PRP Records

Probable Primes Top 10000

(212140 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 ?
3001328^40945+40945^328103013Norbert Schneider12/2014
300265^56809-64^56809102990Robert Price08/2013
30035^147338-6102985Lelio R Paula11/2014
30042^342084-112739102978Enzo Doria06/2014
30059*6^132330+7102974Lelio R Paula11/2014
30062^342034-16737102963Enzo Doria05/2013
3007(9787*2^342011-1)/25102959Lelio R Paula05/2015
3008(3^215802-5)/124343756102956Lelio R Paula12/2013
30092^341991-17421102950Enzo Doria05/2013
30102^341969-112225102943Enzo Doria06/2014
3011(9787*2^341864-1)/3102915Lelio R Paula05/2015
30122^341859+1869413102910Enzo Doria05/2016
301310^102909+61102910Lelio R Paula11/2016
301410^102909-67049102909Patrick De Geest12/2016
30152^341659+1836773102850Enzo Doria03/2016
30162^341608-110639102835Enzo Doria05/2014
301710^102824+49102825Lelio R Paula11/2016
301810^102824-168011102824Patrick De Geest12/2016
301911^98708-8102794Lelio R Paula10/2016
30202^341466+4429102792Lelio R Paula09/2011
30212^341460-107102790Lelio R Paula08/2011
3022(2^341388+47)/21014943102761Lelio R Paula12/2013
30232^341355+21102759Lelio R Paula08/2011
30242^341246+40755102726Lelio R Paula11/2016
3025(2^341256-5)/991699102723Lelio R Paula12/2013
30267^121547+78102720Lelio R Paula10/2016
30272^341223-461197102719Enzo Doria06/2015
30282^341190-20577102709Enzo Doria06/2013
3029(27*2^341212+1)/84674449102709Lelio R Paula12/2013
30306^131976-65102698Lelio R Paula10/2016
30312^341134+2533102692Henri Lifchitz09/2005
303213^92184-54102688Lelio R Paula10/2016
30332^341116-20873102687Enzo Doria06/2013
30342^341094-19953102680Enzo Doria06/2013
30352^341053+129102668Lelio R Paula08/2011
3036(31*2^341006-1)/3102655Lelio R Paula03/2014
30377^121471+94102655Lelio R Paula10/2016
30392^341004-173102653Lelio R Paula08/2011
303820^78901+3102653Lelio R Paula10/2016
30405^146853-52102646Lelio R Paula10/2016
30412^340969-216931102642Enzo Doria05/2014
30422^340952+1870021102637Enzo Doria05/2016
30435*2^340940-3102634Lelio R Paula08/2014
3044(6^131891+1)/7102631Paul Bourdelais01/2010
3045(4*10^102612+83)/3102613Robert Price02/2018
304675^54717+74102598Norbert Schneider01/2015
30472^340806-20393102593Enzo Doria06/2013
3048(2^340790+5)/138267102583Lelio R Paula12/2013
30496^131821+77102577Lelio R Paula10/2016
30502^340688-29102558Henri Lifchitz05/2005
30512^340685-109101102557Enzo Doria04/2014
305265^56567-64102552Norbert Schneider11/2014
30532^340547-108897102515Enzo Doria03/2014
30547^121268+82102484Lelio R Paula10/2016
3055(6883*2^340443-1)/162401102483Lelio R Paula05/2015
30562^340434-5955102481Lelio R Paula11/2016
3057(2^340381+47)/7102465Lelio R Paula12/2013
3058111^50095+110102461Norbert Schneider04/2017
30592^340291-20301102438Enzo Doria06/2013
306012^94915+89102431Lelio R Paula10/2016
30612^340208-20373102413Enzo Doria06/2013
30626^131598-17273102404Enzo Doria02/2013
30632^340115-21181102385Enzo Doria06/2013
3064(55459*2^340090+1)/1591102379Lelio R Paula07/2014
306589^52511-88^52511102365Robert Price06/2015
30663^214539-112756102362Enzo Doria07/2014
30672^340000-19877102351Enzo Doria06/2013
