PRP Records

Probable Primes Top 10000

(288949 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 ?
85022^292929+4387788181Donovan Johnson04/2005
85016^113321+13188181Lelio R Paula12/2015
8503(2^292919+3366)/288178Stefano Morozzi01/2020
85042^292904-58394988173Paul Bourdelais04/2013
85052^292894-11185188170Enzo Doria05/2014
85062^292872-279734988164Enzo Doria03/2016
8507(2^292864+1042)/288161Stefano Morozzi01/2020
85082^292860-10968588160Enzo Doria04/2014
85099*6^113288-588157Lelio R Paula10/2014
8510(2^292735+2166)/288122Stefano Morozzi01/2020
8511(2^292735+2346)/288122Stefano Morozzi01/2020
8512(2^292705+1934)/288113Stefano Morozzi01/2020
8513(2*10^88112-23)/388112Robert Price09/2017
851429622^943+943^2962288111Hans Havermann08/2020
8515(73*10^88105+17)/988106Robert Price10/2015
8516(2^292673+3026)/288104Stefano Morozzi01/2020
851711^84588+7888090Lelio R Paula11/2015
8518(265*10^88077+11)/388079Robert Price03/2017
851991^44959-90^4495988077Robert Price07/2015
85206^113177-5^11317788069Jean-Louis Charton01/2009
85211316^28233+28233^131688066Norbert Schneider07/2020
8522(2^292543+2234)/288064Stefano Morozzi01/2020
8523(10^88020+101)/388020Robert Price04/2016
852452^51285-5188006Norbert Schneider09/2018
852521002^15501+15501^2100288006Hans Havermann08/2020
852620466^19951+19951^2046688004Hans Havermann08/2020
8527(2^292324+2346)/287998Stefano Morozzi01/2020
852821634^11683+11683^2163487998Hans Havermann08/2020
8529(6340^23143-1)/633987988Serge Batalov08/2020
853020674^18013+18013^2067487980Hans Havermann08/2020
8531(10^(2*43982+1)-6*10^43982-1)/387965Robert Price02/2016
8532(11*10^87960-41)/387961Robert Price12/2021
8533(424*10^87930-1)/987932Robert Price11/2017
8534(2^292100+3070)/287931Stefano Morozzi01/2020
8535p(18225)#/2+12887929Robert Price04/2017
8536(10607^21841-1)/1060687919Serge Batalov08/2020
8537(2^292047+1550)/287915Stefano Morozzi01/2020
85384*6^112977+787914Lelio R Paula10/2014
8539(2^292016+1062)/287906Stefano Morozzi01/2020
8540(11359^21673-1)/1135887888Serge Batalov08/2020
854114^76677+6987882Lelio R Paula11/2015
8542(22*10^87863-1)/387864Robert Price12/2014
85432^291822-279781187848Enzo Doria04/2016
8544(22*10^87821-43)/387822Robert Price10/2021
8545(2^291730+1614)/287820Stefano Morozzi01/2020
85462^291716-11138987816Enzo Doria05/2014
8547(782*10^87809-71)/987811Robert Price06/2017
85483^184039+182087809Lelio R Paula12/2015
854912^81356+4187798Lelio R Paula11/2015
855021307^13188+13188^2130787789Hans Havermann08/2020
8551(2527^25801-1)/252687788Serge Batalov08/2020
8552(2^291596+1986)/287779Stefano Morozzi01/2020
85546^112792-1898387770Enzo Doria03/2013
8553(3123^25117-1)/312287770Serge Batalov08/2020
85553*6^112787-587766Lelio R Paula10/2014
85567^103848+8287762Lelio R Paula10/2015
8557(19*2^291534-1)/17869639587754Lelio R Paula02/2014
8558(2^291506+918)/287752Stefano Morozzi01/2020
855924411^3932+3932^2441187749Hans Havermann08/2020
8560(3^183915+5)/12887748Lelio R Paula01/2013
856119^68619+2487747Lelio R Paula12/2015
