PRP Records

Probable Primes Top 10000

(271000 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 ?
2001(19*2^473242+1)/11142461Lelio R Paula09/2015
2002(61*10^142446-1)/3142448Robert Price01/2020
2003(14*10^142440+61)/3142441Robert Price12/2018
2004(10^142425+359)/9142425Serge Batalov12/2014
20052^473101+773027142418Enzo Doria05/2016
2006(13*2^472838-1)/3142340Lelio R Paula09/2015
2007(17*2^472789-1)/187347142320Lelio R Paula09/2015
20082^472634-109511142278Enzo Doria04/2014
2009(48^84589+1)/49142213Robert Price01/2014
20107*10^142189+87142190Robert Price07/2019
20112^472258+7142164Lelio R Paula08/2015
2012(23*10^142105+91)/3142106Robert Price08/2019
2013tau(317^10330)142098Nik Lygeros / Olivier Rozier / LR team10/2013
2014(11*2^471913-1)/21142060Lelio R Paula09/2015
2015(16*10^142058+197)/3142059Robert Price04/2019
20162^471792+1880881142024Enzo Doria11/2016
2017(31*2^471580-1)/135141960Lelio R Paula08/2015
2018(4*10^141926-79)/3141927Robert Price02/2018
2019(904*19^110984-1)/3141924Curtis Bright05/2015
2020(14*10^141853+37)/3141854Robert Price12/2018
2021(41*10^141836-59)/9141837Robert Price10/2018
20224*5^202913-9141831Lelio R Paula04/2015
20232*7^167812-3141818Lelio R Paula12/2014
20242^471043+35141799Robert Price11/2015
2025(11*2^470956-1)/7945141770Lelio R Paula08/2015
2026(11*10^141718-131)/3141719Robert Price09/2018
20272^470692+76771141693Enzo Doria05/2016
2028(21*2^470391+1)/533141601Lelio R Paula09/2015
20292^470305-459373141576Enzo Doria05/2015
20302^470183+72623141540Enzo Doria04/2016
20312^470173-16465141537Enzo Doria04/2013
20322^469974-1841141477Enzo Doria05/2014
2033(23*2^469939+1)/25141466Lelio R Paula08/2015
20342*10^141448+63141449Robert Price05/2018
20352^469824+43141432Lelio R Paula09/2017
20362*10^141407-27141408Robert Price05/2018
20372^469630-59711141373Enzo Doria10/2015
2038(25*10^141366-331)/9141367Robert Price08/2018
2039(2^469564-3)/611141351Lelio R Paula08/2015
2040197^61601+2141342Lelio R Paula08/2017
20412^469372-112949141296Enzo Doria07/2014
2043143^(2^16)+106^(2^16)141253Valeryi Kuryshev02/2011
2042143^65536+106^65536141253Serge Batalov03/2018
20442^469198+782569141243Enzo Doria10/2016
20452^469076-2786939141206Enzo Doria11/2015
20462^468804+1874941141125Enzo Doria06/2016
20472^468787+81353141119Enzo Doria08/2016
20482^468595-350407141062Enzo Doria06/2015
20492^468564+87855141052Lelio R Paula01/2016
20502^468551-21987141048Enzo Doria07/2013
20512^468523-7141040Lelio R Paula08/2015
2052(25*10^141019-13)/3141020Robert Price09/2019
20532^468405+87855141004Lelio R Paula01/2016
20542^467978-113051140876Enzo Doria07/2014
20552^467780-344429140816Enzo Doria07/2015
20569*10^140802-89140803Robert Price04/2020
20572^467605-1855603140764Enzo Doria09/2015
20585*10^140744-7140745Robert Price09/2015
2059(5^201359-1)/4140744Paul Bourdelais12/2008
20602^467401-1850023140702Enzo Doria08/2015
2061(266*10^140681-17)/3140683Robert Price07/2020
2062(2^467270+78557)/23247140658Lelio R Paula07/2015
