PRP Records

Probable Primes Top 10000

(172742 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 ?
500111^74773-9477869Lelio R Paula02/2015
50026^100067+12577868Lelio R Paula03/2015
500315^66205+877864Lelio R Paula07/2014
50045^111373-1813677847Enzo Doria05/2014
50052^258524-10987777824Enzo Doria04/2014
50066^100002-1664377817Enzo Doria02/2013
500765^42916+2877803Lelio R Paula01/2016
5008(89*10^77781-17)/977782Robert Price11/2015
50092^258382-11040577781Enzo Doria05/2014
50105^111278-1499677780Enzo Doria02/2013
501114^67862+6177779Lelio R Paula02/2015
501210^77777+4848377778Patrick De Geest11/2010
501310^77777-18324377777Patrick De Geest11/2010
5014(27*2^258352+1)/4377772Lelio R Paula08/2012
5015337^30756-1000277740Enzo Doria07/2012
501610^77726+9977727Robert Price03/2011
501710^77726-8594777726Patrick De Geest06/2013
501889^39870-277723Lelio R Paula08/2013
50197^91966-3277721Lelio R Paula02/2015
502035^50327+277709Lelio R Paula05/2013
502124^56298+2377704Norbert Schneider12/2016
5022(2^258105+78557)/1977697Lelio R Paula10/2012
50232^258079+17977690Lelio R Paula03/2012
50242^258062-11311177685Enzo Doria07/2014
502580^40807-7977660Norbert Schneider03/2015
5026(10^77637+359)/977637Serge Batalov12/2014
50272^257862-16577625Lelio R Paula03/2012
5028(25*2^257853+1)/377623Lelio R Paula07/2012
5029(2^257869+1)/(3*18645362967379)77613Henri Lifchitz04/2005
50306^99728+7177604Lelio R Paula01/2015
50312^257778-11276777599Enzo Doria06/2014
5032(31*2^257771+1)/53777596Lelio R Paula07/2012
50332^257729-7377585Lelio R Paula03/2012
50342^257689-6377573Lelio R Paula03/2012
5035(78557*2^257665+1)/610872577564Lelio R Paula06/2014
5036(3^162563+8)/288577559Lelio R Paula10/2012
50372^257636-11023577557Enzo Doria05/2014
5038(23*10^77556+97)/377557Robert Price02/2017
50392^257621-11007177552Enzo Doria04/2014
50402^257567-6487577536Lelio R Paula06/2013
50412*7^91674+977474Lelio R Paula10/2014
504210^77418+84168377419Patrick De Geest06/2013
504310^77418-3377418Robert Price05/2011
504419^60539-3677415Lelio R Paula03/2015
504537401!!-102477397Robert Price11/2015
504611^74313-1875077390Enzo Doria12/2012
50472^257044-11288377378Enzo Doria06/2014
50482*7^91553+977372Lelio R Paula10/2014
5049713^27118+27118^71377371Norbert Schneider12/2016
50502^256920-11115577341Enzo Doria05/2014
50512^256896-655577334Lelio R Paula06/2013
5052(52*10^77322-7)/977323Robert Price12/2014
50532^256849-11293977320Enzo Doria06/2014
5054(4*10^77309-31)/977309Erik Branger05/2011
5055(3^161988+7)/4186477284Lelio R Paula10/2012
5056(14^67421-1)/1377272Paul Bourdelais09/2008
50575*3^161923-477258Lelio R Paula06/2014
50582^256552-149977230Yves Minet05/2013
50592^256460-11275777203Enzo Doria06/2014
50602^256398+2329977184Yves Minet02/2011
50612^256391-1155*25639177182Henri Lifchitz03/2005
5062(2^256391-9)/5659377177Lelio R Paula10/2012
5063(2^256308+9)/1058577153Lelio R Paula10/2012
506521^58348-277149Lelio R Paula08/2013
5064(17*2^256291-1)/478577149Lelio R Paula02/2014
5066(5*2^256274-1)/214177144Lelio R Paula02/2014
506719^60321+8277136Lelio R Paula03/2015
50685*2^256233-377135Lelio R Paula06/2014
50693*2^256149+777110Lelio R Paula06/2014
50703^161594-10677100Lelio R Paula02/2015
50712^256114-18577098Lelio R Paula03/2012
50722^256043-278637777077Enzo Doria03/2016
50732^255973+186994777056Enzo Doria05/2016
507412^71393-4377046Lelio R Paula02/2015
507515^65490+4477023Lelio R Paula02/2015
5076(3^161411-7)/94077010Lelio R Paula10/2012
5078lucasU(1107,1,25297)-lucasU(1107,1,25296)77005Mike Oakes05/2009
5077(570^27943-1)/56977005Serge Batalov12/2016
50792^255750-7576989Lelio R Paula03/2012
50803*6^98926-576980Lelio R Paula10/2014
508118^61320-143376974Enzo Doria03/2013
50826^98916-1709376972Enzo Doria02/2013
50832^255659-11013176962Enzo Doria04/2014
