PRP Records

Probable Primes Top 10000

(211563 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(23*2^261642+1)/9378762Lelio R Paula10/2012
5502(2^261724+22571)/3/7243/7321/18046081/4573074121178761Tony Prest / Never Odd Or Even04/2014
5503(2^261724+56495)/3/3/3/7/7/13/9041/512818459/2370858911978760Tony Prest / Never Odd Or Even04/2014
5504(2^261724+604119)/5/7/7/41/14107/19681/211777/90145981/103602083412778750Tony Prest / Never Odd Or Even05/2014
55052^261507-228778722Yves Minet04/2009
55068*10^78717+3978718Robert Price01/2017
5507(78557*2^261440+1)/378706Lelio R Paula06/2014
55086^101128-1643378693Enzo Doria02/2013
550920^60482+9978689Lelio R Paula03/2015
55102^261348-11063378674Enzo Doria05/2014
5511191^34487+278666Lelio R Paula05/2013
55122^261305-11013978661Enzo Doria04/2014
5513(82*10^78635-1)/978636Robert Price12/2014
551410^78632+8178633Robert Price03/2011
551510^78632-40269378632Patrick De Geest07/2013
55163*10^78631+1778632Robert Price03/2017
55172^261174-391178622Yves Minet04/2017
55182^261167+7484378620Enzo Doria04/2016
5519L(376121)+F(376122)78605Henri Lifchitz01/2007
552014^68580-2978602Lelio R Paula02/2015
5521(73*10^78576-1)/978577Robert Price01/2015
5522(17*2^261026-1)/4045178574Lelio R Paula02/2014
55232^261001-19578570Lelio R Paula05/2012
55245*2^260950+978555Lelio R Paula06/2014
55252^260931-760578549Lelio R Paula07/2013
552615^66778-3278538Lelio R Paula02/2015
5527(11*2^260896-1)/24578537Lelio R Paula02/2014
552830^53166+2978533Norbert Schneider03/2017
5529lucasU(2403,1,23229)-lucasU(2403,1,23228)78529Mike Oakes05/2009
55307*3^164574-278523Lelio R Paula06/2014
55312^260830-11213378518Enzo Doria06/2014
553213^70486+4278518Lelio R Paula03/2015
553311^75386-708078507Enzo Doria01/2013
5534(86^40583-1)/8578506Paul Bourdelais08/2017
55352^260711-5869578482Lelio R Paula07/2013
55362^260678-11106578472Enzo Doria05/2014
553718^62501-9778456Lelio R Paula02/2015
553853^45498-278452Lelio R Paula08/2013
55392^260513-11112178423Enzo Doria05/2014
554037845!2-6478412Robert Price06/2015
55412^260469-11069578409Enzo Doria05/2014
5542(11*10^78408-113)/378409Robert Price01/2017
55432^260447+841578403Lelio R Paula07/2013
554437837!2-6478394Robert Price06/2015
5545(19*2^260379-1)/5378382Lelio R Paula02/2014
55462^260377-11323378382Enzo Doria07/2014
55489^82138+6^82138-2^8213878380Mike Oakes08/2010
554769^42624+278380Lelio R Paula05/2013
55492^260369-185971378379Enzo Doria03/2016
555014*10^78362+108978364Jens K. Andersen11/2007
55515^112070-5478334Lelio R Paula02/2015
5552(10^(2*39165+1)+54*10^39165-1)/978331Robert Price04/2017
55532^260182-11345378323Enzo Doria07/2014
5554f(16405)78319Robert Price09/2017
5555(78557*2^260084+1)/51978296Lelio R Paula06/2014
555610^78288+9^(78288+1)78289Robert Price08/2016
555710^78288+3910978289Patrick De Geest12/2016
555810^78288-21629978288Patrick De Geest12/2016
55595^111997+3678283Lelio R Paula02/2015
5560(21^59183+1)/2278252Paul Bourdelais03/2010
5561(88*10^78242-7)/978243Robert Price11/2014
55622*6^100547+778242Lelio R Paula10/2014
55632^259860-11108978226Enzo Doria05/2014
556437^49875-278215Lelio R Paula09/2013
5565(13*10^78213+401)/978214Robert Price10/2017
55667*5^111893-478211Lelio R Paula10/2014
5567(11*2^259809-1)/143778209Lelio R Paula02/2014
55687^92511-678181Theodore Burton11/2005
5569(3^163859-4)/25378179Lelio R Paula10/2012
5570(27*2^259666-1)/62569178163Lelio R Paula02/2014
55713*10^78146+1778147Robert Price03/2017
5572(576^28307+1)/57778137Richard Fischer01/2018
55732^259503+7433378119Enzo Doria04/2016
5574(31*2^259504-1)/1336578116Lelio R Paula02/2014
5576(58547^16384+1)/278111Lelio R Paula11/2011
55756^100379+1378111Lelio R Paula03/2015
55772^259469-10990978108Enzo Doria04/2014
557815^66413-2678108Lelio R Paula02/2015
55797^92410-926678096Mike Oakes02/2010
55802^259398+7579978087Enzo Doria04/2016
