368-11057375068Enzo Doria05/2014
6544NaturalLogarithmOf10(75067)75067Eric W. Weisstein10/2015
6545(2^249375+78557)/4505612575062Lelio R Paula07/2012
6546(26*10^75055-173)/375056Robert Price10/2017
65472^249272+19375039Lelio R Paula03/2012
654814^65468+4375035Lelio R Paula01/2015
654937^47844+3675030Norbert Schneider05/2014
6550(52*10^75027-7)/975028Robert Price12/2014
655120^57653+8975009Lelio R Paula01/2015
65522^249061-186835374975Enzo Doria04/2016
65537^88713+2*3^8871374972Mike Oakes07/2010
65542*6^96313+574947Lelio R Paula10/2014
6555(8*10^74944+49)/374945Robert Price03/2016
6556300^30247+30247^30074926Norbert Schneider11/2014
65572^248866-17174917Lelio R Paula03/2012
65586*5^107168-774908Lelio R Paula10/2014
655911^71926+7874904Lelio R Paula02/2015
65602^248824+186939174904Enzo Doria05/2016
65612^248816+111174902Lelio R Paula01/2011
6562V(388219)74890Serge Batalov03/2015
6563159^34017+15874885Norbert Schneider12/2018
65642*F(358297)-174880Henri Lifchitz12/2009
6565(22*10^74874-31)/974875Robert Price04/2015
656611^71892-7680000074868Enzo Doria01/2013
65679*5^107107-474866Lelio R Paula10/2014
65682^248678-71011174860Paul Bourdelais03/2013
6569(14*10^74858+211)/974859Robert Price11/2017
657013^67194+1274851Lelio R Paula01/2015
6571(7*2^248634+1)/7174846Lelio R Paula08/2012
657211^71867-309074842Enzo Doria12/2012
65732^248609+26214574839Lelio R Paula05/2013
65743^156852+5074838Lelio R Paula01/2015
657518^59607-1174824Lelio R Paula01/2015
65762^248556-11050774823Enzo Doria05/2014
65777^88531-3674818Lelio R Paula01/2015
6578p(15738)#/2+102474814Robert Price07/2017
65794*3^156740-574785Lelio R Paula05/2014
6580(32*10^74773-41)/974774Robert Price05/2015
6581(29*2^248384-1)/1374772Lelio R Paula01/2014
658219401!+19401#+174765D. Gazzoni Filho & Lucas Teixeira06/2005
65832^248357-1279741374763Enzo Doria03/2016
658442^46057+4174762Lelio R Paula07/2012
658511^71784-300074756Enzo Doria12/2012
658619^58458+1874754Lelio R Paula01/2015
658712^69265-3574750Lelio R Paula02/2015
658811^71771-4800074742Enzo Doria12/2012
6589(7*10^74741+197)/374742Robert Price07/2017
6590(2^248282-5)/5012974736Lelio R Paula06/2012
65912^248252-11010574732Enzo Doria04/2014
6592(7*10^74729+71)/374730Robert Price03/2016
65933^156614-5074724Lelio R Paula01/2015
6594(7*2^248213+1)/13574719Lelio R Paula07/2012
6595(2^248173+78557)/76774705Lelio R Paula07/2012
6596125^35622+12474697Norbert Schneider02/2015
6597(19*2^248099-1)/2974686Lelio R Paula01/2014
6598(86*10^74676-41)/974677Robert Price11/2015
6599(p(15711)#-4)/274672Robert Price09/2017
660010^74670+3174671Robert Price01/2011
660110^74670-12246374670Patrick De Geest05/2013
66022^248036-6974667Lelio R Paula03/2012
660311^71698-600074666Enzo Doria12/2012
660458*(10^(3*24887)-1)/111-174661Robert Price10/2014
660514^65139-4574658Lelio R Paula01/2015
66066^95921-13374642Lelio R Paula01/2015
660711^71675+7874642Lelio R Paula02/2015
660818^59449-9174625Lelio R Paula01/2015
66096^95864-1604374597Enzo Doria02/2013
66105*7^88261+674590Lelio R Paula10/2014
66119*5^106710+474589Lelio R Paula10/2014
6612(777*2^247788+1)/(11*754121)74588Jens K. Andersen09/2007
6613(265*10^74579+17)/374581Robert Price05/2016
