PRP Records

Probable Primes Top 10000

(253466 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 ?
975116726^2645+2645^1672657244Hans Havermann04/2019
975218^45590-9757228Lelio R Paula02/2013
9753(3*2^190105-1)/1920557224Lelio R Paula01/2014
9754(16*10^57219-31)/357220Robert Price03/2016
9755(2^190074+47)/5157217Lelio R Paula02/2012
975614899^6912+6912^1489957207Hans Havermann04/2019
97573^119894-14057204Lelio R Paula10/2012
9759(37^36473-1)/3657196Robert Price03/2012
97582^190000-216357196Yves Minet08/2013
97602^189987-279810757192Enzo Doria04/2016
97612^189935-11211757177Enzo Doria05/2014
97622^189909-11223157169Enzo Doria06/2014
9763132049#+14905357161Makoto Morimoto12/2015
976441032!3-2757158Robert Price09/2014
976519^44694+2257153Lelio R Paula02/2013
976616046^3645+3645^1604657151Hans Havermann04/2019
976712^52956-1757150Lelio R Paula02/2013
97682^189823-96757143Yves Minet01/2012
9769(25*10^57138-61)/957139Robert Price02/2015
97705^81743-4^(81743+1)57136Robert Price04/2016
977114476^8843+8843^1447657131Hans Havermann04/2019
977215327^5338+5338^1532757130Hans Havermann04/2019
97737^67593-5457123Lelio R Paula10/2012
97747*3^119712+257118Lelio R Paula03/2014
97755^81700+1657106Lelio R Paula10/2012
97762^189700+7656157106Enzo Doria05/2016
97782^189671+13157097Lelio R Paula04/2011
97774*6^73374+557097Lelio R Paula09/2014
9779(67607*2^189651+1)/4372757091Lelio R Paula05/2014
9780(29*2^189619-1)/39357080Lelio R Paula01/2014
97813^119587+8057058Lelio R Paula10/2012
97822^189502-11345357046Enzo Doria07/2014
97832^189455+15357032Lelio R Paula04/2011
978424^41317-41317^2457027Norbert Schneider07/2016
97852^189414-1757020Lelio R Paula03/2011
978624^41311+2357018Norbert Schneider12/2013
9787norm(Mod(x,x^4+x^3-x+1)^207341-1)/256998Paul Vanderveen05/2018
978814276^9819+9819^1427656991Hans Havermann04/2019
9789(4*10^56989-31)/956989Erik Branger05/2011
979011^54712-162056977Enzo Doria11/2012
97918102^14577-14577^810256976Norbert Schneider01/2019
97922^189237-11223156967Enzo Doria06/2014
979417^46285-4856952Lelio R Paula02/2013
97932^189188+7524156952Enzo Doria04/2016
97952^189181+9439556950Henri Lifchitz01/2005
97967001^14808-10856940Enzo Doria07/2012
97972^189147-11263956939Enzo Doria06/2014
9798(19*10^56933-43)/356934Robert Price10/2017
97992^189110-356928M. Frind & P. Underwood11/2002
98002^189069+1290956916Lelio R Paula04/2011
9801(13*10^56909+191)/356910Robert Price08/2017
9802(35*10^56898-17)/956899Serge Batalov02/2009
98032^189011-595556898Lelio R Paula04/2011
98046^73119-556898Lelio R Paula10/2012
980513^51076-9056896Lelio R Paula02/2013
98062^188997+5689756894Yves Minet02/2010
98075^81388-1376656888Enzo Doria02/2013
9808(104^28201+1)/10556881Richard Fischer04/2018
9809(156^25933+1)/15756873Eric Chen12/2017
981020^43713-640356872Enzo Doria03/2013
9811(71*10^56858-287)/956859Robert Price05/2017
98122^188857-25423356852Gary Barnes09/2009
981415^48338-8856850Lelio R Paula02/2013
981310^56849+13643756850Patrick De Geest07/2017
