PRP Records

Probable Primes Top 10000

(252932 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 ?
92512^192023-192023^257805Henri Lifchitz05/2005
925221^43717+257804Ray Chandler08/2011
92538*5^82687+757797Lelio R Paula09/2014
925416459^3246+3246^1645957794Hans Havermann04/2019
92555^82680-2457791Lelio R Paula10/2012
9257(2^191915+47)/9557771Lelio R Paula02/2012
925612019^14160-14160^1201957771Norbert Schneider02/2019
9258(74*10^57763+133)/957764Robert Price10/2017
92596^74227-9557760Lelio R Paula10/2012
92602^191861+2983557756Lelio R Paula10/2012
92621908^17605+17605^190857755Serge Batalov05/2014
92615*10^57754+5957755Robert Price09/2016
9263(5*2^191821-1)/892406757738Lelio R Paula01/2014
926414100^12431+12431^1410057733Hans Havermann04/2019
92653*8^63917+5^63917-3*4^63917+3*2^6391757724Mike Oakes11/2010
926641399!3-656157723Robert Price11/2015
9267(44*10^57721-233)/957722Robert Price10/2017
92682^191745+1757721Lelio R Paula04/2011
92692^191730-76157717Yves Minet01/2012
9270(2^191733-3)/225157715Lelio R Paula02/2012
92712^191698-11157707Lelio R Paula04/2011
9272(13*10^57691+23)/957692Robert Price02/2015
92732^191640-447557690Yves Minet03/2019
927420^44340-542357688Enzo Doria03/2013
9275(27*2^191629+1)/12557686Lelio R Paula07/2012
92764*10^57684+3*7^5768457685Mike Oakes11/2010
92782*3^120898+557684Lelio R Paula04/2014
927710650^14323-14323^1065057684Norbert Schneider05/2019
9279(6883*2^191610-1)/734757681Lelio R Paula04/2015
92806^74117-4957675Lelio R Paula10/2012
92812^191586-11320157674Enzo Doria07/2014
92822^191580+19357672Lelio R Paula04/2011
9283(103*29^39433+10401)/457669Curtis Bright05/2015
92842^191560+25525557666Lelio R Paula05/2011
92852^191515-8557652Lelio R Paula04/2011
92862^191502-112757648Yves Minet05/2013
92872*5^82473-3^8247357647Mike Oakes08/2010
9288(13*10^57634-61)/357635Robert Price08/2017
928910635^14312-14312^1063557631Norbert Schneider05/2019
929085^29868-29868^8557628Norbert Schneider11/2017
92912^191430+10357627Lelio R Paula04/2011
92923*2^191408+557621Lelio R Paula03/2014
92932^191382-185893157612Enzo Doria04/2016
92946*7^68163+557606Lelio R Paula09/2014
929591^29403-257602Lelio R Paula08/2013
929611^55308-795057598Enzo Doria02/2013
92972^191329+6557596Lelio R Paula04/2011
929811^55302-24057592Enzo Doria07/2012
92992^191299-103146757587Paul Bourdelais11/2012
93002^191295-11199157586Enzo Doria05/2014
930110824^14273-14273^1082457583Norbert Schneider04/2019
93022^191279-129757581Yves Minet08/2012
930314827^7630+7630^1482757567Hans Havermann04/2019
93043*6^73961+557554Lelio R Paula09/2014
930516177^3610+3610^1617757550Hans Havermann04/2019
9306(3^120623+5)/5214457548Lelio R Paula04/2012
9307(17*10^57543-29)/357544Robert Price09/2017
930842^35445-4157537Norbert Schneider06/2014
9309(71^31079-1)/7057534Paul Bourdelais08/2017
93102^191069-72340357518Paul Bourdelais11/2012
93114*10^57506-357507Serge Batalov11/2010
931210^57501+6735957502Patrick De Geest06/2016
