PRP Records

Probable Primes Top 10000

(172142 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 ?
7501(14016^14016+14017^14017)/(23*7103*19913)58115David Broadhurst09/2009
750211^55795-4258105Lelio R Paula03/2013
75033^121779-1658104Lelio R Paula10/2012
75042^192986+19558095Lelio R Paula04/2011
75057^68740+2*3^6874058093Mike Oakes07/2010
750612^53821+1158083Lelio R Paula02/2013
7507119^27979-11858072Norbert Schneider10/2013
7508(10223*2^192828+1)/24358049Lelio R Paula05/2014
75092^192808-112758041Yves Minet05/2013
7510(27*2^192803+1)/982758037Lelio R Paula07/2012
7511(2^192781+lucasV(1,2,192781)+1)/458033Mike Oakes11/2016
75122^192678+7294358002Enzo Doria04/2016
75132^192657-318957996Yves Minet10/2014
75146^74525-14957992Lelio R Paula10/2012
751542^35723-4157988Norbert Schneider06/2014
7516(29*2^192625-1)/18357986Lelio R Paula01/2014
7517(3^121520-8)/384757977Lelio R Paula03/2012
7518(2^192596-5)/13957976Lelio R Paula02/2012
751910^57975+6783357976Patrick De Geest09/2013
752010^57975-4769357975Patrick De Geest09/2013
7521(F(7707)^37-F(7706)^37)/F(7705)57972Wayne Halsdorf03/2012
7522(3^121492-5)/457966Lelio R Paula03/2012
75232^192549+3557964Lelio R Paula04/2011
752428799!2+257962Robert Price10/2012
7525(7*2^192534-1)/134757957Lelio R Paula01/2014
75267001^15069-10057943Enzo Doria07/2012
7527L(277273)/1109092157940Donovan Johnson11/2005
7528(2^192469-1017)/3557938Lelio R Paula02/2012
75292^192457-1155*19245757936Henri Lifchitz02/2005
75302^192443+138557932Lelio R Paula05/2011
7531132^27317-13157928Norbert Schneider03/2015
753241522!3-5904957912Robert Price12/2015
7533(3*2^192380-1)/16957911Lelio R Paula01/2014
75342^192339-251557900Yves Minet07/2014
75352^192303+769557889Lelio R Paula10/2012
75362^192273-595557880Lelio R Paula05/2011
75372^192257+1609557876Lelio R Paula05/2011
75382^192218-11186157864Enzo Doria05/2014
7539(2^192212+3)/25957860Lelio R Paula02/2012
7540(3^121270+8)/15593975357853Lelio R Paula03/2012
754180^30393-7957841Norbert Schneider03/2015
754220^44455-312357838Enzo Doria03/2013
75442^192122-19557835Lelio R Paula04/2011
7543(29*10^57834+91)/357835Robert Price03/2016
75458*6^74306+557823Lelio R Paula09/2014
7546(39^36341-1)/3857820Robert Price04/2012
75472^192037-11180557809Enzo Doria05/2014
75482^192023-192023^257805Henri Lifchitz05/2005
754921^43717+257804Ray Chandler08/2011
75508*5^82687+757797Lelio R Paula09/2014
75515^82680-2457791Lelio R Paula10/2012
7552(2^191915+47)/9557771Lelio R Paula02/2012
75536^74227-9557760Lelio R Paula10/2012
75542^191861+2983557756Lelio R Paula10/2012
75561908^17605+17605^190857755Serge Batalov05/2014
75555*10^57754+5957755Robert Price09/2016
7557(5*2^191821-1)/892406757738Lelio R Paula01/2014
75583*8^63917+5^63917-3*4^63917+3*2^6391757724Mike Oakes11/2010
755941399!3-656157723Robert Price11/2015
75602^191745+1757721Lelio R Paula04/2011
75612^191730-76157717Yves Minet01/2012
7562(2^191733-3)/225157715Lelio R Paula02/2012
75632^191698-11157707Lelio R Paula04/2011
7564(13*10^57691+23)/957692Robert Price02/2015
756520^44340-542357688Enzo Doria03/2013
7566(27*2^191629+1)/12557686Lelio R Paula07/2012
75674*10^57684+3*7^5768457685Mike Oakes11/2010
75682*3^120898+557684Lelio R Paula04/2014
7569(6883*2^191610-1)/734757681Lelio R Paula04/2015
75706^74117-4957675Lelio R Paula10/2012
75712^191586-11320157674Enzo Doria07/2014
75722^191580+19357672Lelio R Paula04/2011
7573(103*29^39433+10401)/457669Curtis Bright05/2015
75742^191560+25525557666Lelio R Paula05/2011
75752^191515-8557652Lelio R Paula04/2011
75762^191502-112757648Yves Minet05/2013
75772*5^82473-3^8247357647Mike Oakes08/2010
75782^191430+10357627Lelio R Paula04/2011
75793*2^191408+557621Lelio R Paula03/2014
75802^191382-185893157612Enzo Doria04/2016
75816*7^68163+557606Lelio R Paula09/2014
758291^29403-257602Lelio R Paula08/2013
