PRP Records

Probable Primes Top 10000

(253476 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 (> 50000) Who ? When ?
9501(7^69247-4^69247)/358521Robert Price06/2012
95022^194358-116758508Lelio R Paula05/2011
9503(2^194366+7)/137358507Lelio R Paula02/2012
950415091^7518+7518^1509158495Hans Havermann04/2019
950515852^4895+4895^1585258490Hans Havermann04/2019
9506(493*10^58486-7)/958488Robert Price07/2016
95073^122579-34058486Lelio R Paula10/2012
9508(11*10^58458-149)/358459Robert Price01/2017
9509(47*10^58456+133)/958457Robert Price04/2017
95102^194186+8558456Lelio R Paula04/2011
95113^122506-2^(122506-1)58451Robert Price01/2016
9512(74^31267-1)/7358444Paul Bourdelais08/2017
9513177^25998-258443Lelio R Paula10/2017
951415^49690-2658440Lelio R Paula03/2013
951510^58437+11072158438Patrick De Geest12/2012
951610^58437-1158437Robert Price05/2011
95172^194095+6958429Lelio R Paula04/2011
9518(29*10^58417-77)/358418Robert Price01/2017
95192^194034+17758411Lelio R Paula04/2011
9520789^20158+20158^78958400Norbert Schneider06/2016
952114^50949+7558395Lelio R Paula03/2013
95222^193974-11476158392Enzo Doria05/2015
95232^193965+558390Henri Lifchitz12/2002
9524(5*10^58384-29)/358385Robert Price02/2017
95253^122360+8058381Lelio R Paula10/2012
952610103^14577-11458373Enzo Doria07/2012
9527(22699*2^193883+1)/2158368Lelio R Paula06/2014
9528(31*2^193886+1)/14076558362Lelio R Paula07/2012
952911^56041-156058361Enzo Doria11/2012
9530(2^193881+9)/1769958360Lelio R Paula02/2012
95313^122313+5858359Lelio R Paula10/2012
95326^74996-11958359Lelio R Paula10/2012
9533(11*2^193859+1)/1358358Lelio R Paula07/2012
95342^193861-11225558358Enzo Doria06/2014
9535(22699*2^193854+1)/492758357Lelio R Paula06/2014
953618^46487+3758354Lelio R Paula03/2013
953717^47419+5458347Lelio R Paula03/2013
95382^193812-479958344Yves Minet05/2019
953915486^5851+5851^1548658340Hans Havermann04/2019
9540(31*2^193791+1)/358338Lelio R Paula02/2012
9541(27*2^193805-1)/98224958337Lelio R Paula01/2014
954214088^13825+13825^1408858334Hans Havermann04/2019
9543144^27025-14358330Norbert Schneider11/2018
954411900^14311-14311^1190058326Norbert Schneider05/2019
954515297^6494+6494^1529758321Hans Havermann04/2019
954616293^3794+3794^1629358315Hans Havermann04/2019
95473^122219-2^12221958314Mike Oakes09/2003
9548(199*10^58306+11)/358308Robert Price05/2017
95492^193674-1882558302Lelio R Paula05/2011
955014897^8172+8172^1489758282Hans Havermann04/2019
95515*10^58275+358276Dmitry Domanov11/2010
95522^193578-11291358273Enzo Doria06/2014
95542^193541+129958262Lelio R Paula05/2011
95538361^14854-14854^836158262Norbert Schneider07/2019
955510^58250+9358251Robert Price01/2011
955610^58250-17560758250Patrick De Geest12/2012
9557(107^28703+1)/10858248Richard Fischer05/2018
95582^193492+841558247Lelio R Paula10/2012
95592^193444+15758233Lelio R Paula04/2011
9560Phi(28754,28754)58231Henri Lifchitz08/2013
95612^193430-11188158229Enzo Doria05/2014