931310^57501-100000000157501Robert Price05/2016
931410^57501-24986157501Patrick De Geest06/2016
9315(9^60251+4^60251)/1357493Robert Price02/2013
931620^44184-600357485Enzo Doria03/2013
93172^190948+1270557482Lelio R Paula10/2012
93182^190945+2957481Henri Lifchitz06/2005
93192^190922-40157474Yves Minet01/2012
932015^48860+4657464Lelio R Paula02/2013
93213^120434+2057462Lelio R Paula10/2012
93227^67964-3857437Lelio R Paula10/2012
93232^190799-11306557437Enzo Doria07/2014
93249*5^82159+257428Lelio R Paula09/2014
9326(F(22898)^13-F(22897)^13)/F(22896)57422Wayne Halsdorf03/2012
932515362^5469+5469^1536257422Hans Havermann04/2019
932714005^12586+12586^1400557419Hans Havermann04/2019
932810159^14330-14330^1015957419Norbert Schneider05/2019
9331lucasU(432,25,21787)-5*lucasU(432,25,21786)57416Mike Oakes05/2009
9329(103*10^57414-1)/357416Serge Batalov12/2014
9330(1654*30^38869-1)/2957416Karsten Bonath05/2017
93322*10^57410+9^5741057411Mike Oakes04/2011
93332^190704-159557408Lelio R Paula05/2011
933411^55121-174057403Enzo Doria11/2012
93352^190644-18557390Lelio R Paula04/2011
933641182!3-3^4118257389Robert Price08/2015
93372^190629-11225557386Enzo Doria06/2014
9338(2*10^57384-71)/357384Robert Price01/2017
93402*6^73735+5^7373557378Mike Oakes11/2009
93392^190605+5957378Lelio R Paula04/2011
93416^73727-757371Lelio R Paula10/2012
93422^190561-11222557365Enzo Doria06/2014
934310^57358+17089957359Patrick De Geest06/2016
934410^57358-800157358Robert Price03/2016
934518^45687-1157350Lelio R Paula02/2013
934611^55069-21057349Enzo Doria07/2012
934711^55068-1257348Lelio R Paula02/2013
934819^44839+5457339Lelio R Paula02/2013
9349(7*2^190468-1)/851157334Lelio R Paula01/2014
9350(23*10^57333-59)/957334Robert Price03/2017
93512^190455-1155*19045557333Henri Lifchitz02/2005
935214376^9721+9721^1437657328Hans Havermann04/2019
935365^31620+2857325Lelio R Paula01/2016
93542^190403+1609557318Lelio R Paula05/2011
9355(19*10^57316+119)/357317Robert Price02/2017
9358(21*2^190393+1)/21157314Lelio R Paula07/2012
93572^190392-11202557314Enzo Doria05/2014
935613173^13912-13912^1317357314Norbert Schneider08/2018
935914092^11633+11633^1409257294Hans Havermann04/2019
936016460^3021+3021^1646057284Hans Havermann04/2019
9361(24737*2^190234+1)/957270Lelio R Paula05/2014
9362(7*2^190230+1)/2357265Lelio R Paula07/2012
9363(10223*2^190197+1)/321157256Lelio R Paula05/2014
936416726^2645+2645^1672657244Hans Havermann04/2019
936518^45590-9757228Lelio R Paula02/2013
9366(3*2^190105-1)/1920557224Lelio R Paula01/2014
9367(16*10^57219-31)/357220Robert Price03/2016
9368(2^190074+47)/5157217Lelio R Paula02/2012
936914899^6912+6912^1489957207Hans Havermann04/2019
93703^119894-14057204Lelio R Paula10/2012
9372(37^36473-1)/3657196Robert Price03/2012
93712^190000-216357196Yves Minet08/2013
93732^189987-279810757192Enzo Doria04/2016
93742^189935-11211757177Enzo Doria05/2014
93752^189909-11223157169Enzo Doria06/2014
9376132049#+14905357161Makoto Morimoto12/2015