758311^55308-795057598Enzo Doria02/2013
75842^191329+6557596Lelio R Paula04/2011
758511^55302-24057592Enzo Doria07/2012
75862^191299-103146757587Paul Bourdelais11/2012
75872^191295-11199157586Enzo Doria05/2014
75882^191279-129757581Yves Minet08/2012
75893*6^73961+557554Lelio R Paula09/2014
7590(3^120623+5)/5214457548Lelio R Paula04/2012
759142^35445-4157537Norbert Schneider06/2014
75922^191069-72340357518Paul Bourdelais11/2012
75934*10^57506-357507Serge Batalov11/2010
759410^57501+6735957502Patrick De Geest06/2016
759510^57501-100000000157501Robert Price05/2016
759610^57501-24986157501Patrick De Geest06/2016
7597(9^60251+4^60251)/1357493Robert Price02/2013
759820^44184-600357485Enzo Doria03/2013
75992^190948+1270557482Lelio R Paula10/2012
76002^190945+2957481Henri Lifchitz06/2005
76012^190922-40157474Yves Minet01/2012
760215^48860+4657464Lelio R Paula02/2013
76033^120434+2057462Lelio R Paula10/2012
76047^67964-3857437Lelio R Paula10/2012
76052^190799-11306557437Enzo Doria07/2014
76069*5^82159+257428Lelio R Paula09/2014
7607(F(22898)^13-F(22897)^13)/F(22896)57422Wayne Halsdorf03/2012
7608lucasU(432,25,21787)-5*lucasU(432,25,21786)57416Mike Oakes05/2009
7609(103*10^57414-1)/357416Serge Batalov12/2014
76102*10^57410+9^5741057411Mike Oakes04/2011
76112^190704-159557408Lelio R Paula05/2011
761211^55121-174057403Enzo Doria11/2012
76132^190644-18557390Lelio R Paula04/2011
761441182!3-3^4118257389Robert Price08/2015
76152^190629-11225557386Enzo Doria06/2014
7616(2*10^57384-71)/357384Robert Price01/2017
76182*6^73735+5^7373557378Mike Oakes11/2009
76172^190605+5957378Lelio R Paula04/2011
76196^73727-757371Lelio R Paula10/2012
76202^190561-11222557365Enzo Doria06/2014
762110^57358+17089957359Patrick De Geest06/2016
762210^57358-800157358Robert Price03/2016
762318^45687-1157350Lelio R Paula02/2013
762411^55069-21057349Enzo Doria07/2012
762511^55068-1257348Lelio R Paula02/2013
762619^44839+5457339Lelio R Paula02/2013
7627(7*2^190468-1)/851157334Lelio R Paula01/2014
7628(23*10^57333-59)/957334Robert Price03/2017
76292^190455-1155*19045557333Henri Lifchitz02/2005
763065^31620+2857325Lelio R Paula01/2016
76312^190403+1609557318Lelio R Paula05/2011
7632(19*10^57316+119)/357317Robert Price02/2017
7633(21*2^190393+1)/21157314Lelio R Paula07/2012
76342^190392-11202557314Enzo Doria05/2014
7635(24737*2^190234+1)/957270Lelio R Paula05/2014
7636(7*2^190230+1)/2357265Lelio R Paula07/2012
7637(10223*2^190197+1)/321157256Lelio R Paula05/2014
763818^45590-9757228Lelio R Paula02/2013
7639(3*2^190105-1)/1920557224Lelio R Paula01/2014
7640(16*10^57219-31)/357220Robert Price03/2016
7641(2^190074+47)/5157217Lelio R Paula02/2012
76423^119894-14057204Lelio R Paula10/2012
7644(37^36473-1)/3657196Robert Price03/2012
76432^190000-216357196Yves Minet08/2013
76452^189987-279810757192Enzo Doria04/2016
76462^189935-11211757177Enzo Doria05/2014
76472^189909-11223157169Enzo Doria06/2014
7648132049#+14905357161Makoto Morimoto12/2015
764941032!3-2757158Robert Price09/2014
765019^44694+2257153Lelio R Paula02/2013
765112^52956-1757150Lelio R Paula02/2013
76522^189823-96757143Yves Minet01/2012
7653(25*10^57138-61)/957139Robert Price02/2015
76545^81743-4^(81743+1)57136Robert Price04/2016
76557^67593-5457123Lelio R Paula10/2012
76567*3^119712+257118Lelio R Paula03/2014
76585^81700+1657106Lelio R Paula10/2012
76572^189700+7656157106Enzo Doria05/2016
76602^189671+13157097Lelio R Paula04/2011
76594*6^73374+557097Lelio R Paula09/2014
7661(67607*2^189651+1)/4372757091Lelio R Paula05/2014
7662(29*2^189619-1)/39357080Lelio R Paula01/2014
76633^119587+8057058Lelio R Paula10/2012
76642^189502-11345357046Enzo Doria07/2014
76652^189455+15357032Lelio R Paula04/2011
766624^41317-41317^2457027Norbert Schneider07/2016
76672^189414-1757020Lelio R Paula03/2011
766824^41311+2357018Norbert Schneider12/2013