30682^339990-114845102348Enzo Doria05/2015
3069(3^214516-2)/51383102346Lelio R Paula12/2013
307020^78661-99102341Lelio R Paula09/2016
30712^339951-19585102336Enzo Doria05/2013
3072(13*2^339943+1)/45102333Lelio R Paula12/2013
30732^339889+29327102317Yves Minet06/2010
30742^339834-109493102301Enzo Doria04/2014
3075(11^98221-5^98221)/6102286Robert Price01/2013
30763^214365+1820102279Lelio R Paula10/2016
3077(11*2^339705-1)/183102261Lelio R Paula03/2014
30782^339694-16995102259Lelio R Paula09/2016
30797^120985-38102245Lelio R Paula10/2016
308010^102244+122961102245Patrick De Geest12/2016
308110^102244-27102244Lelio R Paula09/2016
30827^120982-62102242Lelio R Paula10/2016
30834*6^131382-5102236Lelio R Paula11/2014
30842^339586-1091102226Yves Minet11/2012
308511^98161-3072000102225Enzo Doria12/2012
30869*7^120961-4102225Lelio R Paula11/2014
30875*3^214250+2102224Serge Batalov10/2010
308812^94713-59102213Lelio R Paula10/2016
308912^94705+89102204Lelio R Paula10/2016
30902^339407-177102172Lelio R Paula08/2011
30912^339355+65102157Lelio R Paula07/2011
3092(2^339323+47)/880715102141Lelio R Paula12/2013
30932^339168+21102100Lelio R Paula07/2011
30942^339167-108807102100Enzo Doria03/2014
30952^339156+163102097Lelio R Paula08/2011
3096(2^338982-7)/1754517102038Lelio R Paula12/2013
30972^338891-18885102017Enzo Doria05/2013
30982^338829-113239101998Enzo Doria07/2014
30992^338828-113297101998Enzo Doria07/2014
31002^338796+93101988Donovan Johnson06/2008
3101lucasU(1373,1,32502)-lucasU(1373,1,32501)101978Mike Oakes05/2009
3102(71^55079-1)/70101964Paul Bourdelais08/2017
31032^338682-19865101954Enzo Doria06/2013
3104(2^(112895*3+1)+243)/7101954Kevin Acres12/2013
31052^338568+37101920Lelio R Paula07/2011
31062^338559-1858777101917Enzo Doria04/2016
3107(9*2^338520+1)/365101904Lelio R Paula12/2013
31082^338497-17041101898Enzo Doria05/2013
31092^338475+54615101892Lelio R Paula10/2016
31102^338426-19797101877Enzo Doria06/2013
31112^338368-20369101859Enzo Doria06/2013
31122^338366+74179101859Enzo Doria04/2016
31132^338280-19745101833Enzo Doria06/2013
3114(3*2^338236-1)/347101818Lelio R Paula03/2014
31156^130841+103101815Lelio R Paula10/2016
31162^338122-20117101785Enzo Doria06/2013
3117(2^338139+5)/905333101785Lelio R Paula12/2013
311835^65917-7092101781Enzo Doria03/2013
31192^338010-19833101752Enzo Doria06/2013
31203^213215-76101730Lelio R Paula09/2016
31212^337930+63101728Lelio R Paula07/2011
31222^337920+1869661101725Enzo Doria05/2016
31232^337859-19645101706Enzo Doria05/2013
31242^337754+1869169101675Enzo Doria05/2016
3125(31*2^337677-1)/593101650Lelio R Paula03/2014
312611^97605-24101646Lelio R Paula10/2016
31278^112539-112539101633Robert Price01/2014
31282^337515-19869101603Enzo Doria06/2013
31292^337473+719101590Lelio R Paula08/2011
3130(2^337485-509203)/656647157101585Lelio R Paula12/2013
31322^337452-108815101584Enzo Doria03/2014
31312^337453+1185101584Lelio R Paula09/2016
31332^337410-113561101571Enzo Doria08/2014
31342^337387+855101564Lelio R Paula09/2016
31352^337367-17295101558Lelio R Paula09/2016
31362^337342-109035101551Enzo Doria04/2014