937741032!3-2757158Robert Price09/2014
937819^44694+2257153Lelio R Paula02/2013
937916046^3645+3645^1604657151Hans Havermann04/2019
938012^52956-1757150Lelio R Paula02/2013
93812^189823-96757143Yves Minet01/2012
9382(25*10^57138-61)/957139Robert Price02/2015
93835^81743-4^(81743+1)57136Robert Price04/2016
938414476^8843+8843^1447657131Hans Havermann04/2019
938515327^5338+5338^1532757130Hans Havermann04/2019
93867^67593-5457123Lelio R Paula10/2012
93877*3^119712+257118Lelio R Paula03/2014
93885^81700+1657106Lelio R Paula10/2012
93892^189700+7656157106Enzo Doria05/2016
93912^189671+13157097Lelio R Paula04/2011
93904*6^73374+557097Lelio R Paula09/2014
9392(67607*2^189651+1)/4372757091Lelio R Paula05/2014
9393(29*2^189619-1)/39357080Lelio R Paula01/2014
93943^119587+8057058Lelio R Paula10/2012
93952^189502-11345357046Enzo Doria07/2014
93962^189455+15357032Lelio R Paula04/2011
939724^41317-41317^2457027Norbert Schneider07/2016
93982^189414-1757020Lelio R Paula03/2011
939924^41311+2357018Norbert Schneider12/2013
9400norm(Mod(x,x^4+x^3-x+1)^207341-1)/256998Paul Vanderveen05/2018
940114276^9819+9819^1427656991Hans Havermann04/2019
9402(4*10^56989-31)/956989Erik Branger05/2011
940311^54712-162056977Enzo Doria11/2012
94048102^14577-14577^810256976Norbert Schneider01/2019
94052^189237-11223156967Enzo Doria06/2014
940617^46285-4856952Lelio R Paula02/2013
94072^189188+7524156952Enzo Doria04/2016
94082^189181+9439556950Henri Lifchitz01/2005
94097001^14808-10856940Enzo Doria07/2012
94102^189147-11263956939Enzo Doria06/2014
9411(19*10^56933-43)/356934Robert Price10/2017
94122^189110-356928M. Frind & P. Underwood11/2002
94132^189069+1290956916Lelio R Paula04/2011
9414(13*10^56909+191)/356910Robert Price08/2017
9415(35*10^56898-17)/956899Serge Batalov02/2009
94162^189011-595556898Lelio R Paula04/2011
94176^73119-556898Lelio R Paula10/2012
941813^51076-9056896Lelio R Paula02/2013
94192^188997+5689756894Yves Minet02/2010
94205^81388-1376656888Enzo Doria02/2013
9421(104^28201+1)/10556881Richard Fischer04/2018
9422(156^25933+1)/15756873Eric Chen12/2017
942320^43713-640356872Enzo Doria03/2013
9424(71*10^56858-287)/956859Robert Price05/2017
94252^188857-25423356852Gary Barnes09/2009
942715^48338-8856850Lelio R Paula02/2013
942610^56849+13643756850Patrick De Geest07/2017
942810^56849-70156849Robert Price06/2017
9429(2^188788+78557)/356831Lelio R Paula05/2012
94302^188771+1609556826Lelio R Paula04/2011
94317*2^188742-956818Lelio R Paula03/2014
943212^52646-6556815Lelio R Paula02/2013
94335003^15358-15856813Enzo Doria07/2012
94342^188713+57729457556809Lelio R Paula03/2013
943510060^14193-14193^1006056809Norbert Schneider02/2019
94362^188693-11209956803Enzo Doria05/2014
9437(7^67211+4^67211)/1156799Robert Price10/2012
94382^188678-9439556798Lelio R Paula09/2011
943920^43651-850356792Enzo Doria03/2013
94412^188657-237156792Yves Minet10/2013
9440152^26029-151^2602956792Eric Chen04/2018
9442(14^49549+5^49549)/1956789Robert Price05/2013