2063(29*2^467205+1)/2780517107140635Lelio R Paula08/2015
20642^467166-1854941140631Enzo Doria09/2015
2065(85*10^140609+473)/9140610Robert Price01/2020
20662^466866-1840571140541Enzo Doria06/2015
20672^466829-459523140530Enzo Doria05/2015
20682^466692-113213140489Enzo Doria07/2014
2069(44*10^140410-503)/9140411Robert Price12/2018
2070153^64265-2140400Lelio R Paula11/2017
2071(112*10^140357-1)/3140359Serge Batalov12/2014
2072(29*10^140337-17)/3140338Robert Price09/2019
20732^466181-112735140335Enzo Doria07/2014
2074(5*10^140281-119)/3140282Robert Price03/2018
2075(27*2^465872+1)/691140241Lelio R Paula08/2015
20762^465803-114817140221Enzo Doria05/2015
2077floor(Pi*10^140344)%10^140165140165Serge Batalov08/2012
20782^465503-112735140131Enzo Doria07/2014
2079(16*10^140091+167)/3140092Robert Price06/2019
20806^179964+179964^6-1140040Robert Price04/2014
2081(89*10^140008-179)/9140009Robert Price12/2019
2082(29*2^465077-1)/9140003Lelio R Paula08/2015
20832^465072-344789140001Enzo Doria07/2015
20845*10^139945+81139946Robert Price03/2019
20852^464864-17139939Lelio R Paula09/2017
20868*10^139920+51139921Robert Price08/2019
2087(85*10^139913-1)/3139915Robert Price02/2020
2088(17^113621+1)/18139804Paul Bourdelais09/2011
20892*10^139800-21139801Robert Price09/2020
2090(13*10^139782+191)/3139783Robert Price11/2018
2091(19*2^464312-1)/3139773Lelio R Paula08/2015
2092(74*10^139723+133)/9139724Robert Price06/2019
20933*10^139722+13139723Robert Price07/2018
209477*10^139692+3139694Robert Price06/2020
2095(31*2^463970+1)/5139670Lelio R Paula08/2015
2096(18203^(2^15)+(18201)^(2^15))/2139597Robert Price05/2018
20972^463633-2788423139568Enzo Doria11/2015
20982^463271-109501139459Enzo Doria04/2014
2099(5*10^139457+79)/3139458Robert Price03/2018
21002^463237-99139449Lelio R Paula09/2017
2101(49*10^139442+383)/9139443Robert Price04/2019
2102(7*10^139417-547)/9139417Robert Price01/2018
2103(10^139398+191)/3139398Robert Price02/2018
21042^463019+79463139383Enzo Doria06/2016
21053^292129-112756139381Enzo Doria07/2014
2106(15*2^462951+1)/527139361Lelio R Paula08/2015
21072^462855-1865707139334Enzo Doria02/2016
2108(86*10^139315+121)/9139316Robert Price08/2019
21092^462786-292043139313Enzo Doria08/2015
2110(26*10^139289+1)/9139290Serge Batalov05/2010
2111(17*10^139239+67)/3139240Robert Price01/2019
21122^462238-935139148Yves Minet02/2014
21132^461228+1870441138844Enzo Doria05/2016
21142^461204-113675138837Enzo Doria08/2014
2115(2^461139-7)/47138815Lelio R Paula08/2015
2116(17*10^138812-521)/9138813Robert Price04/2018
21173*10^138811-11138812Robert Price07/2018
2118(28*10^138768+173)/3138769Robert Price12/2019
2119(17*2^460963+1)/124051613138757Lelio R Paula08/2015
2120(379*10^138737-1)/9138739Robert Price02/2020
2121(43*10^138648+101)/9138649Robert Price11/2018
21222^460567-113541138645Enzo Doria08/2014
21237*10^138604+3138605Robert Price08/2015
21242^460330+69138574Lelio R Paula09/2017
2125(17*10^138569-77)/3138570Robert Price08/2019
21262^460078-69581138498Enzo Doria12/2015