981510^56849-70156849Robert Price06/2017
9816(2^188788+78557)/356831Lelio R Paula05/2012
98172^188771+1609556826Lelio R Paula04/2011
98187*2^188742-956818Lelio R Paula03/2014
981912^52646-6556815Lelio R Paula02/2013
98205003^15358-15856813Enzo Doria07/2012
98212^188713+57729457556809Lelio R Paula03/2013
982210060^14193-14193^1006056809Norbert Schneider02/2019
98232^188693-11209956803Enzo Doria05/2014
9824(7^67211+4^67211)/1156799Robert Price10/2012
98252^188678-9439556798Lelio R Paula09/2011
982620^43651-850356792Enzo Doria03/2013
98282^188657-237156792Yves Minet10/2013
9827152^26029-151^2602956792Eric Chen04/2018
9829(14^49549+5^49549)/1956789Robert Price05/2013
9830(45^34351-1)/4456788Robert Price05/2014
98317*10^56785-2356786Robert Price04/2016
9832(10^56781-31)/356781Serge Batalov12/2014
98337*10^56779+356780Erik Branger11/2009
9834((10^14197+1)*((10^28394+10^14197)*(10^14197-10^7099+3)-10^7099+2)-1)/3541/340728156778Makoto Kamada03/2019
983512858^13817-13817^1285856777Norbert Schneider11/2018
983610^56765+25917956766Patrick De Geest09/2013
983710^56765-24949756765Patrick De Geest09/2013
9838t(188706)56764Robert Price04/2015
98392^188551-90432756760Paul Bourdelais11/2012
9840(64*10^56756+17)/956757Robert Price09/2015
9841131101#+14629156757Makoto Morimoto02/2016
98422^188539-11251956756Enzo Doria06/2014
98436^72927+10156749Lelio R Paula10/2012
984420^43617-160356748Enzo Doria03/2013
9845(3^118892-8)/9135892956718Lelio R Paula03/2012
984613339^13748-13748^1333956713Norbert Schneider09/2018
98476693^14824-14824^669356712Norbert Schneider06/2019
9848(509203*2^188338-1)/356701Lelio R Paula03/2015
984920^43567-562356682Enzo Doria03/2013
98502^188234-11318356665Enzo Doria07/2014
9851(139^26437+1)/14056653Richard Fischer03/2018
9852(7*2^188215-1)/149731512556651Lelio R Paula01/2014
9853(1017*2^188171-1)/3556647Lelio R Paula03/2015
9854(34*10^56647-7)/9/37/26356644Makoto Morimoto04/2016
9855(2^188176-1017)/45381454356638Lelio R Paula02/2012
985633*10^56634+756636Robert Price07/2016
9858(F(31)^9241-F(30)^9241)/F(29)56634Wayne Halsdorf08/2010
985714^49413+3356634Lelio R Paula02/2013
985914240^9483+9483^1424056632Hans Havermann04/2019
986015991^3478+3478^1599156630Hans Havermann04/2019
98613^118680+11056625Lelio R Paula10/2012
9862(13*10^56624+161)/356625Robert Price04/2017
9863(3^118676-2)/751665326356613Lelio R Paula03/2012
9864(13*2^188062+1)/1756613Lelio R Paula07/2012
98652^188056-131356611Yves Minet08/2012
986620^43510-558356608Enzo Doria03/2013
98672^188032+1228556604Lelio R Paula03/2011
9868(19*10^56597-43)/356598Robert Price10/2017
9869(265*10^56588+17)/356590Robert Price05/2016
98702^187959+577556582Lelio R Paula03/2011
9871(5*2^187959+1)/5356581Lelio R Paula07/2012
98723*10^56575-1356576Robert Price11/2017
9873(11*2^187889-1)/35156559Lelio R Paula01/2014
9874(100049^11311+1)/10005056553Faysal YAtim09/2007
9875(19*10^56544-1)/956545Serge Batalov03/2009
987620^43447-892356526Enzo Doria03/2013