508412^71303+9176949Lelio R Paula02/2015
508518^61298+5976946Lelio R Paula02/2015
5086(223^32768+1)/13107476945Lelio R Paula02/2009
5087(2^255613-5)/28151776942Lelio R Paula10/2012
508818^61290-1176936Lelio R Paula02/2015
509063^42752-276926Lelio R Paula08/2013
5089(11*2^255545-1)/11776926Lelio R Paula02/2014
50912^255517+5638776919Yves Minet02/2011
50922^255499-11256776913Enzo Doria06/2014
50932^255492+34576911Lelio R Paula06/2013
509410^76875+21759176876Patrick De Geest05/2013
509610^76875-5376875Robert Price05/2011
509511^73819-588076875Enzo Doria01/2013
50972^255313+1891576857Lelio R Paula06/2013
5098(2^255320-1017)/144666776853Lelio R Paula10/2012
50992^255296+577576852Lelio R Paula06/2013
510014^67052-2976851Lelio R Paula02/2015
5101(7*10^76818-313)/976818Robert Price11/2016
510210^76801+6976802Robert Price03/2011
510310^76801-8094376801Patrick De Geest06/2013
51042^255105+5776795Lelio R Paula03/2012
5105(lucasV(1,2,510187)+2)/(3*5*11)76789Mike Oakes04/2017
5106(2^255097-7)/2002005576785Lelio R Paula10/2012
51072^255055+186935376780Enzo Doria05/2016
510817^62396-9076776Lelio R Paula03/2015
51097^90833-6076763Lelio R Paula02/2015
511013^68901-5676752Lelio R Paula03/2015
51112^254961+186991776751Enzo Doria05/2016
51129*5^109791-876742Lelio R Paula10/2014
511382^40089+40089^8276723Serge Batalov02/2012
51142^254861-279001376721Enzo Doria03/2016
511510^76705+1376706Robert Price01/2011
511610^76705-9407776705Patrick De Geest06/2013
5117(5*2^254785-1)/99976696Lelio R Paula02/2014
51182^254758-11040576690Enzo Doria05/2014
51192^254708-11050776675Enzo Doria05/2014
5120(47*10^76672+133)/976673Robert Price04/2017
51212^254670-11290176664Enzo Doria06/2014
5122(3^160665+7)/98135076651Lelio R Paula10/2012
51232^254598-11318376642Enzo Doria07/2014
512419^59932+2276639Lelio R Paula01/2015
51252^254569-11221376633Enzo Doria06/2014
51262*5^109626+976626Lelio R Paula10/2014
51272^254521+187252776619Enzo Doria05/2016
5128(76*10^76615+167)/976616Robert Price08/2016
512925^54799-24^5479976606Robert Price07/2012
5130(24737*2^254464+1)/976605Lelio R Paula06/2014
513112^70961-8576580Lelio R Paula02/2015
51327^90590-3876558Lelio R Paula02/2015
51332^254304+522776554Lelio R Paula06/2013
513418^60979-536376546Enzo Doria03/2013
5135(21181*2^254264+1)/5531437976538Lelio R Paula06/2014
5137(34*10^76547-7)/9/61/94529/21480776536Makoto Morimoto05/2016
5136(7*10^76536-313)/976536Robert Price11/2016
51382^254239-2776534Lelio R Paula03/2012
51392^254238-184176534Yves Minet03/2013
5140(10^76537-1)/9/6612796976529Jens K. Andersen04/2009
51412^254189-11222576519Enzo Doria06/2014
514218^60938-139776494Enzo Doria03/2013
51432^254075-278841776485Enzo Doria03/2016
51447*10^76483-2376484Robert Price04/2016
51452^254042-11291376475Enzo Doria06/2014
514614^66723-3776474Lelio R Paula02/2015
51472^254037-11030576473Enzo Doria05/2014
51482^253931-11110976441Enzo Doria05/2014
51492^253926-116776440Lelio R Paula05/2013
5150(49*10^76438-13)/976439Robert Price07/2015
5151(21*2^253845-1)/14376415Lelio R Paula02/2014
515210^76374+3176375Robert Price03/2011
515310^76374-22215976374Patrick De Geest05/2013
51542^253561-11053376330Enzo Doria05/2014
5155gcd(V(917285),5*F(183457)*(F(183457)+1)+1)76321Serge Batalov04/2015
51569*5^109182+276316Lelio R Paula10/2014
515711^73279-369076313Enzo Doria12/2012
5158(598*10^76309-31)/976311Robert Price02/2017
515911^73274-2400076308Enzo Doria12/2012
51607^90291-676305Theodore Burton11/2005
5161(21181*2^253432+1)/2143776291Lelio R Paula06/2014
51626^98025+14576279Lelio R Paula01/2015
51632^253355+115576268Lelio R Paula05/2013
51642^253292-7121976249Enzo Doria04/2016
51657^90221-3676246Lelio R Paula02/2015
516618^60727-347376229Enzo Doria03/2013
5167(78557*2^253184+1)/376221Lelio R Paula06/2014
5168(44791^20480+1)/(44791^4096+1)76206Serge Batalov01/2017
