PRP Records

Probable Primes Top 10000

(205869 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 ?
5501(31*2^259504-1)/1336578116Lelio R Paula02/2014
5503(58547^16384+1)/278111Lelio R Paula11/2011
55026^100379+1378111Lelio R Paula03/2015
55042^259469-10990978108Enzo Doria04/2014
550515^66413-2678108Lelio R Paula02/2015
55067^92410-926678096Mike Oakes02/2010
55072^259398+7579978087Enzo Doria04/2016
55082^259394+187618978086Enzo Doria07/2016
5509PIPrime(78073)78073Eric W. Weisstein07/2006
55105*2^259344-778072Lelio R Paula06/2014
551114^68097-8778048Lelio R Paula02/2015
55122^259233-47557378037Paul Bourdelais03/2013
5513181^34554-278012Lelio R Paula10/2017
55143^163500-2878010Robert Price12/2013
5515(65*10^77992+691)/977993Robert Price08/2016
55162^259013-11259177971Enzo Doria06/2014
55177*10^77969-1177970Robert Price10/2017
55186^100193-100193^677966Norbert Schneider04/2017
55192^258863-11023577926Enzo Doria05/2014
55202^258852+160577923Lelio R Paula06/2013
5521(11*10^77909+49)/377910Robert Price05/2016
55222*7^92187-977908Lelio R Paula10/2014
55232^258763-11015577896Enzo Doria04/2014
55242^258694-11038777875Enzo Doria05/2014
552511^74773-9477869Lelio R Paula02/2015
55266^100067+12577868Lelio R Paula03/2015
552715^66205+877864Lelio R Paula07/2014
55285^111373-1813677847Enzo Doria05/2014
55292^258524-10987777824Enzo Doria04/2014
55306^100002-1664377817Enzo Doria02/2013
5531(13*10^77811+347)/977812Robert Price10/2017
553265^42916+2877803Lelio R Paula01/2016
5533(89*10^77781-17)/977782Robert Price11/2015
55342^258382-11040577781Enzo Doria05/2014
55355^111278-1499677780Enzo Doria02/2013
553614^67862+6177779Lelio R Paula02/2015
553710^77777+4848377778Patrick De Geest11/2010
553810^77777-18324377777Patrick De Geest11/2010
5539(27*2^258352+1)/4377772Lelio R Paula08/2012
5540337^30756-1000277740Enzo Doria07/2012
554110^77726+9977727Robert Price03/2011
554210^77726-8594777726Patrick De Geest06/2013
554389^39870-277723Lelio R Paula08/2013
55447^91966-3277721Lelio R Paula02/2015
554535^50327+277709Lelio R Paula05/2013
554624^56298+2377704Norbert Schneider12/2016
5547(2^258105+78557)/1977697Lelio R Paula10/2012
55482^258079+17977690Lelio R Paula03/2012
55492^258062-11311177685Enzo Doria07/2014
555080^40807-7977660Norbert Schneider03/2015
5551(10^77637+359)/977637Serge Batalov12/2014
55522^257862-16577625Lelio R Paula03/2012
5553(25*2^257853+1)/377623Lelio R Paula07/2012
5554(2^257869+1)/(3*18645362967379)77613Henri Lifchitz04/2005
55556^99728+7177604Lelio R Paula01/2015
55562^257778-11276777599Enzo Doria06/2014
5557(31*2^257771+1)/53777596Lelio R Paula07/2012
55582^257729-7377585Lelio R Paula03/2012
55592^257689-6377573Lelio R Paula03/2012
5560(47*10^77572+493)/977573Robert Price11/2017
5561(78557*2^257665+1)/610872577564Lelio R Paula06/2014
5562(3^162563+8)/288577559Lelio R Paula10/2012
55632^257636-11023577557Enzo Doria05/2014
5564(23*10^77556+97)/377557Robert Price02/2017
55652^257621-11007177552Enzo Doria04/2014
55662^257567-6487577536Lelio R Paula06/2013
55672*7^91674+977474Lelio R Paula10/2014
5568(17*10^77427-47)/377428Robert Price05/2017
556910^77418+84168377419Patrick De Geest06/2013
557010^77418-3377418Robert Price05/2011
557119^60539-3677415Lelio R Paula03/2015
557237401!!-102477397Robert Price11/2015
557311^74313-1875077390Enzo Doria12/2012
55752^257044-11288377378Enzo Doria06/2014
55748*10^77377+5177378Robert Price05/2017
55762*7^91553+977372Lelio R Paula10/2014
5577713^27118+27118^71377371Norbert Schneider12/2016
55782^256920-11115577341Enzo Doria05/2014
55792^256896-655577334Lelio R Paula06/2013
5580(52*10^77322-7)/977323Robert Price12/2014
55812^256849-11293977320Enzo Doria06/2014
5582(4*10^77309-31)/977309Erik Branger05/2011
5583(3^161988+7)/4186477284Lelio R Paula10/2012
5584(14^67421-1)/1377272Paul Bourdelais09/2008