987710423^14066-14066^1042356518Norbert Schneider11/2018
98782^187743-11217756517Enzo Doria06/2014
9879(F(5879)^47-F(5878)^47)/F(5877)56502Wayne Halsdorf08/2010
98805^80831-2256499Lelio R Paula10/2012
98815^80828-1316656497Enzo Doria02/2013
98827*2^187590-556472Lelio R Paula03/2014
988316361^2826+2826^1636156465Hans Havermann04/2019
98842^187555+7547356460Enzo Doria04/2016
98852^187541-28356456Yves Minet01/2012
9886(55*10^56453-1)/956454Serge Batalov03/2009
988712933^13730-13730^1293356454Norbert Schneider09/2018
98882^187506-145156445Yves Minet08/2012
9889189^24794-256443Lelio R Paula10/2017
989013600^13653-13653^1360056436Norbert Schneider08/2018
98916^72522+14356434Lelio R Paula10/2012
9892(15185*2^187452-1)/94956430Lelio R Paula03/2015
989315992^3369+3369^1599256412Hans Havermann03/2019
98942^187390+7956411Lelio R Paula03/2011
98952^187386+1290956409Lelio R Paula03/2011
98962^187382+61356408Jason Earls04/2008
989713931^11188+11188^1393156404Hans Havermann04/2019
9898(34*10^56392-7)/9/37/883/2388756384Makoto Morimoto04/2016
989920^43337-956383Lelio R Paula02/2013
9900(26*10^56371-173)/356372Robert Price10/2017
9901(F(1008)^269-F(1007)^269)/F(1006)56364Wayne Halsdorf08/2010
99022^187230+42756362Henri Lifchitz01/2005
990311^54121-948056362Enzo Doria02/2013
990410758^13979-13979^1075856360Norbert Schneider09/2018
990510635^13996-13996^1063556359Norbert Schneider09/2018
9906(21*2^187202-1)/4356354Lelio R Paula01/2014
99072^187173-9156345Lelio R Paula03/2011
9908(23*2^187174-1)/2071988356340Lelio R Paula01/2014
99092^187125-283356331Yves Minet09/2014
99109*7^66655-456331Lelio R Paula09/2014
991118^44874-9756330Lelio R Paula02/2013
991213304^13659-13659^1330456330Norbert Schneider08/2018
991360*79^29679+1956322Serge Batalov03/2016
99145^80571+5656317Lelio R Paula10/2012
99155^80551-2256303Lelio R Paula10/2012
9916(76*10^56281+41)/956282Robert Price10/2015
9917(88*10^56271-43)/956272Robert Price11/2015
99189191^14198-14198^919156272Norbert Schneider02/2019
9919(5*10^56256-119)/356257Robert Price04/2016
99202^186840-447556245Yves Minet03/2019
99211508^17691+17691^150856230Serge Batalov05/2014
99223^117844-5856226Lelio R Paula10/2012
9923(19*10^56224+737)/956225Robert Price10/2017
992495^28427+256221Lelio R Paula05/2013
99252^186713+7681756207Enzo Doria05/2016
992616534^2505+2505^1653456196Hans Havermann06/2016
992714428^7849+7849^1442856195Hans Havermann06/2016
99282*10^56194-5156195Robert Price11/2017
992914898^5909+5909^1489856189Hans Havermann06/2016
993018^44758+9556184Lelio R Paula02/2013
99317478^14503-14503^747856182Norbert Schneider11/2018
99322^186555-74156159Lelio R Paula05/2011
9933(4*10^56156+173)/356157Robert Price01/2017
9935(3^117708+7)/44789656156Lelio R Paula03/2012
993415711^3752+3752^1571156156Hans Havermann06/2016
9936(23*2^186549-1)/242902556152Lelio R Paula01/2014
9937387^21694+21694^38756138Norbert Schneider08/2014
99386093^14828-14828^609356122Norbert Schneider06/2019
99392^186422+1723956119Yves Minet01/2010