21272^459768+1531138404Lelio R Paula06/2012
2128(266*10^138328-17)/3138330Robert Price07/2020
21292^459343-113611138277Enzo Doria08/2014
2130(28*10^138240+113)/3138241Robert Price03/2020
21312^459199+1874393138233Enzo Doria06/2016
21322^459063-345307138192Enzo Doria06/2015
21332*10^138162-43138163Robert Price04/2018
21342^458927-112747138151Enzo Doria06/2014
21352^458927-69217138151Enzo Doria11/2015
2136555555*2^458524+1513138036Darren Bedwell08/2009
21372^458465+2^32+1138012T. D. Noe06/2007
21382^458321-113053137969Enzo Doria07/2014
21392^458298+79459137962Enzo Doria06/2016
21402^458248-21815137947Enzo Doria07/2013
21412^458194+1876549137931Enzo Doria07/2016
2142(318259#+325270)/(2^2*5*11*2957)137907Makoto Morimoto10/2017
2143(318259#+2625)/(3^2*5*7^5*22965193)137899Makoto Morimoto06/2019
21442^457937+57137853Lelio R Paula09/2017
2145(8*10^137845+13)/3137846Robert Price06/2018
21462^457822+105137819Donovan Johnson06/2006
21472^457754-113711137798Enzo Doria09/2014
214811^132315-360137792Enzo Doria09/2012
21492^457347-37137676Lelio R Paula09/2017
21502^457322-2786393137668Enzo Doria10/2015
2151gcd(Phi(699340,10),(10^34967+1)^3*(10^34967+1+10^17484)-(10^69934+10^34967)*(10^17484-1)+10^104901)137664Serge Batalov04/2015
21522^457240-59939137643Enzo Doria10/2015
2153(856*10^137633-1)/9137635Robert Price03/2020
21542^457120-21575137607Enzo Doria07/2013
2155(11*2^456978+1)/15137564Lelio R Paula07/2015
2156(7*25^98399+10613)/12137556Curtis Bright05/2015
21572^456796-113513137510Enzo Doria08/2014
2158(7*2^456655+1)/39137467Lelio R Paula07/2015
21592^456503-114361137422Enzo Doria01/2015
2160(11*2^456387+1)/19137386Lelio R Paula07/2015
2161(71*10^137250+1)/9137251Serge Batalov05/2010
21622^455922+76249137247Enzo Doria05/2016
216314^119741-119741^14137239Serge Batalov04/2016
2164(19*2^455760+1)/3455137196Lelio R Paula07/2015
2166124^(2^16)+57^(2^16)137195Valeryi Kuryshev02/2011
2165124^65536+57^65536137195Serge Batalov03/2018
21672^455689+72677137177Enzo Doria04/2016
2168(17948!)^2+Prime(17948)137118Robert Price08/2014
2169(37^87421-1)/36137093Robert Price03/2012
21702^455323-57137066Lelio R Paula09/2017
2171(73*17^111333-9)/16136991Curtis Bright05/2015
21722^455025-112723136977Enzo Doria06/2014
217366*10^136894+7136896Robert Price07/2020
21742^454675-1777136871Yves Minet10/2011
21753*10^136829+29136830Robert Price05/2018
21764*10^136813-57136814Robert Price10/2018
2177(6092*28^94536-143)/9136812Curtis Bright05/2015
21782^454348-53136773Lelio R Paula09/2017
217931^91680-2136729Lelio R Paula05/2017
21802^454199-113697136728Enzo Doria09/2014
21817*10^136716+69136717Robert Price07/2019
21826*10^136692+53136693Robert Price05/2020
2183(13*10^136687+47)/3136688Robert Price10/2018
21842^453935-2791357136649Enzo Doria01/2016
21852^453906-69131136640Enzo Doria11/2015
21862^453791+1873913136605Enzo Doria06/2016
2187(21*2^453740-1)/2735136588Lelio R Paula07/2015
2188580^49413+49413^580136550Norbert Schneider02/2019