55812^259394+187618978086Enzo Doria07/2016
5582PIPrime(78073)78073Eric W. Weisstein07/2006
55835*2^259344-778072Lelio R Paula06/2014
558414^68097-8778048Lelio R Paula02/2015
55852^259233-47557378037Paul Bourdelais03/2013
5586181^34554-278012Lelio R Paula10/2017
55873^163500-2878010Robert Price12/2013
5588(65*10^77992+691)/977993Robert Price08/2016
55892^259013-11259177971Enzo Doria06/2014
55907*10^77969-1177970Robert Price10/2017
55916^100193-100193^677966Norbert Schneider04/2017
55922^258863-11023577926Enzo Doria05/2014
55932^258852+160577923Lelio R Paula06/2013
5594(11*10^77909+49)/377910Robert Price05/2016
55952*7^92187-977908Lelio R Paula10/2014
55962^258763-11015577896Enzo Doria04/2014
55972^258694-11038777875Enzo Doria05/2014
559811^74773-9477869Lelio R Paula02/2015
55996^100067+12577868Lelio R Paula03/2015
560015^66205+877864Lelio R Paula07/2014
56015^111373-1813677847Enzo Doria05/2014
56022^258524-10987777824Enzo Doria04/2014
56036^100002-1664377817Enzo Doria02/2013
5604(13*10^77811+347)/977812Robert Price10/2017
560565^42916+2877803Lelio R Paula01/2016
5606(89*10^77781-17)/977782Robert Price11/2015
56072^258382-11040577781Enzo Doria05/2014
56085^111278-1499677780Enzo Doria02/2013
560914^67862+6177779Lelio R Paula02/2015
561010^77777+4848377778Patrick De Geest11/2010
561110^77777-18324377777Patrick De Geest11/2010
5612(27*2^258352+1)/4377772Lelio R Paula08/2012
5613337^30756-1000277740Enzo Doria07/2012
561410^77726+9977727Robert Price03/2011
561510^77726-8594777726Patrick De Geest06/2013
561689^39870-277723Lelio R Paula08/2013
56177^91966-3277721Lelio R Paula02/2015
561835^50327+277709Lelio R Paula05/2013
561924^56298+2377704Norbert Schneider12/2016
5620(2^258105+78557)/1977697Lelio R Paula10/2012
56212^258079+17977690Lelio R Paula03/2012
56222^258062-11311177685Enzo Doria07/2014
562380^40807-7977660Norbert Schneider03/2015
5624(10^77637+359)/977637Serge Batalov12/2014
56252^257862-16577625Lelio R Paula03/2012
5626(25*2^257853+1)/377623Lelio R Paula07/2012
5627(2^257869+1)/(3*18645362967379)77613Henri Lifchitz04/2005
56286^99728+7177604Lelio R Paula01/2015
56292^257778-11276777599Enzo Doria06/2014
5630(31*2^257771+1)/53777596Lelio R Paula07/2012
56312^257729-7377585Lelio R Paula03/2012
56322^257689-6377573Lelio R Paula03/2012
5633(47*10^77572+493)/977573Robert Price11/2017
5634(78557*2^257665+1)/610872577564Lelio R Paula06/2014
5635(3^162563+8)/288577559Lelio R Paula10/2012
56362^257636-11023577557Enzo Doria05/2014
5637(23*10^77556+97)/377557Robert Price02/2017
56382^257621-11007177552Enzo Doria04/2014
56392^257567-6487577536Lelio R Paula06/2013
56402*7^91674+977474Lelio R Paula10/2014
5641(17*10^77427-47)/377428Robert Price05/2017
564210^77418+84168377419Patrick De Geest06/2013
564310^77418-3377418Robert Price05/2011
564419^60539-3677415Lelio R Paula03/2015
564537401!!-102477397Robert Price11/2015
564611^74313-1875077390Enzo Doria12/2012
56482^257044-11288377378Enzo Doria06/2014
56478*10^77377+5177378Robert Price05/2017
56492*7^91553+977372Lelio R Paula10/2014
5650713^27118+27118^71377371Norbert Schneider12/2016
56512^256920-11115577341Enzo Doria05/2014
56522^256896-655577334Lelio R Paula06/2013
5653(52*10^77322-7)/977323Robert Price12/2014
56542^256849-11293977320Enzo Doria06/2014
5655(4*10^77309-31)/977309Erik Branger05/2011
5656(3^161988+7)/4186477284Lelio R Paula10/2012
5657(14^67421-1)/1377272Paul Bourdelais09/2008
56585*3^161923-477258Lelio R Paula06/2014
56592^256552-149977230Yves Minet05/2013
56602^256460-11275777203Enzo Doria06/2014
56612^256398+2329977184Yves Minet02/2011
56622^256391-1155*25639177182Henri Lifchitz03/2005
5663(2^256391-9)/5659377177Lelio R Paula10/2012
5664(2^256308+9)/1058577153Lelio R Paula10/2012
566621^58348-277149Lelio R Paula08/2013
5665(17*2^256291-1)/478577149Lelio R Paula02/2014
5667(5*2^256274-1)/214177144Lelio R Paula02/2014
