PRP Records

Probable Primes Top 10000

(193407 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 ?
82512^191580+19357672Lelio R Paula04/2011
8252(103*29^39433+10401)/457669Curtis Bright05/2015
82532^191560+25525557666Lelio R Paula05/2011
82542^191515-8557652Lelio R Paula04/2011
82552^191502-112757648Yves Minet05/2013
82562*5^82473-3^8247357647Mike Oakes08/2010
8257(13*10^57634-61)/357635Robert Price08/2017
825885^29868-29868^8557628Norbert Schneider11/2017
82592^191430+10357627Lelio R Paula04/2011
82603*2^191408+557621Lelio R Paula03/2014
82612^191382-185893157612Enzo Doria04/2016
82626*7^68163+557606Lelio R Paula09/2014
826391^29403-257602Lelio R Paula08/2013
826411^55308-795057598Enzo Doria02/2013
82652^191329+6557596Lelio R Paula04/2011
826611^55302-24057592Enzo Doria07/2012
82672^191299-103146757587Paul Bourdelais11/2012
82682^191295-11199157586Enzo Doria05/2014
82692^191279-129757581Yves Minet08/2012
82703*6^73961+557554Lelio R Paula09/2014
8271(3^120623+5)/5214457548Lelio R Paula04/2012
8272(17*10^57543-29)/357544Robert Price09/2017
827342^35445-4157537Norbert Schneider06/2014
8274(71^31079-1)/7057534Paul Bourdelais08/2017
82752^191069-72340357518Paul Bourdelais11/2012
82764*10^57506-357507Serge Batalov11/2010
827710^57501+6735957502Patrick De Geest06/2016
827810^57501-100000000157501Robert Price05/2016
827910^57501-24986157501Patrick De Geest06/2016
8280(9^60251+4^60251)/1357493Robert Price02/2013
828120^44184-600357485Enzo Doria03/2013
82822^190948+1270557482Lelio R Paula10/2012
82832^190945+2957481Henri Lifchitz06/2005
82842^190922-40157474Yves Minet01/2012
828515^48860+4657464Lelio R Paula02/2013
82863^120434+2057462Lelio R Paula10/2012
82877^67964-3857437Lelio R Paula10/2012
82882^190799-11306557437Enzo Doria07/2014
82899*5^82159+257428Lelio R Paula09/2014
8290(F(22898)^13-F(22897)^13)/F(22896)57422Wayne Halsdorf03/2012
8293lucasU(432,25,21787)-5*lucasU(432,25,21786)57416Mike Oakes05/2009
8292(103*10^57414-1)/357416Serge Batalov12/2014
8291(1654*30^38869-1)/2957416Karsten Bonath05/2017
82942*10^57410+9^5741057411Mike Oakes04/2011
82952^190704-159557408Lelio R Paula05/2011
829611^55121-174057403Enzo Doria11/2012
82972^190644-18557390Lelio R Paula04/2011
829841182!3-3^4118257389Robert Price08/2015
82992^190629-11225557386Enzo Doria06/2014
8300(2*10^57384-71)/357384Robert Price01/2017
83012*6^73735+5^7373557378Mike Oakes11/2009
83022^190605+5957378Lelio R Paula04/2011
83036^73727-757371Lelio R Paula10/2012
83042^190561-11222557365Enzo Doria06/2014
830510^57358+17089957359Patrick De Geest06/2016
830610^57358-800157358Robert Price03/2016
830718^45687-1157350Lelio R Paula02/2013
830811^55069-21057349Enzo Doria07/2012
830911^55068-1257348Lelio R Paula02/2013
831019^44839+5457339Lelio R Paula02/2013
8312(7*2^190468-1)/851157334Lelio R Paula01/2014
8311(23*10^57333-59)/957334Robert Price03/2017
83132^190455-1155*19045557333Henri Lifchitz02/2005
831465^31620+2857325Lelio R Paula01/2016
83152^190403+1609557318Lelio R Paula05/2011
8316(19*10^57316+119)/357317Robert Price02/2017
8317(21*2^190393+1)/21157314Lelio R Paula07/2012
83182^190392-11202557314Enzo Doria05/2014
8319(24737*2^190234+1)/957270Lelio R Paula05/2014
8320(7*2^190230+1)/2357265Lelio R Paula07/2012
8321(10223*2^190197+1)/321157256Lelio R Paula05/2014
832218^45590-9757228Lelio R Paula02/2013
8323(3*2^190105-1)/1920557224Lelio R Paula01/2014
8324(16*10^57219-31)/357220Robert Price03/2016
8325(2^190074+47)/5157217Lelio R Paula02/2012
83263^119894-14057204Lelio R Paula10/2012
8328(37^36473-1)/3657196Robert Price03/2012
83272^190000-216357196Yves Minet08/2013
83292^189987-279810757192Enzo Doria04/2016
83302^189935-11211757177Enzo Doria05/2014
83312^189909-11223157169Enzo Doria06/2014
8332132049#+14905357161Makoto Morimoto12/2015
833341032!3-2757158Robert Price09/2014
833419^44694+2257153Lelio R Paula02/2013
