PRP Records

Probable Primes Top 10000

(191107 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 ?
55012^254075-278841776485Enzo Doria03/2016
55027*10^76483-2376484Robert Price04/2016
55032^254042-11291376475Enzo Doria06/2014
550414^66723-3776474Lelio R Paula02/2015
55052^254037-11030576473Enzo Doria05/2014
55062^253931-11110976441Enzo Doria05/2014
55072^253926-116776440Lelio R Paula05/2013
5508(49*10^76438-13)/976439Robert Price07/2015
5509(21*2^253845-1)/14376415Lelio R Paula02/2014
551010^76374+3176375Robert Price03/2011
551110^76374-22215976374Patrick De Geest05/2013
55122^253561-11053376330Enzo Doria05/2014
5513gcd(V(917285),5*F(183457)*(F(183457)+1)+1)76321Serge Batalov04/2015
55149*5^109182+276316Lelio R Paula10/2014
551511^73279-369076313Enzo Doria12/2012
5516(598*10^76309-31)/976311Robert Price02/2017
551711^73274-2400076308Enzo Doria12/2012
55187^90291-676305Theodore Burton11/2005
5519(21181*2^253432+1)/2143776291Lelio R Paula06/2014
55206^98025+14576279Lelio R Paula01/2015
55212^253355+115576268Lelio R Paula05/2013
5522(73*10^76262+413)/976263Robert Price10/2017
55232^253292-7121976249Enzo Doria04/2016
55247^90221-3676246Lelio R Paula02/2015
552518^60727-347376229Enzo Doria03/2013
5527(78557*2^253184+1)/376221Lelio R Paula06/2014
5526(8*10^76220-83)/376221Robert Price10/2017
5528(44791^20480+1)/(44791^4096+1)76206Serge Batalov01/2017
552911^73163-201076192Enzo Doria12/2012
55302^253060+5461576179Lelio R Paula05/2013
55312^253029+186976176170Enzo Doria05/2016
55322^252955-11100776148Enzo Doria05/2014
55332*5^108931+776140Lelio R Paula10/2014
5534(86*10^76128+121)/976129Robert Price03/2017
553522154*29^52050+976123Curtis Bright05/2015
55363^159530-11235876116Enzo Doria06/2014
553711^73089-4876115Lelio R Paula02/2015
553886^39337-8576098Norbert Schneider10/2015
5539(3^159505-7)/31329731676095Lelio R Paula06/2012
55406^97783+7776090Lelio R Paula01/2015
55412^252712-10576074Lelio R Paula03/2012
5542(10^76069-19)/976069Robert Price10/2017
5544131^35927+276068Lelio R Paula05/2013
5543(41*10^76067+373)/976068Robert Price04/2017
55452^252683-13976066Lelio R Paula03/2012
5546137^35597-13676061Norbert Schneider05/2015
55473^159413+10676060Lelio R Paula01/2015
55489^79677+3*8^79677-2*4^79677-3*2^7967776032Mike Oakes12/2010
5549(2^252557-9)/7176026Lelio R Paula07/2012
5550(85*10^76021-103)/976022Robert Price10/2017
555111^72989+8076011Lelio R Paula02/2015
55522^252449-45952375995Enzo Doria05/2015
555320^58408+7375991Lelio R Paula01/2015
55542^252418-142175986Yves Minet01/2013
5555(11*2^252396-1)/575980Lelio R Paula02/2014
55562^252365-11068975970Enzo Doria05/2014
555711^72949-102075969Enzo Doria11/2012
5558(2^252294+47)/654975945Lelio R Paula07/2012
55592^252261-11059575939Enzo Doria05/2014
55607^89853+7675935Lelio R Paula01/2015
55613^159132+5675926Lelio R Paula01/2015
5562730^26513+26513^73075916Norbert Schneider11/2016
5563(27*2^252163-1)/194575907Lelio R Paula01/2014
55645^108596-1484675906Enzo Doria02/2013
55655^108560-1484675881Enzo Doria02/2013
55662^252051-11035975875Enzo Doria05/2014
55672^251971-11050975851Enzo Doria05/2014
5568(42457^16384+1)/32768275819Lelio R Paula11/2011
556999655!6-275811Robert Price07/2017
557014*10^75798+108975800Jens K. Andersen11/2007
55712^251784-45575795Yves Minet03/2012
55722^251780-128975794Yves Minet01/2013
55732^251760-21560975788Paul Bourdelais03/2013
557499^37973+275781Lelio R Paula05/2013
5575(185*10^75777+7)/375779Robert Price02/2017
55765*2^251690+375767Lelio R Paula06/2014
55776^97366+9575766Lelio R Paula01/2015
55788*6^97337-775744Lelio R Paula10/2014
55792^251588-11167775736Enzo Doria05/2014
55805^108346-1325675731Enzo Doria02/2013
5581(31^50777+1)/3275726Robert Price07/2013
5582(10^75707+77)/375707Robert Price01/2017
5583(174907#+1673)/(7*239*15467899)75700Makoto Morimoto10/2017
55842^251466+19375699Lelio R Paula03/2012