566819^60321+8277136Lelio R Paula03/2015
56695*2^256233-377135Lelio R Paula06/2014
56703*2^256149+777110Lelio R Paula06/2014
56713^161594-10677100Lelio R Paula02/2015
56722^256114-18577098Lelio R Paula03/2012
56738^85349-85349^877078Norbert Schneider05/2017
56742^256043-278637777077Enzo Doria03/2016
56752^255973+186994777056Enzo Doria05/2016
567612^71393-4377046Lelio R Paula02/2015
567715^65490+4477023Lelio R Paula02/2015
5678(3^161411-7)/94077010Lelio R Paula10/2012
5679lucasU(1107,1,25297)-lucasU(1107,1,25296)77005Mike Oakes05/2009
5680(570^27943-1)/56977005Serge Batalov12/2016
56812^255750-7576989Lelio R Paula03/2012
56823*6^98926-576980Lelio R Paula10/2014
568318^61320-143376974Enzo Doria03/2013
56846^98916-1709376972Enzo Doria02/2013
56852^255659-11013176962Enzo Doria04/2014
568612^71303+9176949Lelio R Paula02/2015
568718^61298+5976946Lelio R Paula02/2015
5688(223^32768+1)/13107476945Lelio R Paula02/2009
5689(2^255613-5)/28151776942Lelio R Paula10/2012
569018^61290-1176936Lelio R Paula02/2015
569263^42752-276926Lelio R Paula08/2013
5691(11*2^255545-1)/11776926Lelio R Paula02/2014
56932^255517+5638776919Yves Minet02/2011
56942^255499-11256776913Enzo Doria06/2014
56952^255492+34576911Lelio R Paula06/2013
569610^76875+21759176876Patrick De Geest05/2013
569810^76875-5376875Robert Price05/2011
569711^73819-588076875Enzo Doria01/2013
56992^255313+1891576857Lelio R Paula06/2013
5700(2^255320-1017)/144666776853Lelio R Paula10/2012
57012^255296+577576852Lelio R Paula06/2013
570214^67052-2976851Lelio R Paula02/2015
5703(8*10^76840+43)/376841Robert Price10/2017
5704(7*10^76818-313)/976818Robert Price11/2016
570510^76801+6976802Robert Price03/2011
570610^76801-8094376801Patrick De Geest06/2013
57072^255105+5776795Lelio R Paula03/2012
5708(lucasV(1,2,510187)+2)/(3*5*11)76789Mike Oakes04/2017
5709(2^255097-7)/2002005576785Lelio R Paula10/2012
57102^255055+186935376780Enzo Doria05/2016
571117^62396-9076776Lelio R Paula03/2015
57127^90833-6076763Lelio R Paula02/2015
571313^68901-5676752Lelio R Paula03/2015
57142^254961+186991776751Enzo Doria05/2016
57159*5^109791-876742Lelio R Paula10/2014
571682^40089+40089^8276723Serge Batalov02/2012
57172^254861-279001376721Enzo Doria03/2016
571810^76705+1376706Robert Price01/2011
571910^76705-9407776705Patrick De Geest06/2013
5720(5*2^254785-1)/99976696Lelio R Paula02/2014
57212^254758-11040576690Enzo Doria05/2014
57222^254716-377976678Yves Minet04/2017
57232^254708-11050776675Enzo Doria05/2014
5724(47*10^76672+133)/976673Robert Price04/2017
57252^254670-11290176664Enzo Doria06/2014
5726(3^160665+7)/98135076651Lelio R Paula10/2012
57272^254598-11318376642Enzo Doria07/2014
572819^59932+2276639Lelio R Paula01/2015
57292^254569-11221376633Enzo Doria06/2014
57302*5^109626+976626Lelio R Paula10/2014
57312^254521+187252776619Enzo Doria05/2016
5732(76*10^76615+167)/976616Robert Price08/2016
573325^54799-24^5479976606Robert Price07/2012
5734(24737*2^254464+1)/976605Lelio R Paula06/2014
573512^70961-8576580Lelio R Paula02/2015
57367^90590-3876558Lelio R Paula02/2015
57372^254304+522776554Lelio R Paula06/2013
5738(76*10^76547-211)/976548Robert Price10/2017
573918^60979-536376546Enzo Doria03/2013
5740(21181*2^254264+1)/5531437976538Lelio R Paula06/2014
5741(34*10^76547-7)/9/61/94529/21480776536Makoto Morimoto05/2016
5742(7*10^76536-313)/976536Robert Price11/2016
57442^254239-2776534Lelio R Paula03/2012
57432^254238-184176534Yves Minet03/2013
5745(10^76537-1)/9/6612796976529Jens K. Andersen04/2009
57462^254189-11222576519Enzo Doria06/2014
574718^60938-139776494Enzo Doria03/2013
57482^254075-278841776485Enzo Doria03/2016
57497*10^76483-2376484Robert Price04/2016
57502^254042-11291376475Enzo Doria06/2014


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: June, 18 2018 23:06 (Time in France)

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