833512^52956-1757150Lelio R Paula02/2013
83362^189823-96757143Yves Minet01/2012
8337(25*10^57138-61)/957139Robert Price02/2015
83385^81743-4^(81743+1)57136Robert Price04/2016
83397^67593-5457123Lelio R Paula10/2012
83407*3^119712+257118Lelio R Paula03/2014
83415^81700+1657106Lelio R Paula10/2012
83422^189700+7656157106Enzo Doria05/2016
83442^189671+13157097Lelio R Paula04/2011
83434*6^73374+557097Lelio R Paula09/2014
8345(67607*2^189651+1)/4372757091Lelio R Paula05/2014
8346(29*2^189619-1)/39357080Lelio R Paula01/2014
83473^119587+8057058Lelio R Paula10/2012
83482^189502-11345357046Enzo Doria07/2014
83492^189455+15357032Lelio R Paula04/2011
835024^41317-41317^2457027Norbert Schneider07/2016
83512^189414-1757020Lelio R Paula03/2011
835224^41311+2357018Norbert Schneider12/2013
8353(4*10^56989-31)/956989Erik Branger05/2011
835411^54712-162056977Enzo Doria11/2012
83552^189237-11223156967Enzo Doria06/2014
835617^46285-4856952Lelio R Paula02/2013
83572^189188+7524156952Enzo Doria04/2016
83582^189181+9439556950Henri Lifchitz01/2005
83597001^14808-10856940Enzo Doria07/2012
83602^189147-11263956939Enzo Doria06/2014
8361(19*10^56933-43)/356934Robert Price10/2017
83622^189110-356928M. Frind & P. Underwood11/2002
83632^189069+1290956916Lelio R Paula04/2011
8364(13*10^56909+191)/356910Robert Price08/2017
8365(35*10^56898-17)/956899Serge Batalov02/2009
83662^189011-595556898Lelio R Paula04/2011
83676^73119-556898Lelio R Paula10/2012
836813^51076-9056896Lelio R Paula02/2013
83692^188997+5689756894Yves Minet02/2010
83705^81388-1376656888Enzo Doria02/2013
837120^43713-640356872Enzo Doria03/2013
8372(71*10^56858-287)/956859Robert Price05/2017
83732^188857-25423356852Gary Barnes09/2009
837415^48338-8856850Lelio R Paula02/2013
837510^56849+13643756850Patrick De Geest07/2017
837610^56849-70156849Robert Price06/2017
8377(2^188788+78557)/356831Lelio R Paula05/2012
83782^188771+1609556826Lelio R Paula04/2011
83797*2^188742-956818Lelio R Paula03/2014
838012^52646-6556815Lelio R Paula02/2013
83815003^15358-15856813Enzo Doria07/2012
83822^188713+57729457556809Lelio R Paula03/2013
83832^188693-11209956803Enzo Doria05/2014
8384(7^67211+4^67211)/1156799Robert Price10/2012
83852^188678-9439556798Lelio R Paula09/2011
838620^43651-850356792Enzo Doria03/2013
83872^188657-237156792Yves Minet10/2013
8388(14^49549+5^49549)/1956789Robert Price05/2013
8389(45^34351-1)/4456788Robert Price05/2014
83907*10^56785-2356786Robert Price04/2016
8391(10^56781-31)/356781Serge Batalov12/2014
83927*10^56779+356780Erik Branger11/2009
839310^56765+25917956766Patrick De Geest09/2013
839410^56765-24949756765Patrick De Geest09/2013
8395t(188706)56764Robert Price04/2015
83962^188551-90432756760Paul Bourdelais11/2012
8398(64*10^56756+17)/956757Robert Price09/2015
8397131101#+14629156757Makoto Morimoto02/2016
83992^188539-11251956756Enzo Doria06/2014
84006^72927+10156749Lelio R Paula10/2012
840120^43617-160356748Enzo Doria03/2013
8402(3^118892-8)/9135892956718Lelio R Paula03/2012
8403(509203*2^188338-1)/356701Lelio R Paula03/2015
840420^43567-562356682Enzo Doria03/2013
84052^188234-11318356665Enzo Doria07/2014
8406(7*2^188215-1)/149731512556651Lelio R Paula01/2014
8407(1017*2^188171-1)/3556647Lelio R Paula03/2015
8408(34*10^56647-7)/9/37/26356644Makoto Morimoto04/2016
8409(2^188176-1017)/45381454356638Lelio R Paula02/2012
841033*10^56634+756636Robert Price07/2016
8412(F(31)^9241-F(30)^9241)/F(29)56634Wayne Halsdorf08/2010
841114^49413+3356634Lelio R Paula02/2013
84133^118680+11056625Lelio R Paula10/2012
8414(13*10^56624+161)/356625Robert Price04/2017
8415(3^118676-2)/751665326356613Lelio R Paula03/2012
8416(13*2^188062+1)/1756613Lelio R Paula07/2012
84172^188056-131356611Yves Minet08/2012
841820^43510-558356608Enzo Doria03/2013
84192^188032+1228556604Lelio R Paula03/2011
8420(19*10^56597-43)/356598Robert Price10/2017