956210^58225+12457958226Patrick De Geest12/2012
956310^58225-9358225Robert Price05/2011
95642^193375-29558212Yves Minet05/2013
956514018^14037-14037^1401858208Norbert Schneider10/2018
95662^193345+7726758203Enzo Doria05/2016
956721^44017-20^4401758201Robert Price05/2012
9568(17*2^193329-1)/958199Lelio R Paula01/2014
956917^47291+2058190Lelio R Paula03/2013
9570p(12528)#/2-12858170Robert Price05/2017
95712^193214-13558164Lelio R Paula04/2011
957219^45483-8058162Lelio R Paula03/2013
9573(4*10^58155+83)/358156Robert Price01/2017
957514^50739-1358154Lelio R Paula03/2013
9574(1017*2^193184-1)/482358154Lelio R Paula04/2015
9576(2*10^58151+457)/958151Robert Price01/2017
9577(9179*2^193183-1)/399926787958149Lelio R Paula04/2015
957814555^9874+9874^1455558140Hans Havermann05/2019
9579(19*2^193114-1)/118675558129Lelio R Paula01/2014
95812^193091-123758127Yves Minet08/2012
95809*7^68780-258127Lelio R Paula09/2014
95822473^17130+17130^247358126Norbert Schneider10/2018
95832^193083-86968810558124Lelio R Paula10/2012
95842^193058-4558117Lelio R Paula04/2011
9585(14016^14016+14017^14017)/(23*7103*19913)58115David Broadhurst09/2009
958611^55795-4258105Lelio R Paula03/2013
95873^121779-1658104Lelio R Paula10/2012
9588(13*10^58103+191)/358104Robert Price08/2017
958915865^4594+4594^1586558101Hans Havermann05/2019
95902^192986+19558095Lelio R Paula04/2011
95917^68740+2*3^6874058093Mike Oakes07/2010
9592(85*10^58091-1)/358093Robert Price07/2017
9593(404*10^58087-53)/958089Robert Price11/2017
959412^53821+1158083Lelio R Paula02/2013
9595119^27979-11858072Norbert Schneider10/2013
959614380^10899+10899^1438058058Hans Havermann04/2019
9597(10223*2^192828+1)/24358049Lelio R Paula05/2014
95982^192808-112758041Yves Minet05/2013
9599(27*2^192803+1)/982758037Lelio R Paula07/2012
9601(2^192781+lucasV(1,2,192781)+1)/458033Mike Oakes11/2016
96003*10^58032-2358033Robert Price11/2017
96022^192678+7294358002Enzo Doria04/2016
9603(13*10^57997-37)/357998Robert Price08/2017
96042^192657-318957996Yves Minet10/2014
96056^74525-14957992Lelio R Paula10/2012
960642^35723-4157988Norbert Schneider06/2014
9607(29*2^192625-1)/18357986Lelio R Paula01/2014
9608(3^121520-8)/384757977Lelio R Paula03/2012
9609(2^192596-5)/13957976Lelio R Paula02/2012
961010^57975+6783357976Patrick De Geest09/2013
961110^57975-4769357975Patrick De Geest09/2013
9612(F(7707)^37-F(7706)^37)/F(7705)57972Wayne Halsdorf03/2012
961314025^13592+13592^1402557970Hans Havermann04/2019
9614(29*10^57967+673)/957968Robert Price10/2017
9615(3^121492-5)/457966Lelio R Paula03/2012
96162^192549+3557964Lelio R Paula04/2011
961728799!2+257962Robert Price10/2012
9618(7*2^192534-1)/134757957Lelio R Paula01/2014
961911108^14323-14323^1110857946Norbert Schneider05/2019
96207001^15069-10057943Enzo Doria07/2012
9621L(277273)/1109092157940Donovan Johnson11/2005
9622(2^192469-1017)/3557938Lelio R Paula02/2012
96232^192457-1155*19245757936Henri Lifchitz02/2005
962412752^14111-14111^1275257934Norbert Schneider01/2019