516911^73163-201076192Enzo Doria12/2012
51702^253060+5461576179Lelio R Paula05/2013
51712^253029+186976176170Enzo Doria05/2016
51722^252955-11100776148Enzo Doria05/2014
51732*5^108931+776140Lelio R Paula10/2014
5174(86*10^76128+121)/976129Robert Price03/2017
517522154*29^52050+976123Curtis Bright05/2015
51763^159530-11235876116Enzo Doria06/2014
517711^73089-4876115Lelio R Paula02/2015
517886^39337-8576098Norbert Schneider10/2015
5179(3^159505-7)/31329731676095Lelio R Paula06/2012
51806^97783+7776090Lelio R Paula01/2015
51812^252712-10576074Lelio R Paula03/2012
5183131^35927+276068Lelio R Paula05/2013
5182(41*10^76067+373)/976068Robert Price04/2017
51842^252683-13976066Lelio R Paula03/2012
5185137^35597-13676061Norbert Schneider05/2015
51863^159413+10676060Lelio R Paula01/2015
51879^79677+3*8^79677-2*4^79677-3*2^7967776032Mike Oakes12/2010
5188(2^252557-9)/7176026Lelio R Paula07/2012
518911^72989+8076011Lelio R Paula02/2015
51902^252449-45952375995Enzo Doria05/2015
519120^58408+7375991Lelio R Paula01/2015
51922^252418-142175986Yves Minet01/2013
5193(11*2^252396-1)/575980Lelio R Paula02/2014
51942^252365-11068975970Enzo Doria05/2014
519511^72949-102075969Enzo Doria11/2012
5196(2^252294+47)/654975945Lelio R Paula07/2012
51972^252261-11059575939Enzo Doria05/2014
51987^89853+7675935Lelio R Paula01/2015
51993^159132+5675926Lelio R Paula01/2015
5200730^26513+26513^73075916Norbert Schneider11/2016
5201(27*2^252163-1)/194575907Lelio R Paula01/2014
52025^108596-1484675906Enzo Doria02/2013
52035^108560-1484675881Enzo Doria02/2013
52042^252051-11035975875Enzo Doria05/2014
52052^251971-11050975851Enzo Doria05/2014
5206(42457^16384+1)/32768275819Lelio R Paula11/2011
520714*10^75798+108975800Jens K. Andersen11/2007
52082^251784-45575795Yves Minet03/2012
52092^251780-128975794Yves Minet01/2013
52102^251760-21560975788Paul Bourdelais03/2013
521199^37973+275781Lelio R Paula05/2013
5212(185*10^75777+7)/375779Robert Price02/2017
52135*2^251690+375767Lelio R Paula06/2014
52146^97366+9575766Lelio R Paula01/2015
52158*6^97337-775744Lelio R Paula10/2014
52162^251588-11167775736Enzo Doria05/2014
52175^108346-1325675731Enzo Doria02/2013
5218(31^50777+1)/3275726Robert Price07/2013
5219(10^75707+77)/375707Robert Price01/2017
52202^251466+19375699Lelio R Paula03/2012
5221(5*2^251464+1)/942375695Lelio R Paula07/2012
52222^251422-10999175686Enzo Doria04/2014
52234*5^108245-375661Lelio R Paula10/2014
522412^70067-11^7006775615Jean-Louis Charton11/2006
522512^70066+9575614Lelio R Paula02/2015
5226-E20534/206375607Thomas Ritschel02/2017
522719^59120-5075600Lelio R Paula01/2015
522818^60222-469775596Enzo Doria03/2013
522918^60211-435575582Enzo Doria03/2013
52307*2^251014-975564Lelio R Paula06/2014
52316^97101-2575560Lelio R Paula01/2015
52328^83663-7^8366375556Jean-Louis Charton01/2004
52333^158331-14075544Lelio R Paula01/2015
5234(37^48157-1)/3675519Robert Price03/2012
523510^75516+3146775517Patrick De Geest03/2016
523710^75516-10^2256-175516Serge Batalov01/2011
523610^75516-6659175516Patrick De Geest03/2016
52382^250851-18775514Lelio R Paula03/2012
5239(43*10^75498-7)/975499Robert Price12/2014
5240(3^158244-5)/24791675497Lelio R Paula06/2012
52414*5^107971-375470Lelio R Paula10/2014
5242(25*10^75465+71)/375466Robert Price01/2017
5243(5*2^250681-1)/99975461Lelio R Paula01/2014
5244(182*10^75456+1)/375458Robert Price02/2017
5245(2^250669-9)/9889772975451Lelio R Paula07/2012
524610^75441+1375442Robert Price01/2011
524710^75441-992375441Patrick De Geest05/2013
5248(27*2^250546-1)/645775420Lelio R Paula01/2014
52495*7^89231-675410Lelio R Paula10/2014
525011^72411-2875409Lelio R Paula02/2015


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: April, 21 2017 08:01 (Time in France)

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