99402^186418+424242956118Jason Earls10/2008
9941136^26300+13556113Norbert Schneider04/2015
99425*2^186392+956111Lelio R Paula03/2014
994314345^8152+8152^1434556108Hans Havermann07/2016
9944(5*2^186351-1)/3956097Lelio R Paula01/2014
99452^186319-54123756088Paul Bourdelais11/2012
99462*10^56083-4356084Robert Price07/2017
9947(16*10^56082-61)/956083Serge Batalov05/2009
9948(14*10^56080-143)/356081Robert Price01/2017
9949(265*10^56076+17)/356078Robert Price05/2016
99507^66346-5056069Lelio R Paula10/2012
995120^43094-3356067Lelio R Paula02/2013
995220^43090-138356062Enzo Doria03/2013
99533^117482+266056054Lelio R Paula10/2012
9954(22699*2^186193+1)/11156052Lelio R Paula05/2014
9955(68*10^56042+13)/956043Ray Chandler09/2010
99563*6^71992+5^7199256022Mike Oakes03/2010
995713691^12352+12352^1369156020Hans Havermann07/2016
9958(2^186095+7)/7556019Lelio R Paula02/2012
9959247^23412+23412^24756018Norbert Schneider08/2014
99601839^17156+17156^183956008Serge Batalov05/2014
996113736^11949+11949^1373656007Hans Havermann04/2016
9962(5*2^186036-1)/1156003Lelio R Paula01/2014
9963(299*10^55998-17)/356000Robert Price01/2017
9964p(12103)#/2-12855994Robert Price05/2017
99652^186003-17433755993Gary Barnes09/2009
9966(2^186010+78557)/12355993Lelio R Paula05/2012
996720^43037-9355993Lelio R Paula02/2013
996816375^2626+2626^1637555991Hans Havermann03/2016
996911083^13842-13842^1108355987Norbert Schneider11/2018
997015631^3816+3816^1563155985Hans Havermann03/2016
997121^42335-255977Lelio R Paula08/2013
9972Phi(64736,139)55959Enzo Doria07/2012
997315215^4762+4762^1521555958Hans Havermann03/2016
997419317^788+788^1931755953Anatoly F. Selevich12/2006
997513582^13165+13165^1358255950Hans Havermann08/2016
9976(78557*2^185842+1)/18955947Lelio R Paula06/2014
997711867^13730-13730^1186755941Norbert Schneider09/2018
997815^47562-8655938Lelio R Paula02/2013
99794*10^55932+9155933Robert Price11/2017
99803^117222+455930Lelio R Paula03/2012
998124^40519-23^4051955925Robert Price07/2012
998213636^12623+12623^1363655924Hans Havermann07/2016
99832^185767-9955922Lelio R Paula03/2011
9984(19*2^185750-1)/1555917Lelio R Paula01/2014
998615^47542-5855914Lelio R Paula02/2013
998552211!4+255914Robert Price08/2017
998720^42973-558355910Enzo Doria03/2013
99884*10^55906+2155907Robert Price08/2016
99892^185713-11155906Lelio R Paula03/2011
999013^50174+8855891Lelio R Paula01/2013
999114569^6846+6846^1456955879Hans Havermann08/2016
9992Pell-LucasQ(145969)/255874Eric W. Weisstein08/2006
99933^117087-8055865Lelio R Paula10/2012
99948384^14237-14237^838455859Norbert Schneider03/2019
9995(7*10^55851-43)/955851Robert Price10/2014
99962^185519-16955847Lelio R Paula03/2011
99977^66074+1055840Lelio R Paula10/2012
9998(19*10^55833-49)/355834Robert Price02/2017
9999(2*10^55834-59)/355834Robert Price05/2017
100002^185463-423755830Yves Minet08/2018


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: August, 20 2019 14:10 (Time in France)

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