PRP Records

Probable Primes Top 10000

(181746 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 ?
27512^341460-107102790Lelio R Paula08/2011
2752(2^341388+47)/21014943102761Lelio R Paula12/2013
27532^341355+21102759Lelio R Paula08/2011
27542^341246+40755102726Lelio R Paula11/2016
2755(2^341256-5)/991699102723Lelio R Paula12/2013
27567^121547+78102720Lelio R Paula10/2016
27572^341223-461197102719Enzo Doria06/2015
27592^341190-20577102709Enzo Doria06/2013
2758(27*2^341212+1)/84674449102709Lelio R Paula12/2013
27606^131976-65102698Lelio R Paula10/2016
27612^341134+2533102692Henri Lifchitz09/2005
276213^92184-54102688Lelio R Paula10/2016
27632^341116-20873102687Enzo Doria06/2013
27642^341094-19953102680Enzo Doria06/2013
27652^341053+129102668Lelio R Paula08/2011
2766(31*2^341006-1)/3102655Lelio R Paula03/2014
27677^121471+94102655Lelio R Paula10/2016
27692^341004-173102653Lelio R Paula08/2011
276820^78901+3102653Lelio R Paula10/2016
27705^146853-52102646Lelio R Paula10/2016
27712^340969-216931102642Enzo Doria05/2014
27722^340952+1870021102637Enzo Doria05/2016
27735*2^340940-3102634Lelio R Paula08/2014
2774(6^131891+1)/7102631Paul Bourdelais01/2010
277575^54717+74102598Norbert Schneider01/2015
27762^340806-20393102593Enzo Doria06/2013
2777(2^340790+5)/138267102583Lelio R Paula12/2013
27786^131821+77102577Lelio R Paula10/2016
27792^340688-29102558Henri Lifchitz05/2005
27802^340685-109101102557Enzo Doria04/2014
278165^56567-64102552Norbert Schneider11/2014
27822^340547-108897102515Enzo Doria03/2014
27837^121268+82102484Lelio R Paula10/2016
2784(6883*2^340443-1)/162401102483Lelio R Paula05/2015
27852^340434-5955102481Lelio R Paula11/2016
2786(2^340381+47)/7102465Lelio R Paula12/2013
2787111^50095+110102461Norbert Schneider04/2017
27882^340291-20301102438Enzo Doria06/2013
278912^94915+89102431Lelio R Paula10/2016
27902^340208-20373102413Enzo Doria06/2013
27916^131598-17273102404Enzo Doria02/2013
27922^340115-21181102385Enzo Doria06/2013
2793(55459*2^340090+1)/1591102379Lelio R Paula07/2014
279489^52511-88^52511102365Robert Price06/2015
27953^214539-112756102362Enzo Doria07/2014
27962^340000-19877102351Enzo Doria06/2013
27972^339990-114845102348Enzo Doria05/2015
2798(3^214516-2)/51383102346Lelio R Paula12/2013
279920^78661-99102341Lelio R Paula09/2016
28002^339951-19585102336Enzo Doria05/2013
2801(13*2^339943+1)/45102333Lelio R Paula12/2013
28022^339889+29327102317Yves Minet06/2010
28032^339834-109493102301Enzo Doria04/2014
2804(11^98221-5^98221)/6102286Robert Price01/2013
28053^214365+1820102279Lelio R Paula10/2016
2806(11*2^339705-1)/183102261Lelio R Paula03/2014
28072^339694-16995102259Lelio R Paula09/2016
28087^120985-38102245Lelio R Paula10/2016
280910^102244+122961102245Patrick De Geest12/2016
281010^102244-27102244Lelio R Paula09/2016
28117^120982-62102242Lelio R Paula10/2016
28124*6^131382-5102236Lelio R Paula11/2014
28132^339586-1091102226Yves Minet11/2012
281411^98161-3072000102225Enzo Doria12/2012
28159*7^120961-4102225Lelio R Paula11/2014
28165*3^214250+2102224Serge Batalov10/2010
281712^94713-59102213Lelio R Paula10/2016
