PRP Records

Probable Primes Top 10000

(259919 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 ?
35012^346078+7695104180Lelio R Paula12/2016
35022^346055-19537104173Enzo Doria05/2013
3503(3*2^346057+1)/77104173Lelio R Paula12/2013
35042^346037-20125104168Enzo Doria06/2013
3505(34*10^104168-7)/9/13/551179104162Makoto Morimoto05/2016
35066^133854-17993104159Enzo Doria03/2013
35072^345990+1874239104154Enzo Doria06/2016
35082^345988-20373104153Enzo Doria06/2013
3509(26*10^104132-503)/9104133Robert Price07/2018
35103*5^148968+8104125Lelio R Paula11/2014
3511(7*10^104113+53)/3104114Robert Price05/2018
3512p(21253)#/2+8104113Robert Price01/2017
3513322^41507+41507^322104094Norbert Schneider12/2014
35146^133768-17423104092Enzo Doria03/2013
35152^345786-19557104092Enzo Doria05/2013
3516171^46606-2104072Lelio R Paula10/2017
35172^345704-149104068Lelio R Paula09/2011
35186^133704-17273104042Enzo Doria02/2013
3519(3*2^345590-1)/23104033Lelio R Paula03/2014
3520(19*2^345590+1)/33859104030Lelio R Paula12/2013
35212^345547+11104021Lelio R Paula09/2011
3522(19*10^104014-49)/3104015Robert Price05/2019
35232^345504+723104008Lelio R Paula09/2011
35242^345498-20037104006Enzo Doria06/2013
352518^82854-37104005Lelio R Paula01/2017
35262^345486-109065104002Enzo Doria04/2014
35272^345487-1851507104002Enzo Doria08/2015
35282^345476+777103999Lelio R Paula09/2011
35294*10^103981-83103982Robert Price10/2018
3530(5*2^345321-1)/3103953Lelio R Paula03/2014
3531(2^345267-9)/539049127103927Lelio R Paula12/2013
3532(19*10^103907+77)/3103908Robert Price05/2019
3533(78557*2^345163+1)/78589103905Lelio R Paula07/2014
35342^345106-112181103888Enzo Doria06/2014
35352^345079+99103880Lelio R Paula09/2011
353611^99736-1500103865Enzo Doria12/2012
353723263^23784-23784^23263103857Norbert Schneider01/2020
35382^344842-20157103808Enzo Doria06/2013
3539(47*2^344822+1)/1071103801Lelio R Paula05/2015
35402^344802-20765103796Enzo Doria06/2013
35412^344794-3821103794Yves Minet05/2011
35422^344782-109103103790Enzo Doria04/2014
35433^217521-112292103784Enzo Doria06/2014
35442^344759-3505103783Lelio R Paula11/2016
35452^344735-147103776Lelio R Paula09/2011
3546L(496533)-p(496533)103770Robert Price02/2018
35472*10^103749-69103750Robert Price03/2018
3548(55459*2^344617+1)/3103745Lelio R Paula07/2014
35492^344607-108891103738Enzo Doria03/2014
3550(148*10^103718-1)/3103720Robert Price03/2020
35512^344541-19561103718Enzo Doria05/2013
3552(1017*2^344529-1)/569103714Lelio R Paula05/2015
3553(4*10^103703-1)/3103704Serge Batalov08/2009
35542^344444-455103688Yves Minet03/2012
3555(13*53^238539*617^9)/10^307661103673Hans Havermann06/2017
35562^344317-109933103650Enzo Doria04/2014
35572^344309-1852033103648Enzo Doria08/2015
35582^344213-21253103619Enzo Doria06/2013
35592^344196-465103614Lelio R Paula11/2016
35602^344187-20001103611Enzo Doria06/2013
3561(117191#+(355573#)/(117191#))/(200233679)103602Makoto Morimoto10/2017
356220^79621-19^79621103590Jean-Louis Charton03/2011
3563Phi(155391,10)/1243129103586Maksym Voznyy09/2015
35642^344085-20365103580Enzo Doria06/2013
35655^148169+54103566Lelio R Paula11/2016
35662^344017-108795103560Enzo Doria03/2014
35672^343971-5077103546Lelio R Paula09/2011
3568(7*10^103531+71)/3103532Robert Price05/2018
35692^343899+141103524Lelio R Paula08/2011
3570(2^343933+1)/(3*98294339989393)103520Gord Palameta08/2018
35716^133029-67103517Lelio R Paula11/2016
3572(17*2^343877+1)/13625103515Lelio R Paula12/2013
3573(136*10^103474-1)/9103476Serge Batalov12/2014
35745^148014-24103458Lelio R Paula11/2016
3575(22*10^103450+53)/3103451Robert Price07/2019
35762^343604+9931103436Yves Minet01/2011
35772^343601-21189103435Enzo Doria06/2013
35782^343508-115229103407Enzo Doria06/2015
3579(509203*2^343491-1)/16147103403Lelio R Paula05/2015
35803^216685-113056103386Enzo Doria07/2014
358191355!4+1024103381Robert Price09/2019
358244^62903-43^62903103379Jean-Louis Charton08/2012
358311^99262-20103371Lelio R Paula12/2016