9443(45^34351-1)/4456788Robert Price05/2014
94447*10^56785-2356786Robert Price04/2016
9445(10^56781-31)/356781Serge Batalov12/2014
94467*10^56779+356780Erik Branger11/2009
9447((10^14197+1)*((10^28394+10^14197)*(10^14197-10^7099+3)-10^7099+2)-1)/3541/340728156778Makoto Kamada03/2019
944812858^13817-13817^1285856777Norbert Schneider11/2018
944910^56765+25917956766Patrick De Geest09/2013
945010^56765-24949756765Patrick De Geest09/2013
9451t(188706)56764Robert Price04/2015
94522^188551-90432756760Paul Bourdelais11/2012
9453(64*10^56756+17)/956757Robert Price09/2015
9454131101#+14629156757Makoto Morimoto02/2016
94552^188539-11251956756Enzo Doria06/2014
94566^72927+10156749Lelio R Paula10/2012
945720^43617-160356748Enzo Doria03/2013
9458(3^118892-8)/9135892956718Lelio R Paula03/2012
945913339^13748-13748^1333956713Norbert Schneider09/2018
9460(509203*2^188338-1)/356701Lelio R Paula03/2015
946120^43567-562356682Enzo Doria03/2013
94622^188234-11318356665Enzo Doria07/2014
9463(139^26437+1)/14056653Richard Fischer03/2018
9464(7*2^188215-1)/149731512556651Lelio R Paula01/2014
9465(1017*2^188171-1)/3556647Lelio R Paula03/2015
9466(34*10^56647-7)/9/37/26356644Makoto Morimoto04/2016
9467(2^188176-1017)/45381454356638Lelio R Paula02/2012
946833*10^56634+756636Robert Price07/2016
9469(F(31)^9241-F(30)^9241)/F(29)56634Wayne Halsdorf08/2010
947014^49413+3356634Lelio R Paula02/2013
947114240^9483+9483^1424056632Hans Havermann04/2019
947215991^3478+3478^1599156630Hans Havermann04/2019
94733^118680+11056625Lelio R Paula10/2012
9474(13*10^56624+161)/356625Robert Price04/2017
9475(3^118676-2)/751665326356613Lelio R Paula03/2012
9476(13*2^188062+1)/1756613Lelio R Paula07/2012
94772^188056-131356611Yves Minet08/2012
947820^43510-558356608Enzo Doria03/2013
94792^188032+1228556604Lelio R Paula03/2011
9480(19*10^56597-43)/356598Robert Price10/2017
9481(265*10^56588+17)/356590Robert Price05/2016
94822^187959+577556582Lelio R Paula03/2011
9483(5*2^187959+1)/5356581Lelio R Paula07/2012
94843*10^56575-1356576Robert Price11/2017
9485(11*2^187889-1)/35156559Lelio R Paula01/2014
9486(100049^11311+1)/10005056553Faysal YAtim09/2007
9487(19*10^56544-1)/956545Serge Batalov03/2009
948820^43447-892356526Enzo Doria03/2013
948910423^14066-14066^1042356518Norbert Schneider11/2018
94902^187743-11217756517Enzo Doria06/2014
9491(F(5879)^47-F(5878)^47)/F(5877)56502Wayne Halsdorf08/2010
94925^80831-2256499Lelio R Paula10/2012
94935^80828-1316656497Enzo Doria02/2013
94947*2^187590-556472Lelio R Paula03/2014
949516361^2826+2826^1636156465Hans Havermann04/2019
94962^187555+7547356460Enzo Doria04/2016
94972^187541-28356456Yves Minet01/2012
9499(55*10^56453-1)/956454Serge Batalov03/2009
949812933^13730-13730^1293356454Norbert Schneider09/2018
95002^187506-145156445Yves Minet08/2012


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: June, 18 2019 07:14 (Time in France)

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