281812^94705+89102204Lelio R Paula10/2016
28192^339407-177102172Lelio R Paula08/2011
28202^339355+65102157Lelio R Paula07/2011
2821(2^339323+47)/880715102141Lelio R Paula12/2013
28222^339168+21102100Lelio R Paula07/2011
28232^339167-108807102100Enzo Doria03/2014
28242^339156+163102097Lelio R Paula08/2011
2825(2^338982-7)/1754517102038Lelio R Paula12/2013
28262^338891-18885102017Enzo Doria05/2013
28272^338829-113239101998Enzo Doria07/2014
28282^338828-113297101998Enzo Doria07/2014
28292^338796+93101988Donovan Johnson06/2008
2830lucasU(1373,1,32502)-lucasU(1373,1,32501)101978Mike Oakes05/2009
2831(71^55079-1)/70101964Paul Bourdelais08/2017
28332^338682-19865101954Enzo Doria06/2013
2832(2^(112895*3+1)+243)/7101954Kevin Acres12/2013
28342^338568+37101920Lelio R Paula07/2011
28352^338559-1858777101917Enzo Doria04/2016
2836(9*2^338520+1)/365101904Lelio R Paula12/2013
28372^338497-17041101898Enzo Doria05/2013
28382^338475+54615101892Lelio R Paula10/2016
28392^338426-19797101877Enzo Doria06/2013
28402^338368-20369101859Enzo Doria06/2013
28412^338366+74179101859Enzo Doria04/2016
28422^338280-19745101833Enzo Doria06/2013
2843(3*2^338236-1)/347101818Lelio R Paula03/2014
28446^130841+103101815Lelio R Paula10/2016
28452^338122-20117101785Enzo Doria06/2013
2846(2^338139+5)/905333101785Lelio R Paula12/2013
284735^65917-7092101781Enzo Doria03/2013
28482^338010-19833101752Enzo Doria06/2013
28493^213215-76101730Lelio R Paula09/2016
28502^337930+63101728Lelio R Paula07/2011
28512^337920+1869661101725Enzo Doria05/2016
28522^337859-19645101706Enzo Doria05/2013
28532^337754+1869169101675Enzo Doria05/2016
2854(31*2^337677-1)/593101650Lelio R Paula03/2014
285511^97605-24101646Lelio R Paula10/2016
28568^112539-112539101633Robert Price01/2014
28572^337515-19869101603Enzo Doria06/2013
28582^337473+719101590Lelio R Paula08/2011
2859(2^337485-509203)/656647157101585Lelio R Paula12/2013
28602^337452-108815101584Enzo Doria03/2014
28612^337453+1185101584Lelio R Paula09/2016
28622^337410-113561101571Enzo Doria08/2014
28632^337387+855101564Lelio R Paula09/2016
28642^337367-17295101558Lelio R Paula09/2016
28652^337342-109035101551Enzo Doria04/2014
28662^337267-19101528Lelio R Paula07/2011
28672^337183-19989101503Enzo Doria06/2013
28682^337149+72425101492Enzo Doria04/2016
28692^337101-20241101478Enzo Doria06/2013
28702^337035-20001101458Enzo Doria06/2013
28712^337017-16995101453Lelio R Paula09/2016
28722^336979-115315101441Enzo Doria06/2015
28732^336970-20885101439Enzo Doria06/2013
28742^336958+79101435Lelio R Paula10/2009
28752^336942+169101430Lelio R Paula10/2009
2876(15185*2^336894-1)/7939101416Lelio R Paula05/2015
28772^336871+257463101409Tony Prest / Never Odd Or Even04/2016
28782^336871+318105101409Tony Prest / Never Odd Or Even04/2016
28792^336871+1010813101409Tony Prest / Never Odd Or Even04/2016
28802^336871+2302245101409Tony Prest / Never Odd Or Even04/2016
28812^336871+389273101409Tony Prest / Never Odd Or Even04/2016
28822^336871+1685475101409Tony Prest / Never Odd Or Even04/2016
28832^336871+1068119101409Tony Prest / Never Odd Or Even04/2016
28842^336871+586905101409Tony Prest / Never Odd Or Even04/2016