3584(509203*2^343357-1)/5103366Lelio R Paula05/2015
35862^343356-2791889103361Enzo Doria03/2016
3585(25*10^103360-241)/9103361Robert Price05/2018
3587Phi(104989,10)/2939693103350Maksym Voznyy09/2015
35882^343182-171103309Lelio R Paula08/2011
3589(23619^23619+23620^23620)/7187103294David Broadhurst09/2009
35902^343079-1835611103278Enzo Doria05/2015
35912^343063-1147103273Yves Minet06/2013
35929*6^132689+7103254Lelio R Paula11/2014
35932^342979-18085103247Enzo Doria05/2013
3594(16*10^103244-31)/3103245Robert Price03/2019
35952^342966-16995103244Lelio R Paula11/2016
3596(16*10^103214-31)/3103215Robert Price03/2019
3597(37*10^103211+611)/9103212Robert Price11/2018
35985^147650+16103203Lelio R Paula11/2016
3599gcd(Phi(852060,10),(10^42603+1)^3*(10^42603+1-10^21302)+(10^85206+10^42603)*(10^21302+1)+10^127809)103201Serge Batalov04/2015
36002^342817+2707067103199Enzo Doria03/2016
360143^63177-42103198Theodore Burton02/2007
36022^342805-21025103195Enzo Doria06/2013
36032^342714+12285103168Lelio R Paula11/2016
360418^82178-4481103156Enzo Doria03/2013
36052^342665-17349103153Enzo Doria05/2013
36062^342612+175103137Lelio R Paula08/2011
36075*2^342585-3103130Lelio R Paula09/2014
3608(16*10^103127+77)/3103128Robert Price03/2019
36092^342503-19209103104Enzo Doria05/2013
36102^342476+51103096Lelio R Paula08/2011
36112^342460-18885103091Enzo Doria05/2013
36127^121968+82103075Lelio R Paula10/2016
36132^342392-108863103071Enzo Doria03/2014
36143^216014+28103065Lelio R Paula11/2016
36152^342353-108879103059Enzo Doria03/2014
361610^103055+276081103056Patrick De Geest12/2016
361710^103055-53103055Lelio R Paula11/2016
3618(58*10^103046+419)/9103047Robert Price05/2019
36197^121933+4103046Lelio R Paula11/2014
362019^80560-68103017Lelio R Paula10/2016
36212^342209+76607103016Enzo Doria05/2016
3623328^40945+40945^328103013Norbert Schneider12/2014
362212^95454-91103013Lelio R Paula10/2016
362425833^9716+9716^25833103009Hans Havermann01/2019
362565^56809-64^56809102990Robert Price08/2013
36265^147338-6102985Lelio R Paula11/2014
36272^342084-112739102978Enzo Doria06/2014
36289*6^132330+7102974Lelio R Paula11/2014
36292^342034-16737102963Enzo Doria05/2013
3630(9787*2^342011-1)/25102959Lelio R Paula05/2015
3631(3^215802-5)/124343756102956Lelio R Paula12/2013
36322^341991-17421102950Enzo Doria05/2013
36332^341969-112225102943Enzo Doria06/2014
3634(9787*2^341864-1)/3102915Lelio R Paula05/2015
36362^341859+1869413102910Enzo Doria05/2016
363510^102909+61102910Lelio R Paula11/2016
363710^102909-67049102909Patrick De Geest12/2016
363823814^20935+20935^23814102898Hans Havermann02/2019
363928345^4264+4264^28345102888Hans Havermann02/2019
364025665^10204+10204^25665102886Hans Havermann02/2019
364126288^8181+8181^26288102860Hans Havermann02/2019
36422^341659+1836773102850Enzo Doria03/2016
36432^341608-110639102835Enzo Doria05/2014
364410^102824+49102825Lelio R Paula11/2016
364510^102824-168011102824Patrick De Geest12/2016
364611^98708-8102794Lelio R Paula10/2016
36472^341466+4429102792Lelio R Paula09/2011
36482^341460-107102790Lelio R Paula08/2011
3649(2^341388+47)/21014943102761Lelio R Paula12/2013
36502^341355+21102759Lelio R Paula08/2011
36512^341246+40755102726Lelio R Paula11/2016
3652(2^341256-5)/991699102723Lelio R Paula12/2013
36537^121547+78102720Lelio R Paula10/2016
36542^341223-461197102719Enzo Doria06/2015
365527838^4893+4893^27838102711Hans Havermann03/2019
36572^341190-20577102709Enzo Doria06/2013
3656(27*2^341212+1)/84674449102709Lelio R Paula12/2013
36586^131976-65102698Lelio R Paula10/2016
36592^341134+2533102692Henri Lifchitz09/2005
366013^92184-54102688Lelio R Paula10/2016
36612^341116-20873102687Enzo Doria06/2013
36622^341094-19953102680Enzo Doria06/2013
366323761^20950+20950^23761102676Hans Havermann03/2019
36642^341053+129102668Lelio R Paula08/2011
3666(31*2^341006-1)/3102655Lelio R Paula03/2014
36657^121471+94102655Lelio R Paula10/2016
36682^341004-173102653Lelio R Paula08/2011
366720^78901+3102653Lelio R Paula10/2016