85632^291480+118587745Lelio R Paula10/2013
85622^291482+186736987745Enzo Doria03/2016
85642^291467-93787741Yves Minet05/2013
8565(25*10^87726+161)/387727Robert Price01/2017
856611^84239-285087726Enzo Doria12/2012
856710^87720+21554187721Patrick De Geest01/2011
856810^87720-387720Markus Tervooren07/2010
8569(2^291383+3078)/287715Stefano Morozzi01/2020
8571(5*10^87712-473)/987712Robert Price12/2017
8570(2^291373+2946)/287712Stefano Morozzi01/2020
857222591^7630+7630^2259187711Hans Havermann08/2020
857322081^9378+9378^2208187709Hans Havermann08/2020
8574(2^291357+5)/684787704Lelio R Paula01/2013
8575(2^291280+462)/287684Stefano Morozzi01/2020
857620749^16816+16816^2074987680Hans Havermann08/2020
857893^44541-287679Lelio R Paula09/2013
85772^291261-10956187679Enzo Doria04/2014
8579(4*10^87669+149)/987669Robert Price03/2017
85802^291217+425787666Lelio R Paula10/2013
858122748^7137+7137^2274887660Hans Havermann08/2020
85822*12^81214-5^8121487645Mike Oakes12/2010
8583(85*10^87637-139)/987638Robert Price08/2021
8584(5005^23689-1)/500487632Serge Batalov08/2020
8585(5*10^87622-473)/987622Robert Price12/2017
858612^81188+8587617Lelio R Paula11/2015
8587(2^291030+3462)/287609Stefano Morozzi01/2020
8588(21*2^290980-1)/587595Lelio R Paula02/2014
8589(2^290980+1150)/287594Stefano Morozzi01/2020
85902^290958+12787588Lelio R Paula09/2012
859178531!4-887580Robert Price11/2019
85922^290923-6787577Lelio R Paula09/2012
85933*10^87573-9787574Robert Price08/2017
8594(13*10^87565+11)/387566Robert Price05/2015
8595(2^290881+1022)/287564Stefano Morozzi01/2020
8596(2^290857-7)/5587555Lelio R Paula01/2013
8597(2^290808+1498)/287542Stefano Morozzi01/2020
85982^290802+8287587541Lelio R Paula10/2013
8599(509203*2^290792-1)/756098787536Lelio R Paula04/2015
86003^183441+23687524Lelio R Paula12/2015
86012^290618-3387485Lelio R Paula09/2012
8602(184*10^87473-1)/387475Robert Price02/2017
86032^290534-11515187460Enzo Doria06/2015
86042^290512-10975787453Enzo Doria04/2014
8605(32*10^87448-41)/987449Robert Price05/2015
8606(2^290493+3074)/287447Stefano Morozzi01/2020
8607(2^290491+9)/317987444Lelio R Paula01/2013
8608(25*2^290489-1)/5180987443Lelio R Paula02/2014
86092^290426+8287587427Lelio R Paula11/2013
86103*2^290415-787425Lelio R Paula08/2014
861310^87408+5787409Robert Price03/2011
86112^290366+7477987409Enzo Doria04/2016
861222284^8365+8365^2228487409Hans Havermann08/2020
861410^87408-12356987408Patrick De Geest07/2013
861521517^11536+11536^2151787404Hans Havermann08/2020
86166*10^87396+7787397Robert Price06/2020
8617(2^290268+3882)/287380Stefano Morozzi01/2020
86182^290265+5890587379Lelio R Paula10/2013
86197^103391+1687376Lelio R Paula10/2015
8620(115*10^87368-7)/987370Robert Price11/2017
8621(92^44491-1)/9187369Paul Bourdelais08/2017
86228*7^103379+387367Lelio R Paula10/2014
8623(2^290226+7)/7187365Lelio R Paula01/2013
8624(3216^24907-1)/321587354Serge Batalov08/2020
8625(2^290160+2686)/287347Stefano Morozzi01/2020
862613^78407-3087341Lelio R Paula11/2015