6614(2^247759-1017)/331831171774574Lelio R Paula07/2012
66155^106682-2474568Lelio R Paula08/2014
6616474^27863+27863^47474556Norbert Schneider01/2017
6617(14*10^74540+79)/374541Robert Price11/2017
6618(35365^16384+1)/274524Lelio R Paula11/2011
66193^156161+266074508Lelio R Paula01/2015
66202^247474-5869574498Lelio R Paula05/2013
662111^71519-9074480Enzo Doria07/2012
6622(19*2^247419-1)/2320298374475Lelio R Paula01/2014
6624(2^247394-7)/374473Lelio R Paula06/2012
662318^59328+1774473Lelio R Paula01/2015
66252^247379-18174469Lelio R Paula03/2012
6626(15*2^247370-1)/47974465Lelio R Paula01/2014
66272^247344+204774458Lelio R Paula05/2013
66282^247311-101774449Lelio R Paula05/2013
66292^247280+774439Lelio R Paula03/2012
6630(68*10^74434+13)/974435Ray Chandler11/2010
66313^156004-6274433Lelio R Paula01/2015
663236095!2-6474416Robert Price06/2015
66332^247165-374405M. Frind & P. Underwood07/2002
66342^247150+3276974400Lelio R Paula05/2013
663512^68911+7374368Lelio R Paula01/2015
66362^246999+7490374355Enzo Doria04/2016
66372^246989-11064374352Enzo Doria05/2014
663810^74350+27943974351Patrick De Geest07/2017
6641(10^74350+11)/374350Robert Price11/2014
663910^74350-40000000174350Robert Price07/2017
664010^74350-71624174350Patrick De Geest07/2017
664210^74335+1365974336Patrick De Geest05/2013
664310^74335-5374335Robert Price05/2011
66442^246906-121574327Lelio R Paula05/2013
66452^246848+11174309Lelio R Paula03/2012
66466^95490-1844374306Enzo Doria03/2013
664718^59188-236974298Enzo Doria03/2013
6648(1363*2^246767+1)/(3*5*7*13^2*743)74281Jens K. Andersen09/2007
66492^246744+4075574278Lelio R Paula05/2013
6650(29*10^74276+91)/374277Robert Price03/2016
66516^95441+16374268Lelio R Paula01/2015
6652V(390863)74258Serge Batalov03/2015
665310^74254+9174255Robert Price03/2011
6655(19*10^74253-1)/974254Ray Chandler02/2012
665410^74254-13056974254Patrick De Geest05/2013
6656771^25718+25718^77174250Norbert Schneider10/2016
66572^246618+42774240Henri Lifchitz02/2005
665888*10^74234+374236Robert Price11/2016
66598*10^74234-4974235Robert Price04/2016
66602^246578+1228574228Lelio R Paula05/2013
6661(3^155569-5)/274225Lelio R Paula06/2012
666213^66628+4674220Lelio R Paula01/2015
66632^246476-1729574197Lelio R Paula05/2013
6664(61*10^74189-1)/374191Robert Price11/2017
6665(15185*2^246432-1)/1374187Lelio R Paula04/2015
66665*2^246413-374179Lelio R Paula05/2014
66672^246386-2863574170Lelio R Paula05/2013
66682^246334-11124574154Enzo Doria05/2014
66693*9^77708+7^77708-2*4^77708-374153Mike Oakes12/2010
667015^63045+8274147Lelio R Paula01/2015
667119255!+19255#+174140D. Gazzoni Filho & Lucas Teixeira06/2005
66722^246268-11050774135Enzo Doria05/2014
66733^155328+266074111Lelio R Paula01/2015
66742^246148-278624974098Enzo Doria03/2016
6675(16*10^74092-19)/374093Robert Price03/2016
66762^246115-11076774088Enzo Doria05/2014
66777^87666-6874087Lelio R Paula08/2014
667810^74079+114514191974080Marisa Kirisame03/2015
667910^74079+621974080Patrick De Geest03/2016
668010^74079-28270774079Patrick De Geest03/2016
6681129^35098+274078Lelio R Paula05/2013
66822^246025-11212374061Enzo Doria06/2014
6683(67*10^74045+17)/374047Robert Price02/2017
