PRP Records

Probable Primes Top 10000

(277054 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 ?
42512^348003-20377104760Enzo Doria06/2013
42532^347994-741104757Lelio R Paula12/2016
4252(2^347993+2234)/2104757Stefano Morozzi01/2021
4254(2^347990+790)/2104756Stefano Morozzi09/2020
425525137^14702+14702^25137104756Hans Havermann09/2020
4256(13*2^347972-1)/282309104746Lelio R Paula03/2014
42572^347910-109937104732Enzo Doria04/2014
4258(88*10^104709-637)/9104710Robert Price11/2020
42595^149794+28104702Lelio R Paula11/2016
4260105^51800-2104698Lelio R Paula10/2017
4261(16^86939+3^86939)/19104684Robert Price06/2013
4262(15^89009-1)/14104682Paul Bourdelais03/2010
42632^347731-18609104678Enzo Doria05/2013
42644*6^134519+7104677Lelio R Paula11/2014
426525321^13588+13588^25321104656Hans Havermann09/2020
42662^347612-18545104642Enzo Doria05/2013
42686^134465+95104635Lelio R Paula11/2016
4267(2^347588+3718)/2104635Stefano Morozzi09/2020
4269(166*10^104633-7)/3104635Robert Price11/2020
42702^347517-17301104614Enzo Doria05/2013
4271(2^347493+3186)/2104606Stefano Morozzi09/2020
4272(2^347490+2574)/2104605Stefano Morozzi09/2020
42733^219222-310104596Lelio R Paula11/2016
427425993^10554+10554^25993104581Hans Havermann09/2020
4275(15*2^347399-1)/13104578Lelio R Paula03/2014
42762^347372-17853104570Enzo Doria05/2013
42772^347314+99104552Lelio R Paula09/2011
42782^347300-22233104548Enzo Doria06/2013
42792^347287-19845104544Enzo Doria06/2013
4280(31*2^347254-1)/891104533Lelio R Paula03/2014
42815*F(250091)*(F(250091)-1)+1104532Serge Batalov04/2015
42827*2^347239-3104531Lelio R Paula09/2014
4283(3^219098-8)/514147439969104525Lelio R Paula12/2013
42845*3^219047+8104513Lelio R Paula09/2014
42852^347148-109073104502Enzo Doria04/2014
42862^347129-20145104497Enzo Doria06/2013
42874*10^104461-57104462Robert Price10/2018
4288(2^346989+590)/2104454Stefano Morozzi09/2020
42892^346923-19585104435Enzo Doria05/2013
4290(11*2^346864-1)/175104416Lelio R Paula03/2014
42912^346854+346854^2+1104414Robert Price06/2014
42922^346834+11715104408Lelio R Paula04/2015
429324276^19961+19961^24276104392Hans Havermann09/2020
429479^55009+78104387Norbert Schneider02/2015
42953^218744+58104368Lelio R Paula11/2016
42969*10^104361+89104362Robert Price11/2019
429725048^14665+14665^25048104358Hans Havermann09/2020
42982^346649+65104352Lelio R Paula09/2011
42992^346638-17265104349Enzo Doria05/2013
4300(2^346606+2082)/2104339Stefano Morozzi09/2020
4301(2^346607+2070)/2104339Stefano Morozzi09/2020
4302(2^346582+3202)/2104332Stefano Morozzi09/2020
430326092^9967+9967^26092104331Hans Havermann09/2020
43045*10^104326+77104327Robert Price12/2018
4305(2^346564+2026)/2104326Stefano Morozzi09/2020
43062^346527-111817104316Enzo Doria05/2014
43076^134055+101104316Lelio R Paula11/2016
430892105!4+8104312Robert Price09/2019
43096^134013+163104283Lelio R Paula11/2016
431018^83049-89104250Lelio R Paula01/2017
4311(2^346311+606)/2104250Stefano Morozzi09/2020
43122^346213+484049104221Enzo Doria04/2017
431318^83021-91104214Lelio R Paula01/2017
