PRP Records

Probable Primes Top 10000

(218736 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) !!!


Submit your PRPs


See the Top discoverers
See the Latest PRPs
Search by form



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 ?
550210^79040-100729779040Robert Price02/2015
550110^79040-7742779040Patrick De Geest02/2016
55032^262551-1729579036Lelio R Paula07/2013
55043^165597+34079010Lelio R Paula02/2015
5505(23*2^262435+1)/5579001Lelio R Paula10/2012
550611^75860-210079001Enzo Doria12/2012
55078*7^93463+978987Lelio R Paula10/2014
550867^43240-278960Lelio R Paula09/2013
55091000001^13159-1000000^1315978953Jean-Louis Charton10/2003
55102^262199-11028778930Enzo Doria05/2014
5511(19*2^262180-1)/17778924Lelio R Paula02/2014
5512(3^165403+4)/778917Lelio R Paula10/2012
55142^21068*(2^241076+1)-178914Makoto Morimoto03/2014
55152^29258*(2^232886+1)-178914Makoto Morimoto03/2014
55132^262144+1853178914Makoto Morimoto12/2015
5516(2^(2^18)+2450)/(2*3^2*137*577)78908Makoto Morimoto08/2017
5517(2^(2^18)-5719)/(3*599*3623)78907Makoto Morimoto08/2017
551814^68837+7578897Lelio R Paula02/2015
5519106^38949+10578884Norbert Schneider12/2016
5520(70^42737+1)/7178853Paul Bourdelais08/2017
5521(25*2^261917-1)/2092778842Lelio R Paula02/2014
55222^261881-185971378835Enzo Doria03/2016
55232^261874+191578832Lelio R Paula07/2013
55242^261856+9876533178827Jason Earls01/2009
5525(5*2^261857-1)/2050127778821Lelio R Paula02/2014
55262^261724+9269178787Tony Prest / Never Odd Or Even03/2014
55272^261724+28511178787Tony Prest / Never Odd Or Even04/2014
55282^261724+29371378787Tony Prest / Never Odd Or Even04/2014
5529(2^261724+381949)/578787Tony Prest / Never Odd Or Even04/2014
55302^261724+57297178787Tony Prest / Never Odd Or Even05/2014
5531(2^261724+392705)/3/778786Tony Prest / Never Odd Or Even04/2014
5532(2^261724+629709)/5/578786Tony Prest / Never Odd Or Even05/2014
5533(2^261724+67397)/3/10378785Tony Prest / Never Odd Or Even04/2014
5534(2^261724+323043)/11/10378784Tony Prest / Never Odd Or Even04/2014
5535(2^261724+370143)/128978784Tony Prest / Never Odd Or Even04/2014
5536(2^261724+560259)/5/5/7378784Tony Prest / Never Odd Or Even05/2014
5537(2^261724+64109)/3/3/3/5/5/1978783Tony Prest / Never Odd Or Even04/2014
5538(2^261724+394491)/5578778783Tony Prest / Never Odd Or Even04/2014
5539(2^261724+625897)/23/88378783Tony Prest / Never Odd Or Even05/2014
5540(2^261724+292471)/13/97/15178782Tony Prest / Never Odd Or Even04/2014
5541(2^261724+154303)/11/67/12778782Tony Prest / Never Odd Or Even04/2014
5542(2^261724+313319)/3/3/3/3/5/11/11378782Tony Prest / Never Odd Or Even04/2014
5543(2^261724+383949)/5/41/43/8378781Tony Prest / Never Odd Or Even04/2014
5544(2^261724+626567)/3/331/63178781Tony Prest / Never Odd Or Even05/2014
5545(2^261724+32987)/3/3/19/223/103178780Tony Prest / Never Odd Or Even04/2014
5546(2^261724+5813)/3/599139778780Tony Prest / Never Odd Or Even04/2014
5547(2^261724+13481)/3/11/239/208778780Tony Prest / Never Odd Or Even04/2014
5548(2^261724+103399)/5/13/37/1060778780Tony Prest / Never Odd Or Even04/2014
5549(2^261724+18477)/367/6511178780Tony Prest / Never Odd Or Even04/2014
5550(2^261724+121285)/167/227/121778780Tony Prest / Never Odd Or Even04/2014
5551(2^261724+262037)/3/3/11/23/1851778780Tony Prest / Never Odd Or Even04/2014
5552(2^261724+586157)/3/7/457/125978780Tony Prest / Never Odd Or Even05/2014
5553(2^261724+315287)/3/4582254178779Tony Prest / Never Odd Or Even04/2014