28852^336871+674571101409Tony Prest / Never Odd Or Even04/2016
28862^336871+707009101409Tony Prest / Never Odd Or Even04/2016
28872^336871+1210299101409Tony Prest / Never Odd Or Even04/2016
28882^336871+1921185101409Tony Prest / Never Odd Or Even04/2016
28892^336871+2003973101409Tony Prest / Never Odd Or Even04/2016
28902^336871+2656475101409Tony Prest / Never Odd Or Even04/2016
28912^336871+2703023101409Tony Prest / Never Odd Or Even04/2016
28922^336871+2704545101409Tony Prest / Never Odd Or Even04/2016
28932^336871+2766801101409Tony Prest / Never Odd Or Even04/2016
28942^336871+2127735101409Tony Prest / Never Odd Or Even04/2016
2895(2^336871+821089)/3101408Tony Prest / Never Odd Or Even05/2016
2896(2^336871+119567)/5101408Tony Prest / Never Odd Or Even05/2016
2897(2^336871+398161)/3101408Tony Prest / Never Odd Or Even05/2016
2898(2^336871+625889)/7101408Tony Prest / Never Odd Or Even05/2016
28992^336842+94065101400Lelio R Paula09/2016
2900(2^336871+904417)/3/3/3/5/19/9287177/9690011663/29993043103101378Tony Prest / Never Odd Or Even04/2016
2901(2^336871+631971)/13/251/1601/294277/614362921/30324278867101377Tony Prest / Never Odd Or Even04/2016
2902(2^336871+1443541)/3/89/1655197/11018131/47972707/468862691879101374Tony Prest / Never Odd Or Even04/2016
2903(2^336871+689863)/3/11/109/137/1867/7151/20800501/29243857/127778489101373Tony Prest / Never Odd Or Even04/2016
2904(2^336871+219839)/191/643/3011/9479/117127/175750007/4578271757101373Tony Prest / Never Odd Or Even04/2016
2905(2^336871+272895)/19/661/977572033/95853078653/520779768241101373Tony Prest / Never Odd Or Even04/2016
2906(2^336871+1023429)/2311/415873/991889/3630648341/207732189179101373Tony Prest / Never Odd Or Even04/2016
290710^101369+203811101370Patrick De Geest11/2016
290810^101369-99101369Lelio R Paula09/2016
2909(2^336871+1832627)/5/5/23/181/4397/91373/3746673331/115602484097/279351383917101363Tony Prest / Never Odd Or Even04/2016
29102^336701-113563101358Enzo Doria08/2014
29112^336644-109023101340Enzo Doria04/2014
29122^336601-21081101327Enzo Doria06/2013
291320^77869+63101310Lelio R Paula09/2016
2914(13*2^336523-1)/19101304Lelio R Paula03/2014
29156^130179-137101299Lelio R Paula10/2016
2916(2^336506+lucasV(1,2,336506)+1)/2101299Mike Oakes11/2016
2917(24737*2^336485+1)/7285101293Lelio R Paula07/2014
2918(2^336448+9)/497405101276Lelio R Paula12/2013
29192^336369-19753101258Enzo Doria05/2013
29202^336350-344291101252Enzo Doria07/2015
29212^336243-108777101220Enzo Doria03/2014
2922(31*2^336189-1)/19101204Lelio R Paula03/2014
2923(78557*2^336178+1)/1268757101199Lelio R Paula07/2014
29242^336150-20393101192Enzo Doria06/2013
29252^336112-1865249101180Enzo Doria03/2016
29262^336103-109015101178Enzo Doria04/2014
292713^90809-96101157Lelio R Paula10/2016
292819^79098-30101147Lelio R Paula10/2016
292919^79095+88101144Lelio R Paula10/2016
293015^85976+32101116Lelio R Paula10/2016
2931(3^211950+7)/28854513015920697088101107Lelio R Paula11/2013
2932(4^167933+17)/3101106Robert Price02/2017
29332^335858+153101104Lelio R Paula10/2009
29346^129918-35101096Lelio R Paula10/2016