86274*10^87337-9987338Robert Price12/2016
86287*10^87319+3987320Robert Price07/2016
86293*5^124921+287317Lelio R Paula10/2014
863078315!4-1687316Robert Price11/2019
86313^182984+8887306Lelio R Paula12/2015
8632(10^87323-1)/(9*33909262597306826117)87303Alfred Reich02/2019
8633(10^87323-1)/30518336337576143505387303Anonymous10/2020
8634(2^290008+958)/287301Stefano Morozzi01/2020
8635(10536^21701-1)/1053587293Serge Batalov08/2020
86364*10^87287-9987288Robert Price12/2016
863811^83813-186087283Enzo Doria12/2012
8637(3068^25033-1)/306787283Serge Batalov08/2020
8639734^30453+30453^73487270Norbert Schneider04/2017
864012^80855+2987258Lelio R Paula11/2015
864122209^8482+8482^2220987249Hans Havermann08/2020
86423*6^112119-587247Lelio R Paula10/2014
864312^80806+7987205Lelio R Paula11/2015
864491382^9+9^9138287201Andrey Kulsha11/2004
8645(21181*2^289657+1)/8187198Lelio R Paula06/2014
86466^112054-4787195Lelio R Paula12/2015
8647(55459*2^289632+1)/5587191Lelio R Paula06/2014
864815^74131-6887185Lelio R Paula11/2015
86492^289583-74187174Lelio R Paula10/2013
86507^103146+1287169Lelio R Paula10/2015
8651(2^289562+2182)/287167Stefano Morozzi01/2020
86525*2^289556-387166Lelio R Paula08/2014
86532^289543-11273587162Enzo Doria06/2014
865420204^20243-20243^2020487155Norbert Schneider04/2020
86558*3^182655-787150Lelio R Paula08/2014
86562*10^87144+8187145Robert Price01/2017
865720541^17468+17468^2054187140Hans Havermann07/2020
86597^103106+2*3^10310687135Mike Oakes08/2010
8658(65*10^87134-29)/987135Robert Price01/2021
86608*3^182614+787130Lelio R Paula08/2014
86613*10^87121-7387122Robert Price02/2021
8662(4982^23563-1)/498187119Serge Batalov08/2020
8663(2^289368-509203)/987108Lelio R Paula01/2013
86643^182566+1487107Robert Price09/2013
86651738^26881+26881^173887096Norbert Schneider04/2020
866624290^3849+3849^2429087089Hans Havermann08/2020
8667(10^87038+7)/43/53/75187032Alfred Reich06/2021
8668(3^182385-5)/287020Lelio R Paula01/2013
866911^83534-886992Lelio R Paula11/2015
86704^144479-1426786986Mike Oakes03/2011
8671(145*10^86982-1)/986984Serge Batalov12/2014
8672(151*10^86963-1)/386965Robert Price04/2017
8673(2^288892+826)/286965Stefano Morozzi01/2020
867415^73940-5886961Lelio R Paula11/2015
86752^288761-11314386926Enzo Doria07/2014
867624440^3603+3603^2444086925Hans Havermann08/2020
86782^288747+308386922Yves Minet03/2011
8677(2^288749+3102)/286922Stefano Morozzi01/2020
867930^58842+2986917Norbert Schneider03/2017
8680(2^288705+2186)/286909Stefano Morozzi01/2020
8681(10^86906-13)/386906Robert Price02/2017
86822^288692-11002786905Enzo Doria04/2014
8683(2^288682+7)/25989544986894Lelio R Paula01/2013
8684(26*10^86885+79)/386886Robert Price09/2020
8685(2^288636+47)/129386885Lelio R Paula01/2013
86863^182089-3486879Robert Price11/2013
8687(2^288571+1698)/286869Stefano Morozzi01/2020
86882^288543-10980186861Enzo Doria04/2014
868960^48847-5986858Norbert Schneider10/2014
8690(2^288484+3186)/286843Stefano Morozzi01/2020