8421(265*10^56588+17)/356590Robert Price05/2016
84222^187959+577556582Lelio R Paula03/2011
8423(5*2^187959+1)/5356581Lelio R Paula07/2012
84243*10^56575-1356576Robert Price11/2017
8425(11*2^187889-1)/35156559Lelio R Paula01/2014
8426(100049^11311+1)/10005056553Faysal YAtim09/2007
8427(19*10^56544-1)/956545Serge Batalov03/2009
842820^43447-892356526Enzo Doria03/2013
84292^187743-11217756517Enzo Doria06/2014
8430(F(5879)^47-F(5878)^47)/F(5877)56502Wayne Halsdorf08/2010
84315^80831-2256499Lelio R Paula10/2012
84325^80828-1316656497Enzo Doria02/2013
84337*2^187590-556472Lelio R Paula03/2014
84342^187555+7547356460Enzo Doria04/2016
84352^187541-28356456Yves Minet01/2012
8436(55*10^56453-1)/956454Serge Batalov03/2009
84372^187506-145156445Yves Minet08/2012
8438189^24794-256443Lelio R Paula10/2017
84396^72522+14356434Lelio R Paula10/2012
8440(15185*2^187452-1)/94956430Lelio R Paula03/2015
84412^187390+7956411Lelio R Paula03/2011
84422^187386+1290956409Lelio R Paula03/2011
84432^187382+61356408Jason Earls04/2008
8444(34*10^56392-7)/9/37/883/2388756384Makoto Morimoto04/2016
844520^43337-956383Lelio R Paula02/2013
8446(26*10^56371-173)/356372Robert Price10/2017
8447(F(1008)^269-F(1007)^269)/F(1006)56364Wayne Halsdorf08/2010
84492^187230+42756362Henri Lifchitz01/2005
844811^54121-948056362Enzo Doria02/2013
8450(21*2^187202-1)/4356354Lelio R Paula01/2014
84512^187173-9156345Lelio R Paula03/2011
8452(23*2^187174-1)/2071988356340Lelio R Paula01/2014
84532^187125-283356331Yves Minet09/2014
84549*7^66655-456331Lelio R Paula09/2014
845518^44874-9756330Lelio R Paula02/2013
845660*79^29679+1956322Serge Batalov03/2016
84575^80571+5656317Lelio R Paula10/2012
84585^80551-2256303Lelio R Paula10/2012
8459(76*10^56281+41)/956282Robert Price10/2015
8460(88*10^56271-43)/956272Robert Price11/2015
8461(5*10^56256-119)/356257Robert Price04/2016
84621508^17691+17691^150856230Serge Batalov05/2014
84633^117844-5856226Lelio R Paula10/2012
8464(19*10^56224+737)/956225Robert Price10/2017
846595^28427+256221Lelio R Paula05/2013
84662^186713+7681756207Enzo Doria05/2016
846716534^2505+2505^1653456196Hans Havermann06/2016
846814428^7849+7849^1442856195Hans Havermann06/2016
84692*10^56194-5156195Robert Price11/2017
847014898^5909+5909^1489856189Hans Havermann06/2016
847118^44758+9556184Lelio R Paula02/2013
84722^186555-74156159Lelio R Paula05/2011
8473(4*10^56156+173)/356157Robert Price01/2017
8474(3^117708+7)/44789656156Lelio R Paula03/2012
847515711^3752+3752^1571156156Hans Havermann06/2016
8476(23*2^186549-1)/242902556152Lelio R Paula01/2014
8477387^21694+21694^38756138Norbert Schneider08/2014
84782^186422+1723956119Yves Minet01/2010
84792^186418+424242956118Jason Earls10/2008
8480136^26300+13556113Norbert Schneider04/2015
84815*2^186392+956111Lelio R Paula03/2014
848214345^8152+8152^1434556108Hans Havermann07/2016
8483(5*2^186351-1)/3956097Lelio R Paula01/2014
84842^186319-54123756088Paul Bourdelais11/2012
84852*10^56083-4356084Robert Price07/2017
8486(16*10^56082-61)/956083Serge Batalov05/2009
8487(14*10^56080-143)/356081Robert Price01/2017
8488(265*10^56076+17)/356078Robert Price05/2016
84897^66346-5056069Lelio R Paula10/2012
849020^43094-3356067Lelio R Paula02/2013
849120^43090-138356062Enzo Doria03/2013
84923^117482+266056054Lelio R Paula10/2012
8493(22699*2^186193+1)/11156052Lelio R Paula05/2014
8494(68*10^56042+13)/956043Ray Chandler09/2010
84953*6^71992+5^7199256022Mike Oakes03/2010
849613691^12352+12352^1369156020Hans Havermann07/2016
8497(2^186095+7)/7556019Lelio R Paula02/2012
8498247^23412+23412^24756018Norbert Schneider08/2014
84991839^17156+17156^183956008Serge Batalov05/2014
850013736^11949+11949^1373656007Hans Havermann04/2016


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: December, 12 2017 10:35 (Time in France)

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