431510^104212+128779104213Patrick De Geest05/2016
431610^104212+237447104213Patrick De Geest05/2016
431710^104212+242139104213Patrick De Geest05/2016
431810^104212+269199104213Patrick De Geest05/2016
431424254^19803+19803^24254104213Hans Havermann09/2020
4319(10^104212-71)/1104212Serge Batalov12/2014
432023678^23821-23821^23678104202Norbert Schneider01/2020
43212^346078+7695104180Lelio R Paula12/2016
43222^346055-19537104173Enzo Doria05/2013
4323(3*2^346057+1)/77104173Lelio R Paula12/2013
43242^346037-20125104168Enzo Doria06/2013
4325(34*10^104168-7)/9/13/551179104162Makoto Morimoto05/2016
43266^133854-17993104159Enzo Doria03/2013
43272^345990+1874239104154Enzo Doria06/2016
43282^345988-20373104153Enzo Doria06/2013
4329(2^345965+2214)/2104146Stefano Morozzi09/2020
4330(26*10^104132-503)/9104133Robert Price07/2018
43313*5^148968+8104125Lelio R Paula11/2014
4332(7*10^104113+53)/3104114Robert Price05/2018
4333p(21253)#/2+8104113Robert Price01/2017
433433582^1259+1259^33582104106Hans Havermann09/2020
433532958^1441+1441^32958104104Hans Havermann09/2020
433629127^3748+3748^29127104095Hans Havermann09/2020
4337322^41507+41507^322104094Norbert Schneider12/2014
43386^133768-17423104092Enzo Doria03/2013
43392^345786-19557104092Enzo Doria05/2013
4340171^46606-2104072Lelio R Paula10/2017
4341(29*10^104071+91)/3104072Robert Price04/2020
43422^345704-149104068Lelio R Paula09/2011
434325821^10712+10712^25821104056Hans Havermann09/2020
4344(2^345662+2038)/2104055Stefano Morozzi09/2020
43456^133704-17273104042Enzo Doria02/2013
4346(3*2^345590-1)/23104033Lelio R Paula03/2014
4347(19*2^345590+1)/33859104030Lelio R Paula12/2013
43482^345547+11104021Lelio R Paula09/2011
4349(19*10^104014-49)/3104015Robert Price05/2019
4350(2^345519+1794)/2104012Stefano Morozzi01/2021
43512^345504+723104008Lelio R Paula09/2011
43522^345498-20037104006Enzo Doria06/2013
435418^82854-37104005Lelio R Paula01/2017
4353(2^345497+2070)/2104005Stefano Morozzi09/2020
43552^345486-109065104002Enzo Doria04/2014
43562^345487-1851507104002Enzo Doria08/2015
43582^345476+777103999Lelio R Paula09/2011
4357(2^345477+1554)/2103999Stefano Morozzi09/2020
43594*10^103981-83103982Robert Price10/2018
4360(2^345327+3206)/2103954Stefano Morozzi09/2020
4361(5*2^345321-1)/3103953Lelio R Paula03/2014
4362(2^345267-9)/539049127103927Lelio R Paula12/2013
4363(19*10^103907+77)/3103908Robert Price05/2019
4364(78557*2^345163+1)/78589103905Lelio R Paula07/2014
43652^345106-112181103888Enzo Doria06/2014
43662^345079+99103880Lelio R Paula09/2011
4367(2^345034+1198)/2103866Stefano Morozzi09/2020
436811^99736-1500103865Enzo Doria12/2012
4369(2^345010+2082)/2103859Stefano Morozzi09/2020
437023263^23784-23784^23263103857Norbert Schneider01/2020
437123927^21814+21814^23927103813Hans Havermann09/2020
43722^344842-20157103808Enzo Doria06/2013
4373(47*2^344822+1)/1071103801Lelio R Paula05/2015
43742^344802-20765103796Enzo Doria06/2013
43752^344794-3821103794Yves Minet05/2011
43762^344782-109103103790Enzo Doria04/2014
43773^217521-112292103784Enzo Doria06/2014