5554(2^261724+605675)/3/3/3/103/20748178779Tony Prest / Never Odd Or Even05/2014
5555(2^261724+60031)/13/31/702487778778Tony Prest / Never Odd Or Even04/2014
5556(2^261724+121879)/5/78943321778778Tony Prest / Never Odd Or Even04/2014
5557(2^261724+290135)/3/3/8467/905978778Tony Prest / Never Odd Or Even04/2014
5558(2^261724+79857)/59/3847/16533178777Tony Prest / Never Odd Or Even04/2014
5559(2^261724+22883)/3/17/23/2351/1007978777Tony Prest / Never Odd Or Even04/2014
5560(2^261724+154799)/3/5/365565371978777Tony Prest / Never Odd Or Even04/2014
5561(2^261724+391001)/3/11/17/41/43/2407178777Tony Prest / Never Odd Or Even04/2014
5562(2^261724+622383)/34843/55071778777Tony Prest / Never Odd Or Even05/2014
5563(2^261724+302829)/5/37/37/3707814778776Tony Prest / Never Odd Or Even04/2014
5564(2^261724+315837)/43/217613624378776Tony Prest / Never Odd Or Even04/2014
5565(2^261724+582373)/53/307/311/3211778776Tony Prest / Never Odd Or Even05/2014
5566(2^261724+295283)/3/3/3/29/43/1781227378775Tony Prest / Never Odd Or Even04/2014
5567(2^261724+27491)/3/22787/10597844978774Tony Prest / Never Odd Or Even04/2014
5568(2^261724+392751)/193813/28782668978774Tony Prest / Never Odd Or Even04/2014
5569(2^261724+328501)/7/1091/3149561051978773Tony Prest / Never Odd Or Even04/2014
5570(2^261724+111267)/19/4637/1514056042778772Tony Prest / Never Odd Or Even04/2014
5571(2^261724+572133)/127/131/7378775233378772Tony Prest / Never Odd Or Even05/2014
5572(2^261724+608733)/59/7079/18451/90915178771Tony Prest / Never Odd Or Even05/2014
5573(2^261724+255449)/3/3/5/7/1759/10177/3315886978770Tony Prest / Never Odd Or Even04/2014
5574(2^261724+99509)/3/5/5/6507271/674965928978769Tony Prest / Never Odd Or Even04/2014
5575(2^261724+52501)/563/53939/2794283139178769Tony Prest / Never Odd Or Even04/2014
5576(2^261724+117089)/3/5/37/149/967/2027/416374178769Tony Prest / Never Odd Or Even04/2014
5577(2^261724+372571)/1487/9209/21559/226324978769Tony Prest / Never Odd Or Even04/2014
5578(2^261724+184549)/5/8699/44053/140932299778769Tony Prest / Never Odd Or Even04/2014
5579(2^261724+363351)/937/159683/5952320022778768Tony Prest / Never Odd Or Even04/2014
5580(2^261724+326501)/3/43/193/263/19403/25350140378768Tony Prest / Never Odd Or Even04/2014
5581(2^261724+629477)/3/17/17/137/263/1993/16187/5734778768Tony Prest / Never Odd Or Even05/2014
5582(2^261724+94871)/3/3/13/6734017/167342524578778766Tony Prest / Never Odd Or Even04/2014
5583(2^261724+25981)/577/1181/3643/51778633474378766Tony Prest / Never Odd Or Even04/2014
5585(23*2^261642+1)/9378762Lelio R Paula10/2012
5584(2^261724+351227)/3/3/3/3/71/13997/9595373/819397800778762Tony Prest / Never Odd Or Even04/2014
5586(2^261724+22571)/3/7243/7321/18046081/4573074121178761Tony Prest / Never Odd Or Even04/2014
5587(2^261724+56495)/3/3/3/7/7/13/9041/512818459/2370858911978760Tony Prest / Never Odd Or Even04/2014
5588(2^261724+604119)/5/7/7/41/14107/19681/211777/90145981/103602083412778750Tony Prest / Never Odd Or Even05/2014
55892^261507-228778722Yves Minet04/2009
55908*10^78717+3978718Robert Price01/2017
5591(78557*2^261440+1)/378706Lelio R Paula06/2014
55926^101128-1643378693Enzo Doria02/2013
559320^60482+9978689Lelio R Paula03/2015
55942^261348-11063378674Enzo Doria05/2014
5595191^34487+278666Lelio R Paula05/2013
55962^261305-11013978661Enzo Doria04/2014
5597(82*10^78635-1)/978636Robert Price12/2014
559810^78632+8178633Robert Price03/2011