66842^245823+6683174001Marek Hubal02/2017
66855^105869+4274000Lelio R Paula08/2014
6686(21*2^245806+1)/63455573991Lelio R Paula08/2012
6687(22699*2^245762+1)/11973985Lelio R Paula06/2014
6688(3^155048-7)/26273975Lelio R Paula06/2012
66899998*2^245696+373966Donovan Johnson10/2004
669013^66400-8073966Lelio R Paula01/2015
6691(2^245704+9)/2573963Lelio R Paula07/2012
669311^71023-717073963Enzo Doria01/2013
66923*10^73962+1373963Robert Price08/2017
6694(31*2^245660-1)/11419573948Lelio R Paula01/2014
66952^245629-279781373942Eric Chen03/2016
66962^245557-15373921Lelio R Paula03/2012
6697(77*10^73917-59)/973918Robert Price11/2017
66982^245525+186988173911Enzo Doria06/2016
66992^245522+15973910Lelio R Paula03/2012
6700(13*10^73891-43)/373892Robert Price08/2017
670119^57783-5673891Lelio R Paula01/2015
67027*10^73888+7973889Robert Price02/2017
67036^94948+17428173884Mike Oakes02/2011
670411^70939-486073876Enzo Doria01/2013
67052^245372+5461573865Lelio R Paula05/2013
67062^245362-14373862Lelio R Paula03/2012
67077^87396+6^(87396-1)73859Robert Price03/2016
6708(22*10^73853-37)/373854Robert Price05/2017
67095^105646-1424673844Enzo Doria02/2013
67112^245290-4173840Lelio R Paula03/2012
67102^245290-9439573840Lelio R Paula05/2013
67128*5^105600-773813Lelio R Paula10/2014
67137*5^105573-473794Lelio R Paula10/2014
671418^58742-480573738Enzo Doria03/2013
671513^66179+6673720Lelio R Paula01/2015
6716(82*10^73714-1)/973715Robert Price12/2014
6717(29*2^244856-1)/18612173706Lelio R Paula01/2014
6718(13*2^244840-1)/279973702Lelio R Paula01/2014
6719(13*10^73701+17)/373702Robert Price06/2015
6720(2^244787-1017)/2841173684Lelio R Paula07/2012
6721(3^154421-4)/2373677Lelio R Paula06/2012
67228*7^87170+573669Lelio R Paula10/2014
6723(29*10^73659-113)/373660Robert Price11/2017
6724Phi(40100,-40100)73651Henri Lifchitz06/2013
6725(4*10^73647-19)/373648Robert Price06/2017
67262^244618-229773638Yves Minet10/2009
67273*5^105344+873633Lelio R Paula10/2014
67285^105334-1409673626Enzo Doria02/2013
6729(2^244584-7)/1323707424303373614Lelio R Paula07/2012
67302^244465-11018573592Enzo Doria05/2014
67312^244443+4075573585Lelio R Paula05/2013
67322^244404+384173573Yves Minet03/2011
67332^244372-11062773564Enzo Doria05/2014
6734(3*2^244255+1)/24573527Lelio R Paula08/2012
6735(11*2^244245+1)/2373525Lelio R Paula08/2012
6736(15185*2^244187-1)/611173509Lelio R Paula04/2015
673717063^17362+17362^1706373477Norbert Schneider04/2019
6738(91^37507+1)/9273476Paul Bourdelais08/2017
673918^58521+6573460Lelio R Paula01/2015
674013^65940+3673454Lelio R Paula01/2015
6741(625^26267+1)/62673437Richard Fischer12/2017
67425^105050-1473427Lelio R Paula08/2014
6743(((((((((((((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
674415^62410-4673400Lelio R Paula01/2015
67452^243733+186970773371Enzo Doria05/2016
674611^70439-543073355Enzo Doria01/2013
67472^243676-8773354Lelio R Paula03/2012
6748(101*10^73346-17)/373348Robert Price08/2016
67492^243621-11318573338Enzo Doria07/2014
6750(5*2^243610-1)/166973332Lelio R Paula01/2014


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: June, 18 2019 07:14 (Time in France)

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