36695^146853-52102646Lelio R Paula10/2016
36702^340969-216931102642Enzo Doria05/2014
3671122^49196+121102641Norbert Schneider10/2018
36722^340952+1870021102637Enzo Doria05/2016
36735*2^340940-3102634Lelio R Paula08/2014
3674(6^131891+1)/7102631Paul Bourdelais01/2010
367525876^9239+9239^25876102615Hans Havermann02/2019
3676(4*10^102612+83)/3102613Robert Price02/2018
367775^54717+74102598Norbert Schneider01/2015
3678(17*10^102597+13)/3102598Robert Price01/2019
36792^340806-20393102593Enzo Doria06/2013
3680(2^340790+5)/138267102583Lelio R Paula12/2013
36816^131821+77102577Lelio R Paula10/2016
36822^340688-29102558Henri Lifchitz05/2005
36832^340685-109101102557Enzo Doria04/2014
368465^56567-64102552Norbert Schneider11/2014
368526230^8121+8121^26230102550Hans Havermann03/2019
3686(536*10^102533-23)/9102535Robert Price02/2020
36872^340547-108897102515Enzo Doria03/2014
368825592^10119+10119^25592102500Hans Havermann02/2019
36897^121268+82102484Lelio R Paula10/2016
3690(6883*2^340443-1)/162401102483Lelio R Paula05/2015
36912^340434-5955102481Lelio R Paula11/2016
3692(2^340381+47)/7102465Lelio R Paula12/2013
3693111^50095+110102461Norbert Schneider04/2017
36942^340291-20301102438Enzo Doria06/2013
369512^94915+89102431Lelio R Paula10/2016
369624466^15349+15349^24466102417Hans Havermann03/2019
36972^340208-20373102413Enzo Doria06/2013
36986^131598-17273102404Enzo Doria02/2013
36992^340115-21181102385Enzo Doria06/2013
3700(55459*2^340090+1)/1591102379Lelio R Paula07/2014
370189^52511-88^52511102365Robert Price06/2015
37023^214539-112756102362Enzo Doria07/2014
370323159^23450-23450^23159102353Norbert Schneider12/2019
37042^340000-19877102351Enzo Doria06/2013
37052^339990-114845102348Enzo Doria05/2015
3706(3^214516-2)/51383102346Lelio R Paula12/2013
370720^78661-99102341Lelio R Paula09/2016
37082^339951-19585102336Enzo Doria05/2013
3709(13*2^339943+1)/45102333Lelio R Paula12/2013
37102^339889+29327102317Yves Minet06/2010
3711(167*10^102315-17)/3102317Robert Price03/2020
371226348^7641+7641^26348102314Hans Havermann03/2019
3713Phi(239414,10)/6333218543102303Makoto Kamada08/2019
37142^339834-109493102301Enzo Doria04/2014
3715(16*10^102299-19)/3102300Robert Price02/2019
3716(11^98221-5^98221)/6102286Robert Price01/2013
37173^214365+1820102279Lelio R Paula10/2016
371831978^1579+1579^31978102278Hans Havermann03/2019
3719(11*2^339705-1)/183102261Lelio R Paula03/2014
37202^339694-16995102259Lelio R Paula09/2016
3721(56*10^102255+691)/9102256Robert Price05/2019
3722122^49008+121102249Norbert Schneider10/2018
37247^120985-38102245Lelio R Paula10/2016
372310^102244+122961102245Patrick De Geest12/2016
372510^102244-27102244Lelio R Paula09/2016
37267^120982-62102242Lelio R Paula10/2016
37274*6^131382-5102236Lelio R Paula11/2014
37282^339586-1091102226Yves Minet11/2012
372911^98161-3072000102225Enzo Doria12/2012
37309*7^120961-4102225Lelio R Paula11/2014
37315*3^214250+2102224Serge Batalov10/2010
373212^94713-59102213Lelio R Paula10/2016
373312^94705+89102204Lelio R Paula10/2016
37342^339407-177102172Lelio R Paula08/2011
37354*10^102163-57102164Robert Price10/2018
37362^339355+65102157Lelio R Paula07/2011
3737(28*10^102142-31)/3102143Robert Price12/2019
3738(2^339323+47)/880715102141Lelio R Paula12/2013
37392^339168+21102100Lelio R Paula07/2011
37402^339167-108807102100Enzo Doria03/2014
37412^339156+163102097Lelio R Paula08/2011
3742(25*10^102076-67)/3102077Robert Price06/2019
37432^339081-4543102074Yves Minet03/2019
374424327^15668+15668^24327102053Hans Havermann02/2019
374525080^11711+11711^25080102041Hans Havermann02/2019
3746(2^338982-7)/1754517102038Lelio R Paula12/2013
37472^338891-18885102017Enzo Doria05/2013
37488*10^102000+51102001Robert Price08/2019
37492^338829-113239101998Enzo Doria07/2014
37502^338828-113297101998Enzo Doria07/2014


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: March, 29 2020 17:41 (Time in France)

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