5585(5*2^251464+1)/942375695Lelio R Paula07/2012
55862^251422-10999175686Enzo Doria04/2014
55874*5^108245-375661Lelio R Paula10/2014
558812^70067-11^7006775615Jean-Louis Charton11/2006
558912^70066+9575614Lelio R Paula02/2015
5590-E20534/206375607Thomas Ritschel02/2017
559119^59120-5075600Lelio R Paula01/2015
559218^60222-469775596Enzo Doria03/2013
559318^60211-435575582Enzo Doria03/2013
55947*2^251014-975564Lelio R Paula06/2014
55956^97101-2575560Lelio R Paula01/2015
55968^83663-7^8366375556Jean-Louis Charton01/2004
55973^158331-14075544Lelio R Paula01/2015
5598(37^48157-1)/3675519Robert Price03/2012
5599(19*10^75518-43)/375519Robert Price10/2017
560010^75516+3146775517Patrick De Geest03/2016
560210^75516-10^2256-175516Serge Batalov01/2011
560110^75516-6659175516Patrick De Geest03/2016
56032^250851-18775514Lelio R Paula03/2012
5604(43*10^75498-7)/975499Robert Price12/2014
5605(3^158244-5)/24791675497Lelio R Paula06/2012
56064*5^107971-375470Lelio R Paula10/2014
5607(25*10^75465+71)/375466Robert Price01/2017
5608(5*2^250681-1)/99975461Lelio R Paula01/2014
5609(182*10^75456+1)/375458Robert Price02/2017
5610(2^250669-9)/9889772975451Lelio R Paula07/2012
561110^75441+1375442Robert Price01/2011
561210^75441-992375441Patrick De Geest05/2013
5613(27*2^250546-1)/645775420Lelio R Paula01/2014
56145*7^89231-675410Lelio R Paula10/2014
56162^250503-1699575409Lelio R Paula05/2013
561511^72411-2875409Lelio R Paula02/2015
56173*5^107860-875392Lelio R Paula10/2014
5618(34*10^75387-403)/975388Robert Price10/2017
56202^250426+2983575386Lelio R Paula05/2013
56198*3^157999-775386Lelio R Paula05/2014
5621(88*10^75381-43)/975382Robert Price11/2015
56222^250382-11175575373Enzo Doria05/2014
56232^250374-279805175371Eric Chen03/2016
5624(22*10^75368-1)/375369Robert Price12/2014
5625(19*10^75338+119)/375339Robert Price02/2017
56262^250223-185916775325Enzo Doria03/2016
5627(3^157854-7)/6602528275308Lelio R Paula06/2012
56283^157831-9875305Lelio R Paula01/2015
5629(46^45281+11^45281)/5775290Serge Batalov12/2016
563092^38335-9175282Norbert Schneider01/2016
56312^250020+1891575264Lelio R Paula05/2013
56322^250002+819375259Lelio R Paula05/2013
5633(11*2^249977-7)/1575251Renaud Lifchitz02/2011
5634(2^249968+78557)/6375247Lelio R Paula07/2012
5635(5*10^75244+91)/375245Robert Price11/2016
5636(10489!)^2+Prime(10489)75242Robert Price08/2014
563714^65644+6775237Lelio R Paula01/2015
5638(2^249928-5)/1185905975229Lelio R Paula06/2012
5639129^35638+275218Lelio R Paula05/2013
56402^249853-11047575214Enzo Doria05/2014
56412^249762+7540975186Enzo Doria04/2016
5642565^27318+27318^56575181Norbert Schneider12/2016
5643(2^249741-7)/68575177Lelio R Paula06/2012
56442^249726-11218175176Enzo Doria06/2014
56452^249721+1171575174Lelio R Paula05/2013
5646(38661^16384+1)/275158Lelio R Paula11/2011
56472^249658-4735575155Lelio R Paula05/2013
5648155^34311+275153Lelio R Paula05/2013
5649(10^87682+1)/(10^12526+1)/99009900990175145Maksym Voznyy06/2015
5650(23*2^249602+1)/9375138Lelio R Paula08/2012
56512^249522+841575114Lelio R Paula05/2013
56522^249489-11091175104Enzo Doria05/2014
5653(28*10^75078+131)/375079Robert Price02/2017
5654(206*10^75073-17)/975075Robert Price03/2017
56552^249368-11057375068Enzo Doria05/2014
5656NaturalLogarithmOf10(75067)75067Eric W. Weisstein10/2015
5657(2^249375+78557)/4505612575062Lelio R Paula07/2012
5658(26*10^75055-173)/375056Robert Price10/2017
56592^249272+19375039Lelio R Paula03/2012
566014^65468+4375035Lelio R Paula01/2015
566137^47844+3675030Norbert Schneider05/2014
5662(52*10^75027-7)/975028Robert Price12/2014
566320^57653+8975009Lelio R Paula01/2015
56642^249061-186835374975Enzo Doria04/2016
56657^88713+2*3^8871374972Mike Oakes07/2010
56662*6^96313+574947Lelio R Paula10/2014
5667(8*10^74944+49)/374945Robert Price03/2016
5668300^30247+30247^30074926Norbert Schneider11/2014