7669(4*10^56989-31)/956989Erik Branger05/2011
767011^54712-162056977Enzo Doria11/2012
76712^189237-11223156967Enzo Doria06/2014
767217^46285-4856952Lelio R Paula02/2013
76732^189188+7524156952Enzo Doria04/2016
76742^189181+9439556950Henri Lifchitz01/2005
76757001^14808-10856940Enzo Doria07/2012
76762^189147-11263956939Enzo Doria06/2014
76772^189110-356928M. Frind & P. Underwood11/2002
76782^189069+1290956916Lelio R Paula04/2011
7679(35*10^56898-17)/956899Serge Batalov02/2009
76802^189011-595556898Lelio R Paula04/2011
76816^73119-556898Lelio R Paula10/2012
768213^51076-9056896Lelio R Paula02/2013
76832^188997+5689756894Yves Minet02/2010
76845^81388-1376656888Enzo Doria02/2013
768520^43713-640356872Enzo Doria03/2013
76862^188857-25423356852Gary Barnes09/2009
768715^48338-8856850Lelio R Paula02/2013
7688(2^188788+78557)/356831Lelio R Paula05/2012
76892^188771+1609556826Lelio R Paula04/2011
76907*2^188742-956818Lelio R Paula03/2014
769112^52646-6556815Lelio R Paula02/2013
76925003^15358-15856813Enzo Doria07/2012
76932^188713+57729457556809Lelio R Paula03/2013
76942^188693-11209956803Enzo Doria05/2014
7695(7^67211+4^67211)/1156799Robert Price10/2012
76962^188678-9439556798Lelio R Paula09/2011
769720^43651-850356792Enzo Doria03/2013
76982^188657-237156792Yves Minet10/2013
7699(14^49549+5^49549)/1956789Robert Price05/2013
7700(45^34351-1)/4456788Robert Price05/2014
77017*10^56785-2356786Robert Price04/2016
7702(10^56781-31)/356781Serge Batalov12/2014
77037*10^56779+356780Erik Branger11/2009
770410^56765+25917956766Patrick De Geest09/2013
770510^56765-24949756765Patrick De Geest09/2013
7706t(188706)56764Robert Price04/2015
77072^188551-90432756760Paul Bourdelais11/2012
7708(64*10^56756+17)/956757Robert Price09/2015
7709131101#+14629156757Makoto Morimoto02/2016
77102^188539-11251956756Enzo Doria06/2014
77116^72927+10156749Lelio R Paula10/2012
771220^43617-160356748Enzo Doria03/2013
7713(3^118892-8)/9135892956718Lelio R Paula03/2012
7714(509203*2^188338-1)/356701Lelio R Paula03/2015
771520^43567-562356682Enzo Doria03/2013
77162^188234-11318356665Enzo Doria07/2014
7717(7*2^188215-1)/149731512556651Lelio R Paula01/2014
7718(1017*2^188171-1)/3556647Lelio R Paula03/2015
7719(34*10^56647-7)/9/37/26356644Makoto Morimoto04/2016
7720(2^188176-1017)/45381454356638Lelio R Paula02/2012
772133*10^56634+756636Robert Price07/2016
7722(F(31)^9241-F(30)^9241)/F(29)56634Wayne Halsdorf08/2010
772314^49413+3356634Lelio R Paula02/2013
77243^118680+11056625Lelio R Paula10/2012
7725(3^118676-2)/751665326356613Lelio R Paula03/2012
7726(13*2^188062+1)/1756613Lelio R Paula07/2012
77272^188056-131356611Yves Minet08/2012
772820^43510-558356608Enzo Doria03/2013
77292^188032+1228556604Lelio R Paula03/2011
7730(265*10^56588+17)/356590Robert Price05/2016
77312^187959+577556582Lelio R Paula03/2011
7732(5*2^187959+1)/5356581Lelio R Paula07/2012
7733(11*2^187889-1)/35156559Lelio R Paula01/2014
7734(100049^11311+1)/10005056553Faysal YAtim09/2007
7735(19*10^56544-1)/956545Serge Batalov03/2009
773620^43447-892356526Enzo Doria03/2013
77372^187743-11217756517Enzo Doria06/2014
7738(F(5879)^47-F(5878)^47)/F(5877)56502Wayne Halsdorf08/2010
77395^80831-2256499Lelio R Paula10/2012
77405^80828-1316656497Enzo Doria02/2013
77417*2^187590-556472Lelio R Paula03/2014
77422^187555+7547356460Enzo Doria04/2016
77432^187541-28356456Yves Minet01/2012
7744(55*10^56453-1)/956454Serge Batalov03/2009
77452^187506-145156445Yves Minet08/2012
77466^72522+14356434Lelio R Paula10/2012
7747(15185*2^187452-1)/94956430Lelio R Paula03/2015
77482^187390+7956411Lelio R Paula03/2011
77492^187386+1290956409Lelio R Paula03/2011
77502^187382+61356408Jason Earls04/2008


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: March, 18 2017 12:02 (Time in France)

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