559910^78632-40269378632Patrick De Geest07/2013
56003*10^78631+1778632Robert Price03/2017
56012^261174-391178622Yves Minet04/2017
56022^261167+7484378620Enzo Doria04/2016
5603L(376121)+F(376122)78605Henri Lifchitz01/2007
560414^68580-2978602Lelio R Paula02/2015
5605(73*10^78576-1)/978577Robert Price01/2015
5606(17*2^261026-1)/4045178574Lelio R Paula02/2014
56072^261001-19578570Lelio R Paula05/2012
56085*2^260950+978555Lelio R Paula06/2014
56092^260931-760578549Lelio R Paula07/2013
561015^66778-3278538Lelio R Paula02/2015
5611(11*2^260896-1)/24578537Lelio R Paula02/2014
561230^53166+2978533Norbert Schneider03/2017
5613lucasU(2403,1,23229)-lucasU(2403,1,23228)78529Mike Oakes05/2009
56147*3^164574-278523Lelio R Paula06/2014
56152^260830-11213378518Enzo Doria06/2014
561613^70486+4278518Lelio R Paula03/2015
561711^75386-708078507Enzo Doria01/2013
5618(86^40583-1)/8578506Paul Bourdelais08/2017
56192^260711-5869578482Lelio R Paula07/2013
56202^260678-11106578472Enzo Doria05/2014
562118^62501-9778456Lelio R Paula02/2015
562253^45498-278452Lelio R Paula08/2013
56232^260513-11112178423Enzo Doria05/2014
562437845!2-6478412Robert Price06/2015
56252^260469-11069578409Enzo Doria05/2014
5626(11*10^78408-113)/378409Robert Price01/2017
56272^260447+841578403Lelio R Paula07/2013
562837837!2-6478394Robert Price06/2015
5629(19*2^260379-1)/5378382Lelio R Paula02/2014
56302^260377-11323378382Enzo Doria07/2014
56329^82138+6^82138-2^8213878380Mike Oakes08/2010
563169^42624+278380Lelio R Paula05/2013
56332^260369-185971378379Enzo Doria03/2016
563414*10^78362+108978364Jens K. Andersen11/2007
56355^112070-5478334Lelio R Paula02/2015
5636(10^(2*39165+1)+54*10^39165-1)/978331Robert Price04/2017
56372^260182-11345378323Enzo Doria07/2014
5638f(16405)78319Robert Price09/2017
5639(78557*2^260084+1)/51978296Lelio R Paula06/2014
564010^78288+9^(78288+1)78289Robert Price08/2016
564110^78288+3910978289Patrick De Geest12/2016
564210^78288-21629978288Patrick De Geest12/2016
56435^111997+3678283Lelio R Paula02/2015
5644(21^59183+1)/2278252Paul Bourdelais03/2010
5645(88*10^78242-7)/978243Robert Price11/2014
56462*6^100547+778242Lelio R Paula10/2014
56472^259860-11108978226Enzo Doria05/2014
564837^49875-278215Lelio R Paula09/2013
5649(13*10^78213+401)/978214Robert Price10/2017
56507*5^111893-478211Lelio R Paula10/2014
5651(11*2^259809-1)/143778209Lelio R Paula02/2014
56527^92511-678181Theodore Burton11/2005
5653(3^163859-4)/25378179Lelio R Paula10/2012
5654(27*2^259666-1)/62569178163Lelio R Paula02/2014
56553*10^78146+1778147Robert Price03/2017
5656(576^28307+1)/57778137Richard Fischer01/2018
56572^259503+7433378119Enzo Doria04/2016
5658(31*2^259504-1)/1336578116Lelio R Paula02/2014
5660(58547^16384+1)/278111Lelio R Paula11/2011
56596^100379+1378111Lelio R Paula03/2015
56612^259469-10990978108Enzo Doria04/2014
566215^66413-2678108Lelio R Paula02/2015
56637^92410-926678096Mike Oakes02/2010
56642^259398+7579978087Enzo Doria04/2016
56652^259394+187618978086Enzo Doria07/2016
5666PIPrime(78073)78073Eric W. Weisstein07/2006
56675*2^259344-778072Lelio R Paula06/2014
566814^68097-8778048Lelio R Paula02/2015
56692^259233-47557378037Paul Bourdelais03/2013
5670181^34554-278012Lelio R Paula10/2017
56713^163500-2878010Robert Price12/2013
5672(65*10^77992+691)/977993Robert Price08/2016
56732^259013-11259177971Enzo Doria06/2014
56747*10^77969-1177970Robert Price10/2017
56756^100193-100193^677966Norbert Schneider04/2017
56762^258863-11023577926Enzo Doria05/2014