96252^192443+138557932Lelio R Paula05/2011
9626132^27317-13157928Norbert Schneider03/2015
962741522!3-5904957912Robert Price12/2015
9628(3*2^192380-1)/16957911Lelio R Paula01/2014
96292^192339-251557900Yves Minet07/2014
96302^192303+769557889Lelio R Paula10/2012
96312^192273-595557880Lelio R Paula05/2011
96322^192257+1609557876Lelio R Paula05/2011
9633109^28401-257865Lelio R Paula10/2017
96342^192218-11186157864Enzo Doria05/2014
96352^192214-394157863Yves Minet04/2017
9636(2^192212+3)/25957860Lelio R Paula02/2012
9637(3^121270+8)/15593975357853Lelio R Paula03/2012
963880^30393-7957841Norbert Schneider03/2015
963920^44455-312357838Enzo Doria03/2013
96402^192122-19557835Lelio R Paula04/2011
9641(29*10^57834+91)/357835Robert Price03/2016
96428*6^74306+557823Lelio R Paula09/2014
9643(39^36341-1)/3857820Robert Price04/2012
96442^192037-11180557809Enzo Doria05/2014
96452^192023-192023^257805Henri Lifchitz05/2005
964621^43717+257804Ray Chandler08/2011
96478*5^82687+757797Lelio R Paula09/2014
964816459^3246+3246^1645957794Hans Havermann04/2019
96495^82680-2457791Lelio R Paula10/2012
9651(2^191915+47)/9557771Lelio R Paula02/2012
965012019^14160-14160^1201957771Norbert Schneider02/2019
9652(74*10^57763+133)/957764Robert Price10/2017
96536^74227-9557760Lelio R Paula10/2012
96542^191861+2983557756Lelio R Paula10/2012
96561908^17605+17605^190857755Serge Batalov05/2014
96555*10^57754+5957755Robert Price09/2016
965710418^14373-14373^1041857748Norbert Schneider06/2019
9658(5*2^191821-1)/892406757738Lelio R Paula01/2014
965914100^12431+12431^1410057733Hans Havermann04/2019
96603*8^63917+5^63917-3*4^63917+3*2^6391757724Mike Oakes11/2010
966141399!3-656157723Robert Price11/2015
9662(44*10^57721-233)/957722Robert Price10/2017
96632^191745+1757721Lelio R Paula04/2011
96642^191730-76157717Yves Minet01/2012
9665(2^191733-3)/225157715Lelio R Paula02/2012
96662^191698-11157707Lelio R Paula04/2011
9667(13*10^57691+23)/957692Robert Price02/2015
96682^191640-447557690Yves Minet03/2019
966920^44340-542357688Enzo Doria03/2013
9670(27*2^191629+1)/12557686Lelio R Paula07/2012
96714*10^57684+3*7^5768457685Mike Oakes11/2010
96732*3^120898+557684Lelio R Paula04/2014
967210650^14323-14323^1065057684Norbert Schneider05/2019
9674(6883*2^191610-1)/734757681Lelio R Paula04/2015
96756^74117-4957675Lelio R Paula10/2012
96762^191586-11320157674Enzo Doria07/2014
96772^191580+19357672Lelio R Paula04/2011
9678(103*29^39433+10401)/457669Curtis Bright05/2015
96792^191560+25525557666Lelio R Paula05/2011
96802^191515-8557652Lelio R Paula04/2011
96812^191502-112757648Yves Minet05/2013
96822*5^82473-3^8247357647Mike Oakes08/2010
9683(13*10^57634-61)/357635Robert Price08/2017
968410635^14312-14312^1063557631Norbert Schneider05/2019
968585^29868-29868^8557628Norbert Schneider11/2017
96862^191430+10357627Lelio R Paula04/2011
96873*2^191408+557621Lelio R Paula03/2014
96882^191382-185893157612Enzo Doria04/2016
96896*7^68163+557606Lelio R Paula09/2014