21892^453503-2788297136519Enzo Doria11/2015
21902^453267-113827136447Enzo Doria09/2014
21912^453102+1877629136398Enzo Doria08/2016
2192(62*10^136384-791)/9136385Robert Price06/2019
2193(25*10^136303+161)/3136304Robert Price09/2019
2194(182*10^136291+1)/3136293Robert Price02/2020
219523*10^136225-7136227Robert Price02/2020
2196L(651821)136223Henri Lifchitz09/2008
21972^452460+77701136205Enzo Doria05/2016
21982^452440-114755136199Enzo Doria04/2015
2199(47*10^136141+493)/9136142Robert Price03/2019
22002*10^136057-43136058Robert Price04/2018
2201(2^451956-5)/181136051Lelio R Paula07/2015
22022^451947-22165136050Enzo Doria07/2013
22032^451787-21805136002Enzo Doria07/2013
22042^451734-112817135986Enzo Doria06/2014
2205(11*2^451714+1)/75135979Lelio R Paula07/2015
22062^451705-21879135977Enzo Doria07/2013
22072^451560-112349135934Enzo Doria06/2014
22082^451530+45135925Lelio R Paula08/2017
2209(25*10^135906-73)/3135907Robert Price09/2019
22102^451450-21743135900Enzo Doria07/2013
22112^450805+65135706Lelio R Paula08/2017
22122*10^135663+69135664Robert Price06/2020
2213(13725^32768+1)/131074135573Lelio R Paula03/2012
2214(313007#+121876)/(2*30469*424867)135559Makoto Morimoto08/2020
2215(5^193939+1)/6135557Paul Bourdelais12/2008
22162^449944-113247135447Enzo Doria07/2014
22172^449770-113247135395Enzo Doria07/2014
22182^449637-21471135355Enzo Doria07/2013
22192^449571-75135335Lelio R Paula08/2017
2220(14*10^135301-53)/3135302Robert Price12/2018
2221(3*2^449494+1)/61340334013135301Lelio R Paula07/2015
2222(13*10^135279+437)/9135280Robert Price04/2018
22232^449330-35135262Lelio R Paula08/2017
2224(19*2^449325+1)/9135261Lelio R Paula07/2015
2225(13*10^135184-43)/3135185Robert Price11/2018
22262^449049-115309135178Enzo Doria07/2015
2227(10^135174+191)/3135174Robert Price02/2018
22282^449030-15135172Lelio R Paula08/2017
2229(27*2^448936-1)/11135144Lelio R Paula07/2015
22302^448762-351401135091Enzo Doria07/2015
22312*10^135083-43135084Robert Price04/2018
2232k(198476)135054Robert Price07/2020
22335*10^135019+77135020Robert Price12/2018
2234(10^135011+719)/9135011Serge Batalov12/2014
22352^448386-2786261134978Enzo Doria03/2016
2236(73*10^134939+143)/9134940Robert Price07/2019
22372^448113-113949134896Enzo Doria11/2014
22382^447888-2786639134828Enzo Doria03/2016
22392^447870-396765134823Enzo Doria07/2013
22402^447766-21791134791Enzo Doria07/2013
2241(19*10^134786-49)/3134787Robert Price05/2019
2242Phi(202173,10)/10064306514895399941409134758Makoto Kamada05/2019
2243(23*2^447647+1)/155134755Lelio R Paula07/2015
22442^447552-1019134727Yves Minet02/2014
2245(2*10^134720-41)/3134720Robert Price02/2018
22462^447437-113569134692Enzo Doria08/2014
22472^447426-65134689Lelio R Paula08/2017
22482^447357-2797573134668Enzo Doria04/2016
22492^447278+93134645Lelio R Paula08/2017
22502^447094-113193134589Enzo Doria07/2014


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: September, 29 2020 00:24 (Time in France)

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