56772^258852+160577923Lelio R Paula06/2013
5678(11*10^77909+49)/377910Robert Price05/2016
56792*7^92187-977908Lelio R Paula10/2014
56802^258763-11015577896Enzo Doria04/2014
56812^258694-11038777875Enzo Doria05/2014
568211^74773-9477869Lelio R Paula02/2015
56836^100067+12577868Lelio R Paula03/2015
568415^66205+877864Lelio R Paula07/2014
56855^111373-1813677847Enzo Doria05/2014
56862^258524-10987777824Enzo Doria04/2014
56876^100002-1664377817Enzo Doria02/2013
5688(13*10^77811+347)/977812Robert Price10/2017
568965^42916+2877803Lelio R Paula01/2016
5690(89*10^77781-17)/977782Robert Price11/2015
56912^258382-11040577781Enzo Doria05/2014
56925^111278-1499677780Enzo Doria02/2013
569314^67862+6177779Lelio R Paula02/2015
569410^77777+4848377778Patrick De Geest11/2010
569510^77777-18324377777Patrick De Geest11/2010
5696(27*2^258352+1)/4377772Lelio R Paula08/2012
5697337^30756-1000277740Enzo Doria07/2012
569810^77726+9977727Robert Price03/2011
569910^77726-8594777726Patrick De Geest06/2013
570089^39870-277723Lelio R Paula08/2013
57017^91966-3277721Lelio R Paula02/2015
570235^50327+277709Lelio R Paula05/2013
570324^56298+2377704Norbert Schneider12/2016
5704(2^258105+78557)/1977697Lelio R Paula10/2012
57052^258079+17977690Lelio R Paula03/2012
57062^258062-11311177685Enzo Doria07/2014
570780^40807-7977660Norbert Schneider03/2015
5708(10^77637+359)/977637Serge Batalov12/2014
57092^257862-16577625Lelio R Paula03/2012
5710(25*2^257853+1)/377623Lelio R Paula07/2012
5711(2^257869+1)/(3*18645362967379)77613Henri Lifchitz04/2005
57126^99728+7177604Lelio R Paula01/2015
57132^257778-11276777599Enzo Doria06/2014
5714(31*2^257771+1)/53777596Lelio R Paula07/2012
57152^257729-7377585Lelio R Paula03/2012
57162^257689-6377573Lelio R Paula03/2012
5717(47*10^77572+493)/977573Robert Price11/2017
5718(78557*2^257665+1)/610872577564Lelio R Paula06/2014
5719(3^162563+8)/288577559Lelio R Paula10/2012
57202^257636-11023577557Enzo Doria05/2014
5721(23*10^77556+97)/377557Robert Price02/2017
57222^257621-11007177552Enzo Doria04/2014
57232^257567-6487577536Lelio R Paula06/2013
57242*7^91674+977474Lelio R Paula10/2014
5725(17*10^77427-47)/377428Robert Price05/2017
572610^77418+84168377419Patrick De Geest06/2013
572710^77418-3377418Robert Price05/2011
572819^60539-3677415Lelio R Paula03/2015
572937401!!-102477397Robert Price11/2015
573011^74313-1875077390Enzo Doria12/2012
57322^257044-11288377378Enzo Doria06/2014
57318*10^77377+5177378Robert Price05/2017
57332*7^91553+977372Lelio R Paula10/2014
5734713^27118+27118^71377371Norbert Schneider12/2016
57352^256920-11115577341Enzo Doria05/2014
57362^256896-655577334Lelio R Paula06/2013
5737(52*10^77322-7)/977323Robert Price12/2014
57382^256849-11293977320Enzo Doria06/2014
5739(4*10^77309-31)/977309Erik Branger05/2011
5740(3^161988+7)/4186477284Lelio R Paula10/2012
5741(14^67421-1)/1377272Paul Bourdelais09/2008
57425*3^161923-477258Lelio R Paula06/2014
57432^256552-149977230Yves Minet05/2013
57442^256460-11275777203Enzo Doria06/2014
57452^256398+2329977184Yves Minet02/2011
57462^256391-1155*25639177182Henri Lifchitz03/2005
5747(2^256391-9)/5659377177Lelio R Paula10/2012
5748(2^256308+9)/1058577153Lelio R Paula10/2012
575021^58348-277149Lelio R Paula08/2013
5749(17*2^256291-1)/478577149Lelio R Paula02/2014


Find by discoverer :


Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: August, 14 2018 21:45 (Time in France)

Go back
Valid XHTML 1.0!    Valid CSS!