55855*3^161923-477258Lelio R Paula06/2014
55862^256552-149977230Yves Minet05/2013
55872^256460-11275777203Enzo Doria06/2014
55882^256398+2329977184Yves Minet02/2011
55892^256391-1155*25639177182Henri Lifchitz03/2005
5590(2^256391-9)/5659377177Lelio R Paula10/2012
5591(2^256308+9)/1058577153Lelio R Paula10/2012
559321^58348-277149Lelio R Paula08/2013
5592(17*2^256291-1)/478577149Lelio R Paula02/2014
5594(5*2^256274-1)/214177144Lelio R Paula02/2014
559519^60321+8277136Lelio R Paula03/2015
55965*2^256233-377135Lelio R Paula06/2014
55973*2^256149+777110Lelio R Paula06/2014
55983^161594-10677100Lelio R Paula02/2015
55992^256114-18577098Lelio R Paula03/2012
56008^85349-85349^877078Norbert Schneider05/2017
56012^256043-278637777077Enzo Doria03/2016
56022^255973+186994777056Enzo Doria05/2016
560312^71393-4377046Lelio R Paula02/2015
560415^65490+4477023Lelio R Paula02/2015
5605(3^161411-7)/94077010Lelio R Paula10/2012
5606lucasU(1107,1,25297)-lucasU(1107,1,25296)77005Mike Oakes05/2009
5607(570^27943-1)/56977005Serge Batalov12/2016
56082^255750-7576989Lelio R Paula03/2012
56093*6^98926-576980Lelio R Paula10/2014
561018^61320-143376974Enzo Doria03/2013
56116^98916-1709376972Enzo Doria02/2013
56122^255659-11013176962Enzo Doria04/2014
561312^71303+9176949Lelio R Paula02/2015
561418^61298+5976946Lelio R Paula02/2015
5615(223^32768+1)/13107476945Lelio R Paula02/2009
5616(2^255613-5)/28151776942Lelio R Paula10/2012
561718^61290-1176936Lelio R Paula02/2015
561963^42752-276926Lelio R Paula08/2013
5618(11*2^255545-1)/11776926Lelio R Paula02/2014
56202^255517+5638776919Yves Minet02/2011
56212^255499-11256776913Enzo Doria06/2014
56222^255492+34576911Lelio R Paula06/2013
562310^76875+21759176876Patrick De Geest05/2013
562510^76875-5376875Robert Price05/2011
562411^73819-588076875Enzo Doria01/2013
56262^255313+1891576857Lelio R Paula06/2013
5627(2^255320-1017)/144666776853Lelio R Paula10/2012
56282^255296+577576852Lelio R Paula06/2013
562914^67052-2976851Lelio R Paula02/2015
5630(8*10^76840+43)/376841Robert Price10/2017
5631(7*10^76818-313)/976818Robert Price11/2016
563210^76801+6976802Robert Price03/2011
563310^76801-8094376801Patrick De Geest06/2013
56342^255105+5776795Lelio R Paula03/2012
5635(lucasV(1,2,510187)+2)/(3*5*11)76789Mike Oakes04/2017
5636(2^255097-7)/2002005576785Lelio R Paula10/2012
56372^255055+186935376780Enzo Doria05/2016
563817^62396-9076776Lelio R Paula03/2015
56397^90833-6076763Lelio R Paula02/2015
564013^68901-5676752Lelio R Paula03/2015
56412^254961+186991776751Enzo Doria05/2016
56429*5^109791-876742Lelio R Paula10/2014
564382^40089+40089^8276723Serge Batalov02/2012
56442^254861-279001376721Enzo Doria03/2016
564510^76705+1376706Robert Price01/2011
564610^76705-9407776705Patrick De Geest06/2013
5647(5*2^254785-1)/99976696Lelio R Paula02/2014
56482^254758-11040576690Enzo Doria05/2014
56492^254716-377976678Yves Minet04/2017
56502^254708-11050776675Enzo Doria05/2014
5651(47*10^76672+133)/976673Robert Price04/2017
56522^254670-11290176664Enzo Doria06/2014
5653(3^160665+7)/98135076651Lelio R Paula10/2012
56542^254598-11318376642Enzo Doria07/2014
565519^59932+2276639Lelio R Paula01/2015
56562^254569-11221376633Enzo Doria06/2014
56572*5^109626+976626Lelio R Paula10/2014
56582^254521+187252776619Enzo Doria05/2016
5659(76*10^76615+167)/976616Robert Price08/2016
566025^54799-24^5479976606Robert Price07/2012
5661(24737*2^254464+1)/976605Lelio R Paula06/2014
566212^70961-8576580Lelio R Paula02/2015
56637^90590-3876558Lelio R Paula02/2015
56642^254304+522776554Lelio R Paula06/2013
5665(76*10^76547-211)/976548Robert Price10/2017
566618^60979-536376546Enzo Doria03/2013
5667(21181*2^254264+1)/5531437976538Lelio R Paula06/2014
5669(34*10^76547-7)/9/61/94529/21480776536Makoto Morimoto05/2016