56692^248866-17174917Lelio R Paula03/2012
56706*5^107168-774908Lelio R Paula10/2014
567111^71926+7874904Lelio R Paula02/2015
56722^248824+186939174904Enzo Doria05/2016
56732^248816+111174902Lelio R Paula01/2011
5674V(388219)74890Serge Batalov03/2015
56752*F(358297)-174880Henri Lifchitz12/2009
5676(22*10^74874-31)/974875Robert Price04/2015
567711^71892-7680000074868Enzo Doria01/2013
56789*5^107107-474866Lelio R Paula10/2014
56792^248678-71011174860Paul Bourdelais03/2013
5680(14*10^74858+211)/974859Robert Price11/2017
568113^67194+1274851Lelio R Paula01/2015
5682(7*2^248634+1)/7174846Lelio R Paula08/2012
568311^71867-309074842Enzo Doria12/2012
56842^248609+26214574839Lelio R Paula05/2013
56853^156852+5074838Lelio R Paula01/2015
568618^59607-1174824Lelio R Paula01/2015
56872^248556-11050774823Enzo Doria05/2014
56887^88531-3674818Lelio R Paula01/2015
5689p(15738)#/2+102474814Robert Price07/2017
56904*3^156740-574785Lelio R Paula05/2014
5691(32*10^74773-41)/974774Robert Price05/2015
5692(29*2^248384-1)/1374772Lelio R Paula01/2014
569319401!+19401#+174765D. Gazzoni Filho & Lucas Teixeira06/2005
56942^248357-1279741374763Enzo Doria03/2016
569542^46057+4174762Lelio R Paula07/2012
569611^71784-300074756Enzo Doria12/2012
569719^58458+1874754Lelio R Paula01/2015
569812^69265-3574750Lelio R Paula02/2015
569911^71771-4800074742Enzo Doria12/2012
5700(7*10^74741+197)/374742Robert Price07/2017
5701(2^248282-5)/5012974736Lelio R Paula06/2012
57022^248252-11010574732Enzo Doria04/2014
5703(7*10^74729+71)/374730Robert Price03/2016
57043^156614-5074724Lelio R Paula01/2015
5705(7*2^248213+1)/13574719Lelio R Paula07/2012
5706(2^248173+78557)/76774705Lelio R Paula07/2012
5707125^35622+12474697Norbert Schneider02/2015
5708(19*2^248099-1)/2974686Lelio R Paula01/2014
5709(86*10^74676-41)/974677Robert Price11/2015
5710(p(15711)#-4)/274672Robert Price09/2017
571110^74670+3174671Robert Price01/2011
571210^74670-12246374670Patrick De Geest05/2013
57132^248036-6974667Lelio R Paula03/2012
571411^71698-600074666Enzo Doria12/2012
571558*(10^(3*24887)-1)/111-174661Robert Price10/2014
571614^65139-4574658Lelio R Paula01/2015
57176^95921-13374642Lelio R Paula01/2015
571811^71675+7874642Lelio R Paula02/2015
571918^59449-9174625Lelio R Paula01/2015
57206^95864-1604374597Enzo Doria02/2013
57215*7^88261+674590Lelio R Paula10/2014
57229*5^106710+474589Lelio R Paula10/2014
5723(777*2^247788+1)/(11*754121)74588Jens K. Andersen09/2007
5724(265*10^74579+17)/374581Robert Price05/2016
5725(2^247759-1017)/331831171774574Lelio R Paula07/2012
57265^106682-2474568Lelio R Paula08/2014
5727474^27863+27863^47474556Norbert Schneider01/2017
5728(35365^16384+1)/274524Lelio R Paula11/2011
57293^156161+266074508Lelio R Paula01/2015
57302^247474-5869574498Lelio R Paula05/2013
573111^71519-9074480Enzo Doria07/2012
5732(19*2^247419-1)/2320298374475Lelio R Paula01/2014
5734(2^247394-7)/374473Lelio R Paula06/2012
573318^59328+1774473Lelio R Paula01/2015
57352^247379-18174469Lelio R Paula03/2012
5736(15*2^247370-1)/47974465Lelio R Paula01/2014
57372^247344+204774458Lelio R Paula05/2013
57382^247311-101774449Lelio R Paula05/2013
57392^247280+774439Lelio R Paula03/2012
5740(68*10^74434+13)/974435Ray Chandler11/2010
57413^156004-6274433Lelio R Paula01/2015
574236095!2-6474416Robert Price06/2015
57432^247165-374405M. Frind & P. Underwood07/2002
57442^247150+3276974400Lelio R Paula05/2013
574512^68911+7374368Lelio R Paula01/2015
57462^246999+7490374355Enzo Doria04/2016
57472^246989-11064374352Enzo Doria05/2014
574810^74350+27943974351Patrick De Geest07/2017
574910^74350-40000000174350Robert Price07/2017
575010^74350-71624174350Patrick De Geest07/2017


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: November, 22 2017 23:29 (Time in France)

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