29353^211885-70101095Lelio R Paula09/2016
2936(29*2^335835-1)/550599101093Lelio R Paula03/2014
29372^335818-20033101092Enzo Doria06/2013
29382^335813-110083101090Enzo Doria04/2014
29392^335804+2155101088Lelio R Paula09/2016
29402^335784-16145101082Enzo Doria04/2013
294111^97051+62101069Lelio R Paula10/2016
2942(2^335691-3)/26515101049Lelio R Paula12/2013
29432^335658-94395101044Lelio R Paula09/2016
29442^335586+169101022Lelio R Paula10/2009
2945(56^57787-1)/55101021Paul Bourdelais08/2017
294647599!2+1024100991Robert Price02/2015
29472^335468-18629100986Enzo Doria05/2013
29482^335454-20961100982Enzo Doria06/2013
294910^100978+61100979Lelio R Paula09/2016
295010^100978-156437100978Patrick De Geest11/2016
2951(15*2^335417+1)/481100970Lelio R Paula12/2013
29522^335403-1859167100967Enzo Doria03/2016
29539*2^335364-5100956Lelio R Paula08/2014
29542^335349+72287100951Enzo Doria04/2016
29552^335329+16095100945Lelio R Paula09/2016
29562^335237-20893100917Enzo Doria06/2013
29572^335222-19337100912Enzo Doria05/2013
29582^335222-109985100912Enzo Doria04/2014
29592^335182-17237100900Enzo Doria05/2013
29602^335043-16737100858Enzo Doria05/2013
2961(21181*2^335049+1)/1343811100858Lelio R Paula07/2014
29622^335038-20633100857Enzo Doria06/2013
29632^335031+1873373100855Enzo Doria06/2016
29643^211354-8816100842Enzo Doria05/2014
29652^334984-112757100841Enzo Doria06/2014
29672^334857+48527100803Lelio R Paula08/2011
296612^93406+29100803Lelio R Paula10/2016
2968(5*2^334825+1)/47100792Lelio R Paula12/2013
29692^334809-13100788Lelio R Paula04/2011
2970(82*10^100780-1)/9100781Robert Price12/2014
2971(2^334779+47)/5100778Lelio R Paula12/2013
29722^334751+2049100771Lelio R Paula09/2016
297313^90443-98100749Lelio R Paula10/2016
2974(24737*2^334628+1)/3100737Lelio R Paula07/2014
297515^85639-28100720Lelio R Paula10/2016
29762^334562+577294575100711Lelio R Paula09/2016
29774*3^211077-5100710Lelio R Paula08/2014
29782^334524+145100702Lelio R Paula07/2009
2979(1017*2^334391-1)/3535100662Lelio R Paula05/2015
29802^334294-113111100633Enzo Doria07/2014
29816^129308-17723100622Enzo Doria03/2013
29826^129305+95100619Lelio R Paula10/2016
29832^334244-1167100618Lelio R Paula09/2016
2984(21*2^334050+1)/935100558Lelio R Paula12/2013
2985(78557*2^334018+1)/4326021100548Lelio R Paula07/2014
2986(35*10^100542+1)/9100543Serge Batalov11/2010
298713^90251+24100535Lelio R Paula10/2016
29882^333963+789100533Lelio R Paula08/2011
29892^333919-1840087100520Enzo Doria06/2015
29902^333911+72623100518Enzo Doria04/2016
299118^80064-67100503Lelio R Paula10/2016
29925^143742-48100472Lelio R Paula10/2016
29932^333757-112123100471Enzo Doria06/2014
29942^333603-108861100425Enzo Doria03/2014
29959*7^118818-2100414Lelio R Paula11/2014
29962^333546-17097100408Enzo Doria05/2013
299717^81597+72100401Lelio R Paula10/2016
2998p(20559)#/2+8100384Robert Price01/2017
299911^96390-24100380Lelio R Paula10/2016
30004832563059*2^333333+30029100353Donovan Johnson01/2008


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: September, 14 2017 17:05 (Time in France)

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