43782^344759-3505103783Lelio R Paula11/2016
43792^344735-147103776Lelio R Paula09/2011
4380L(496533)-p(496533)103770Robert Price02/2018
43812*10^103749-69103750Robert Price03/2018
4382(55459*2^344617+1)/3103745Lelio R Paula07/2014
43832^344607-108891103738Enzo Doria03/2014
4384(148*10^103718-1)/3103720Robert Price03/2020
43852^344541-19561103718Enzo Doria05/2013
4386(1017*2^344529-1)/569103714Lelio R Paula05/2015
4387(2^344503+1758)/2103706Stefano Morozzi09/2020
4388(4*10^103703-1)/3103704Serge Batalov08/2009
43892^344444-455103688Yves Minet03/2012
4390(13*53^238539*617^9)/10^307661103673Hans Havermann06/2017
4391(2^344367+2738)/2103665Stefano Morozzi01/2021
43932^344317-109933103650Enzo Doria04/2014
439226055^9508+9508^26055103650Hans Havermann09/2020
43942^344309-1852033103648Enzo Doria08/2015
439525729^10672+10672^25729103643Hans Havermann09/2020
4396(2^344289+1166)/2103642Stefano Morozzi09/2020
43973*10^103637+61103638Robert Price09/2020
4398(2^344246+1614)/2103629Stefano Morozzi09/2020
43992^344213-21253103619Enzo Doria06/2013
44002^344196-465103614Lelio R Paula11/2016
44012^344187-20001103611Enzo Doria06/2013
4402(117191#+(355573#)/(117191#))/(200233679)103602Makoto Morimoto10/2017
440320^79621-19^79621103590Jean-Louis Charton03/2011
4404Phi(155391,10)/1243129103586Maksym Voznyy09/2015
44052^344085-20365103580Enzo Doria06/2013
44065^148169+54103566Lelio R Paula11/2016
44072^344017-108795103560Enzo Doria03/2014
4408(2^343974+2670)/2103547Stefano Morozzi09/2020
44092^343971-5077103546Lelio R Paula09/2011
4410(7*10^103531+71)/3103532Robert Price05/2018
44112^343899+141103524Lelio R Paula08/2011
4412(2^343933+1)/(3*98294339989393)103520Gord Palameta08/2018
44136^133029-67103517Lelio R Paula11/2016
4414(17*2^343877+1)/13625103515Lelio R Paula12/2013
441566*10^103507+7103509Robert Price07/2020
441626297^8614+8614^26297103485Hans Havermann09/2020
4417(2^343764+2658)/2103483Stefano Morozzi09/2020
441826499^8036+8036^26499103480Hans Havermann09/2020
4419(136*10^103474-1)/9103476Serge Batalov12/2014
44205^148014-24103458Lelio R Paula11/2016
442128316^4503+4503^28316103453Hans Havermann09/2020
4422(22*10^103450+53)/3103451Robert Price07/2019
44232^343604+9931103436Yves Minet01/2011
44242^343601-21189103435Enzo Doria06/2013
44252^343508-115229103407Enzo Doria06/2015
4426(509203*2^343491-1)/16147103403Lelio R Paula05/2015
44273^216685-113056103386Enzo Doria07/2014
442824829^14580+14580^24829103382Hans Havermann08/2020
442991355!4+1024103381Robert Price09/2019
443044^62903-43^62903103379Jean-Louis Charton08/2012
443111^99262-20103371Lelio R Paula12/2016
4432(509203*2^343357-1)/5103366Lelio R Paula05/2015
4433(2^343363+3570)/2103363Stefano Morozzi09/2020
44342^343356-2791889103361Enzo Doria03/2016
4435(25*10^103360-241)/9103361Robert Price05/2018
4436Phi(104989,10)/2939693103350Maksym Voznyy09/2015
443724826^14511+14511^24826103319Hans Havermann09/2020
44382^343182-171103309Lelio R Paula08/2011
4439(23619^23619+23620^23620)/7187103294David Broadhurst09/2009
44402^343079-1835611103278Enzo Doria05/2015