86912^288470-6487586839Lelio R Paula10/2013
869210^86816+3299786817Patrick De Geest07/2013
869310^86816-9986816Robert Price05/2011
8694(89*10^86802-539)/986803Robert Price11/2017
869520272^19123+19123^2027286796Hans Havermann07/2020
8696(2^288316+1530)/286792Stefano Morozzi01/2020
8697(2^288316+2218)/286792Stefano Morozzi01/2020
869841487!2+25686786Robert Price01/2015
8699(5*2^288301-1)/99986785Lelio R Paula02/2014
8700(2^288278+1750)/286781Stefano Morozzi01/2020
87012^288243+7604386770Enzo Doria04/2016
8702(29*2^288232+1)/1586767Lelio R Paula01/2013
87039*6^111495+586761Lelio R Paula10/2014
8704(5*2^288202+1)/8186757Lelio R Paula01/2013
87059*7^102654-286754Lelio R Paula10/2014
8706(2^288155+1154)/286743Stefano Morozzi01/2020
87072^288122-11284186734Enzo Doria06/2014
87085^124062-6886716Lelio R Paula10/2015
8709(2^288007-3)/12586697Lelio R Paula01/2013
8710379*10^86691+986694Arkadiusz Wesolowski10/2011
87117^102555+4886670Lelio R Paula10/2015
87122^287902-496186668Yves Minet05/2019
871377779!4+286660Robert Price08/2017
8714(2^287842+3250)/286649Stefano Morozzi01/2020
87152^287809-11135586640Enzo Doria05/2014
8716(47*2^287795+1)/786636Lelio R Paula04/2015
87179*7^102504+886627Lelio R Paula10/2014
87183^181551+3286622Robert Price11/2013
87192^287735-52134786617Paul Bourdelais05/2013
872021912^8953+8953^2191286596Hans Havermann08/2020
8721(1017*2^287600-1)/9186578Lelio R Paula04/2015
8722(2^287552+1302)/286562Stefano Morozzi01/2020
87232^287540-11296786559Enzo Doria06/2014
87243^181407+2086554Robert Price10/2013
8725(28*10^86550+101)/386551Robert Price09/2020
8727(13*10^86546+83)/386547Robert Price09/2016
8726(2^287502+2238)/286547Stefano Morozzi01/2020
87282^287482-471586541Yves Minet05/2019
87293^181378-2^(181378-1)86540Robert Price01/2016
873024588^3305+3305^2458886530Hans Havermann08/2020
873183^45080-286513Lelio R Paula08/2013
8732(2^287367+2570)/286506Stefano Morozzi01/2020
8734(78557*2^287351+1)/61186504Lelio R Paula06/2014
8733(2^287360+1006)/286504Stefano Morozzi01/2020
873525*29^59147+2093686498Curtis Bright05/2015
87362^287298+187135986486Enzo Doria05/2016
8737118^41740-11786481Norbert Schneider08/2018
87383*10^86478+8986479Robert Price03/2017
87392^287272-7904986478Paul Bourdelais02/2012
8740(2^287259+2846)/286474Stefano Morozzi01/2020
8741906705*2*((10^86453-1)/9)+186459Danilo Nitsche01/2016
8742811824*2*((10^86453-1)/9)+186459Danilo Nitsche01/2016
8743779064*2*((10^86453-1)/9)+186459Danilo Nitsche01/2016
8744768385*2*((10^86453-1)/9)+186459Danilo Nitsche01/2016
8745700891*2*((10^86453-1)/9)+186459Danilo Nitsche01/2016
8746652320*2*((10^86453-1)/9)+186459Danilo Nitsche01/2016
8747377920*2*((10^86453-1)/9)+186458Danilo Nitsche01/2016
8748255060*2*((10^86453-1)/9)+186458Danilo Nitsche01/2016
8749187111*2*((10^86453-1)/9)+186458Danilo Nitsche01/2016
8750(10^86453-1)/986453Lew Baxter10/2000


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: January, 19 2022 17:15 (Time in France)

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