31372^337267-19101528Lelio R Paula07/2011
31382^337183-19989101503Enzo Doria06/2013
31392^337149+72425101492Enzo Doria04/2016
31402^337101-20241101478Enzo Doria06/2013
31412^337035-20001101458Enzo Doria06/2013
31422^337017-16995101453Lelio R Paula09/2016
31432^336979-115315101441Enzo Doria06/2015
31442^336970-20885101439Enzo Doria06/2013
31452^336958+79101435Lelio R Paula10/2009
31462^336942+169101430Lelio R Paula10/2009
3147(15185*2^336894-1)/7939101416Lelio R Paula05/2015
31482^336871+257463101409Tony Prest / Never Odd Or Even04/2016
31492^336871+318105101409Tony Prest / Never Odd Or Even04/2016
31502^336871+1010813101409Tony Prest / Never Odd Or Even04/2016
31512^336871+2302245101409Tony Prest / Never Odd Or Even04/2016
31522^336871+389273101409Tony Prest / Never Odd Or Even04/2016
31532^336871+1685475101409Tony Prest / Never Odd Or Even04/2016
31542^336871+1068119101409Tony Prest / Never Odd Or Even04/2016
31552^336871+586905101409Tony Prest / Never Odd Or Even04/2016
31562^336871+674571101409Tony Prest / Never Odd Or Even04/2016
31572^336871+707009101409Tony Prest / Never Odd Or Even04/2016
31582^336871+1210299101409Tony Prest / Never Odd Or Even04/2016
31592^336871+1921185101409Tony Prest / Never Odd Or Even04/2016
31602^336871+2003973101409Tony Prest / Never Odd Or Even04/2016
31612^336871+2656475101409Tony Prest / Never Odd Or Even04/2016
31622^336871+2703023101409Tony Prest / Never Odd Or Even04/2016
31632^336871+2704545101409Tony Prest / Never Odd Or Even04/2016
31642^336871+2766801101409Tony Prest / Never Odd Or Even04/2016
31652^336871+2127735101409Tony Prest / Never Odd Or Even04/2016
3166(2^336871+821089)/3101408Tony Prest / Never Odd Or Even05/2016
3167(2^336871+119567)/5101408Tony Prest / Never Odd Or Even05/2016
3168(2^336871+398161)/3101408Tony Prest / Never Odd Or Even05/2016
3169(2^336871+625889)/7101408Tony Prest / Never Odd Or Even05/2016
31702^336842+94065101400Lelio R Paula09/2016
3171(2^336871+904417)/3/3/3/5/19/9287177/9690011663/29993043103101378Tony Prest / Never Odd Or Even04/2016
3172(2^336871+631971)/13/251/1601/294277/614362921/30324278867101377Tony Prest / Never Odd Or Even04/2016
3173(2^336871+1443541)/3/89/1655197/11018131/47972707/468862691879101374Tony Prest / Never Odd Or Even04/2016
3174(2^336871+689863)/3/11/109/137/1867/7151/20800501/29243857/127778489101373Tony Prest / Never Odd Or Even04/2016
3175(2^336871+219839)/191/643/3011/9479/117127/175750007/4578271757101373Tony Prest / Never Odd Or Even04/2016
3176(2^336871+272895)/19/661/977572033/95853078653/520779768241101373Tony Prest / Never Odd Or Even04/2016
3177(2^336871+1023429)/2311/415873/991889/3630648341/207732189179101373Tony Prest / Never Odd Or Even04/2016
317810^101369+203811101370Patrick De Geest11/2016
317910^101369-99101369Lelio R Paula09/2016
3180(2^336871+1832627)/5/5/23/181/4397/91373/3746673331/115602484097/279351383917101363Tony Prest / Never Odd Or Even04/2016
31812^336701-113563101358Enzo Doria08/2014
31822^336644-109023101340Enzo Doria04/2014
31832^336601-21081101327Enzo Doria06/2013
318420^77869+63101310Lelio R Paula09/2016
3185(13*2^336523-1)/19101304Lelio R Paula03/2014