44412^343063-1147103273Yves Minet06/2013
444224741^14930+14930^24741103271Hans Havermann09/2020
4443(16*10^103255-73)/3103256Robert Price07/2020
44449*6^132689+7103254Lelio R Paula11/2014
44452^342979-18085103247Enzo Doria05/2013
4446(16*10^103244-31)/3103245Robert Price03/2019
44472^342966-16995103244Lelio R Paula11/2016
444823797^21774+21774^23797103230Hans Havermann09/2020
444925388^11637+11637^25388103224Hans Havermann09/2020
4450(2^342876+2086)/2103216Stefano Morozzi09/2020
4451(16*10^103214-31)/3103215Robert Price03/2019
4453(37*10^103211+611)/9103212Robert Price11/2018
4452(238*10^103210-1)/3103212Robert Price04/2020
44545^147650+16103203Lelio R Paula11/2016
4455gcd(Phi(852060,10),(10^42603+1)^3*(10^42603+1-10^21302)+(10^85206+10^42603)*(10^21302+1)+10^127809)103201Serge Batalov04/2015
44562^342817+2707067103199Enzo Doria03/2016
445743^63177-42103198Theodore Burton02/2007
44582^342805-21025103195Enzo Doria06/2013
445924129^18890+18890^24129103182Hans Havermann09/2020
44602^342714+12285103168Lelio R Paula11/2016
446118^82178-4481103156Enzo Doria03/2013
44622^342665-17349103153Enzo Doria05/2013
446330408^2467+2467^30408103150Hans Havermann09/2020
4464(2^342615+3090)/2103138Stefano Morozzi09/2020
44652^342612+175103137Lelio R Paula08/2011
44665*2^342585-3103130Lelio R Paula09/2014
4467(16*10^103127+77)/3103128Robert Price03/2019
44682^342503-19209103104Enzo Doria05/2013
4469(2^342484+2586)/2103098Stefano Morozzi09/2020
44702^342476+51103096Lelio R Paula08/2011
44712^342460-18885103091Enzo Doria05/2013
4472(194*10^103074-17)/3103076Robert Price09/2020
44737^121968+82103075Lelio R Paula10/2016
44742^342392-108863103071Enzo Doria03/2014
4475(2^342389+806)/2103070Stefano Morozzi01/2021
44763^216014+28103065Lelio R Paula11/2016
44772^342353-108879103059Enzo Doria03/2014
447810^103055+276081103056Patrick De Geest12/2016
447910^103055-53103055Lelio R Paula11/2016
4480(58*10^103046+419)/9103047Robert Price05/2019
44817^121933+4103046Lelio R Paula11/2014
4482(2^342235+3618)/2103023Stefano Morozzi09/2020
448319^80560-68103017Lelio R Paula10/2016
44842^342209+76607103016Enzo Doria05/2016
4486328^40945+40945^328103013Norbert Schneider12/2014
448512^95454-91103013Lelio R Paula10/2016
448725833^9716+9716^25833103009Hans Havermann01/2019
448865^56809-64^56809102990Robert Price08/2013
44895^147338-6102985Lelio R Paula11/2014
44902^342084-112739102978Enzo Doria06/2014
44919*6^132330+7102974Lelio R Paula11/2014
44922^342034-16737102963Enzo Doria05/2013
4493(9787*2^342011-1)/25102959Lelio R Paula05/2015
4494(3^215802-5)/124343756102956Lelio R Paula12/2013
44952^341991-17421102950Enzo Doria05/2013
44962^341969-112225102943Enzo Doria06/2014
4497(9787*2^341864-1)/3102915Lelio R Paula05/2015
44982^341859+1869413102910Enzo Doria05/2016
449910^102909+61102910Lelio R Paula11/2016
450010^102909-67049102909Patrick De Geest12/2016


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: January, 25 2021 11:23 (Time in France)

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