969091^29403-257602Lelio R Paula08/2013
969111^55308-795057598Enzo Doria02/2013
96922^191329+6557596Lelio R Paula04/2011
969311^55302-24057592Enzo Doria07/2012
96942^191299-103146757587Paul Bourdelais11/2012
96952^191295-11199157586Enzo Doria05/2014
969610824^14273-14273^1082457583Norbert Schneider04/2019
96972^191279-129757581Yves Minet08/2012
969814827^7630+7630^1482757567Hans Havermann04/2019
969910047^14384-14384^1004757566Norbert Schneider06/2019
97003*6^73961+557554Lelio R Paula09/2014
970116177^3610+3610^1617757550Hans Havermann04/2019
9702(3^120623+5)/5214457548Lelio R Paula04/2012
9703(17*10^57543-29)/357544Robert Price09/2017
970442^35445-4157537Norbert Schneider06/2014
9705(71^31079-1)/7057534Paul Bourdelais08/2017
97062^191069-72340357518Paul Bourdelais11/2012
97074*10^57506-357507Serge Batalov11/2010
970810^57501+6735957502Patrick De Geest06/2016
970910^57501-100000000157501Robert Price05/2016
971010^57501-24986157501Patrick De Geest06/2016
971110090^14361-14361^1009057500Norbert Schneider06/2019
9712(9^60251+4^60251)/1357493Robert Price02/2013
971320^44184-600357485Enzo Doria03/2013
97142^190948+1270557482Lelio R Paula10/2012
97152^190945+2957481Henri Lifchitz06/2005
97162^190922-40157474Yves Minet01/2012
971715^48860+4657464Lelio R Paula02/2013
97183^120434+2057462Lelio R Paula10/2012
97197^67964-3857437Lelio R Paula10/2012
97202^190799-11306557437Enzo Doria07/2014
97219*5^82159+257428Lelio R Paula09/2014
9723(F(22898)^13-F(22897)^13)/F(22896)57422Wayne Halsdorf03/2012
972215362^5469+5469^1536257422Hans Havermann04/2019
972414005^12586+12586^1400557419Hans Havermann04/2019
972510159^14330-14330^1015957419Norbert Schneider05/2019
9728lucasU(432,25,21787)-5*lucasU(432,25,21786)57416Mike Oakes05/2009
9726(103*10^57414-1)/357416Serge Batalov12/2014
9727(1654*30^38869-1)/2957416Karsten Bonath05/2017
97292*10^57410+9^5741057411Mike Oakes04/2011
97302^190704-159557408Lelio R Paula05/2011
973111^55121-174057403Enzo Doria11/2012
97322^190644-18557390Lelio R Paula04/2011
973341182!3-3^4118257389Robert Price08/2015
97342^190629-11225557386Enzo Doria06/2014
9735(2*10^57384-71)/357384Robert Price01/2017
97372*6^73735+5^7373557378Mike Oakes11/2009
97362^190605+5957378Lelio R Paula04/2011
97386^73727-757371Lelio R Paula10/2012
97392^190561-11222557365Enzo Doria06/2014
974010^57358+17089957359Patrick De Geest06/2016
974110^57358-800157358Robert Price03/2016
974218^45687-1157350Lelio R Paula02/2013
974311^55069-21057349Enzo Doria07/2012
974411^55068-1257348Lelio R Paula02/2013
974519^44839+5457339Lelio R Paula02/2013
9746(7*2^190468-1)/851157334Lelio R Paula01/2014
9747(23*10^57333-59)/957334Robert Price03/2017
97482^190455-1155*19045557333Henri Lifchitz02/2005
974914376^9721+9721^1437657328Hans Havermann04/2019
975065^31620+2857325Lelio R Paula01/2016


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: August, 25 2019 15:53 (Time in France)

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