31866^130179-137101299Lelio R Paula10/2016
3187(2^336506+lucasV(1,2,336506)+1)/2101299Mike Oakes11/2016
3188(24737*2^336485+1)/7285101293Lelio R Paula07/2014
3189(2^336448+9)/497405101276Lelio R Paula12/2013
31902^336369-19753101258Enzo Doria05/2013
31912^336350-344291101252Enzo Doria07/2015
31922^336243-108777101220Enzo Doria03/2014
3193(31*2^336189-1)/19101204Lelio R Paula03/2014
3194(78557*2^336178+1)/1268757101199Lelio R Paula07/2014
31952^336150-20393101192Enzo Doria06/2013
31962^336112-1865249101180Enzo Doria03/2016
31972^336103-109015101178Enzo Doria04/2014
319813^90809-96101157Lelio R Paula10/2016
319919^79098-30101147Lelio R Paula10/2016
320019^79095+88101144Lelio R Paula10/2016
320115^85976+32101116Lelio R Paula10/2016
3202(3^211950+7)/28854513015920697088101107Lelio R Paula11/2013
3203(4^167933+17)/3101106Robert Price02/2017
32042^335858+153101104Lelio R Paula10/2009
32056^129918-35101096Lelio R Paula10/2016
32063^211885-70101095Lelio R Paula09/2016
3207(29*2^335835-1)/550599101093Lelio R Paula03/2014
32082^335818-20033101092Enzo Doria06/2013
32092^335813-110083101090Enzo Doria04/2014
32102^335804+2155101088Lelio R Paula09/2016
32112^335784-16145101082Enzo Doria04/2013
321211^97051+62101069Lelio R Paula10/2016
3213(2^335691-3)/26515101049Lelio R Paula12/2013
32142^335658-94395101044Lelio R Paula09/2016
32152^335586+169101022Lelio R Paula10/2009
3216(56^57787-1)/55101021Paul Bourdelais08/2017
321747599!2+1024100991Robert Price02/2015
32182^335468-18629100986Enzo Doria05/2013
32192^335454-20961100982Enzo Doria06/2013
322010^100978+61100979Lelio R Paula09/2016
322110^100978-156437100978Patrick De Geest11/2016
3222(15*2^335417+1)/481100970Lelio R Paula12/2013
32232^335403-1859167100967Enzo Doria03/2016
32249*2^335364-5100956Lelio R Paula08/2014
32252^335349+72287100951Enzo Doria04/2016
32262^335329+16095100945Lelio R Paula09/2016
3227232823#+233663100937Makoto Morimoto10/2017
32282^335237-20893100917Enzo Doria06/2013
32292^335222-19337100912Enzo Doria05/2013
32302^335222-109985100912Enzo Doria04/2014
32312^335182-17237100900Enzo Doria05/2013
32322^335043-16737100858Enzo Doria05/2013
3233(21181*2^335049+1)/1343811100858Lelio R Paula07/2014
32342^335038-20633100857Enzo Doria06/2013
32352^335031+1873373100855Enzo Doria06/2016
32363^211354-8816100842Enzo Doria05/2014
32372^334984-112757100841Enzo Doria06/2014
32382^334857+48527100803Lelio R Paula08/2011
323912^93406+29100803Lelio R Paula10/2016
3240(5*2^334825+1)/47100792Lelio R Paula12/2013
32412^334809-13100788Lelio R Paula04/2011
3242(82*10^100780-1)/9100781Robert Price12/2014
3243(2^334779+47)/5100778Lelio R Paula12/2013
32442^334751+2049100771Lelio R Paula09/2016
324513^90443-98100749Lelio R Paula10/2016
3246(7*10^100737+71)/3100738Robert Price05/2018
3247(24737*2^334628+1)/3100737Lelio R Paula07/2014
324815^85639-28100720Lelio R Paula10/2016
32492^334562+577294575100711Lelio R Paula09/2016
32504*3^211077-5100710Lelio R Paula08/2014


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: June, 20 2018 08:38 (Time in France)

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