5668(7*10^76536-313)/976536Robert Price11/2016
56712^254239-2776534Lelio R Paula03/2012
56702^254238-184176534Yves Minet03/2013
5672(10^76537-1)/9/6612796976529Jens K. Andersen04/2009
56732^254189-11222576519Enzo Doria06/2014
567418^60938-139776494Enzo Doria03/2013
56752^254075-278841776485Enzo Doria03/2016
56767*10^76483-2376484Robert Price04/2016
56772^254042-11291376475Enzo Doria06/2014
567814^66723-3776474Lelio R Paula02/2015
56792^254037-11030576473Enzo Doria05/2014
56802^253931-11110976441Enzo Doria05/2014
56812^253926-116776440Lelio R Paula05/2013
5682(49*10^76438-13)/976439Robert Price07/2015
5683(21*2^253845-1)/14376415Lelio R Paula02/2014
568410^76374+3176375Robert Price03/2011
568510^76374-22215976374Patrick De Geest05/2013
56862^253561-11053376330Enzo Doria05/2014
5687gcd(V(917285),5*F(183457)*(F(183457)+1)+1)76321Serge Batalov04/2015
56889*5^109182+276316Lelio R Paula10/2014
568911^73279-369076313Enzo Doria12/2012
5690(598*10^76309-31)/976311Robert Price02/2017
569111^73274-2400076308Enzo Doria12/2012
56927^90291-676305Theodore Burton11/2005
5693(21181*2^253432+1)/2143776291Lelio R Paula06/2014
56946^98025+14576279Lelio R Paula01/2015
56952^253355+115576268Lelio R Paula05/2013
5696(73*10^76262+413)/976263Robert Price10/2017
56972^253292-7121976249Enzo Doria04/2016
56987^90221-3676246Lelio R Paula02/2015
569918^60727-347376229Enzo Doria03/2013
5700(78557*2^253184+1)/376221Lelio R Paula06/2014
5701(8*10^76220-83)/376221Robert Price10/2017
5702(44791^20480+1)/(44791^4096+1)76206Serge Batalov01/2017
570311^73163-201076192Enzo Doria12/2012
57042^253060+5461576179Lelio R Paula05/2013
57052^253029+186976176170Enzo Doria05/2016
57062^252955-11100776148Enzo Doria05/2014
57072*5^108931+776140Lelio R Paula10/2014
5708(86*10^76128+121)/976129Robert Price03/2017
570922154*29^52050+976123Curtis Bright05/2015
57103^159530-11235876116Enzo Doria06/2014
571111^73089-4876115Lelio R Paula02/2015
571286^39337-8576098Norbert Schneider10/2015
5713(3^159505-7)/31329731676095Lelio R Paula06/2012
57146^97783+7776090Lelio R Paula01/2015
57152^252712-10576074Lelio R Paula03/2012
5716(10^76069-19)/976069Robert Price10/2017
5718131^35927+276068Lelio R Paula05/2013
5717(41*10^76067+373)/976068Robert Price04/2017
57192^252683-13976066Lelio R Paula03/2012
5720137^35597-13676061Norbert Schneider05/2015
57213^159413+10676060Lelio R Paula01/2015
57229^79677+3*8^79677-2*4^79677-3*2^7967776032Mike Oakes12/2010
5723(2^252557-9)/7176026Lelio R Paula07/2012
5724(85*10^76021-103)/976022Robert Price10/2017
572511^72989+8076011Lelio R Paula02/2015
57262^252449-45952375995Enzo Doria05/2015
572720^58408+7375991Lelio R Paula01/2015
57282^252418-142175986Yves Minet01/2013
5729(11*2^252396-1)/575980Lelio R Paula02/2014
57302^252365-11068975970Enzo Doria05/2014
573111^72949-102075969Enzo Doria11/2012
5732(2^252294+47)/654975945Lelio R Paula07/2012
57332^252261-11059575939Enzo Doria05/2014
57347^89853+7675935Lelio R Paula01/2015
57353^159132+5675926Lelio R Paula01/2015
5736730^26513+26513^73075916Norbert Schneider11/2016
5737(27*2^252163-1)/194575907Lelio R Paula01/2014
57385^108596-1484675906Enzo Doria02/2013
57395^108560-1484675881Enzo Doria02/2013
57402^252051-11035975875Enzo Doria05/2014
57412^251971-11050975851Enzo Doria05/2014
5742(42457^16384+1)/32768275819Lelio R Paula11/2011
574399655!6-275811Robert Price07/2017
574414*10^75798+108975800Jens K. Andersen11/2007
57452^251784-45575795Yves Minet03/2012
57462^251780-128975794Yves Minet01/2013
57472^251760-21560975788Paul Bourdelais03/2013
574899^37973+275781Lelio R Paula05/2013
5749(185*10^75777+7)/375779Robert Price02/2017
57505*2^251690+375767Lelio R Paula06/2014


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: April, 22 2018 09:48 (Time in France)

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