PRP Records

Probable Primes Top 10000

(290751 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) !!!


Submit your PRPs


See the Top discoverers
See the Latest PRPs
Search by form



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 ?
95018^97731-7^(97731-1)88260Robert Price04/2016
95025*10^88254+5988255Robert Price09/2016
95034*3^184968-788253Lelio R Paula08/2014
950434*10^88251-988253Robert Price06/2020
95057^104426+8888251Lelio R Paula10/2015
95062^293142+9988245Lelio R Paula10/2012
950711^84736-213088244Enzo Doria12/2012
950823884^4945+4945^2388488232Hans Havermann08/2020
950922080^9907+9907^2208088231Hans Havermann08/2020
9510(10^110315+1)/(10^22063+1)/582481268216764857846028164188225Makoto Kamada04/2019
95112^293068-8988223Lelio R Paula10/2012
95122126^26511+26511^212688218Norbert Schneider02/2020
95132^293014-10965588207Enzo Doria04/2014
95148*7^104371-388205Lelio R Paula10/2014
95152^292995-214588201Lelio R Paula10/2013
951628534^1233+1233^2853488198Hans Havermann08/2020
95175*10^88182+7788183Robert Price06/2016
95192^292929+4387788181Donovan Johnson04/2005
95186^113321+13188181Lelio R Paula12/2015
9520(2^292919+3366)/288178Stefano Morozzi01/2020
95212^292904-58394988173Paul Bourdelais04/2013
95222^292894-11185188170Enzo Doria05/2014
95232^292872-279734988164Enzo Doria03/2016
9524(2^292864+1042)/288161Stefano Morozzi01/2020
95252^292860-10968588160Enzo Doria04/2014
95269*6^113288-588157Lelio R Paula10/2014
9527(2^292735+2166)/288122Stefano Morozzi01/2020
9528(2^292735+2346)/288122Stefano Morozzi01/2020
9529(2^292705+1934)/288113Stefano Morozzi01/2020
9530(2*10^88112-23)/388112Robert Price09/2017
953129622^943+943^2962288111Hans Havermann08/2020
9532(73*10^88105+17)/988106Robert Price10/2015
9533(2^292673+3026)/288104Stefano Morozzi01/2020
953411^84588+7888090Lelio R Paula11/2015
9535(265*10^88077+11)/388079Robert Price03/2017
953691^44959-90^4495988077Robert Price07/2015
95376^113177-5^11317788069Jean-Louis Charton01/2009
95381316^28233+28233^131688066Norbert Schneider07/2020
9539(2^292543+2234)/288064Stefano Morozzi01/2020
9540(10^88020+101)/388020Robert Price04/2016
954152^51285-5188006Norbert Schneider09/2018
954221002^15501+15501^2100288006Hans Havermann08/2020
954320466^19951+19951^2046688004Hans Havermann08/2020
9544(2^292324+2346)/287998Stefano Morozzi01/2020
954521634^11683+11683^2163487998Hans Havermann08/2020
9546(6340^23143-1)/633987988Serge Batalov08/2020
954720674^18013+18013^2067487980Hans Havermann08/2020
9548(10^(2*43982+1)-6*10^43982-1)/387965Robert Price02/2016
9549(11*10^87960-41)/387961Robert Price12/2021
9550(424*10^87930-1)/987932Robert Price11/2017
9551(2^292100+3070)/287931Stefano Morozzi01/2020
9552p(18225)#/2+12887929Robert Price04/2017
9553(10607^21841-1)/1060687919Serge Batalov08/2020
9554(2^292047+1550)/287915Stefano Morozzi01/2020
95554*6^112977+787914Lelio R Paula10/2014
9556(2^292016+1062)/287906Stefano Morozzi01/2020
9557(11359^21673-1)/1135887888Serge Batalov08/2020
955814^76677+6987882Lelio R Paula11/2015
9559(22*10^87863-1)/387864Robert Price12/2014
95602^291822-279781187848Enzo Doria04/2016
9561(22*10^87821-43)/387822Robert Price10/2021
9562(2^291730+1614)/287820Stefano Morozzi01/2020
9563(277*10^87817-7)/987819Robert Price02/2022
95642^291716-11138987816Enzo Doria05/2014
9565(782*10^87809-71)/987811Robert Price06/2017
95663^184039+182087809Lelio R Paula12/2015
956712^81356+4187798Lelio R Paula11/2015
956821307^13188+13188^2130787789Hans Havermann08/2020
9569(2527^25801-1)/252687788Serge Batalov08/2020
9570(2^291596+1986)/287779Stefano Morozzi01/2020
95726^112792-1898387770Enzo Doria03/2013
9571(3123^25117-1)/312287770Serge Batalov08/2020
95733*6^112787-587766Lelio R Paula10/2014
95747^103848+8287762Lelio R Paula10/2015
9575(19*2^291534-1)/17869639587754Lelio R Paula02/2014
9576(2^291506+918)/287752Stefano Morozzi01/2020
957724411^3932+3932^2441187749Hans Havermann08/2020
9578(3^183915+5)/12887748Lelio R Paula01/2013
957919^68619+2487747Lelio R Paula12/2015
95812^291480+118587745Lelio R Paula10/2013
95802^291482+186736987745Enzo Doria03/2016
95822^291467-93787741Yves Minet05/2013
9583(25*10^87726+161)/387727Robert Price01/2017
958411^84239-285087726Enzo Doria12/2012
958510^87720+21554187721Patrick De Geest01/2011
958610^87720-387720Markus Tervooren07/2010
9587(2^291383+3078)/287715Stefano Morozzi01/2020
9589(5*10^87712-473)/987712Robert Price12/2017
9588(2^291373+2946)/287712Stefano Morozzi01/2020
959022591^7630+7630^2259187711Hans Havermann08/2020
959122081^9378+9378^2208187709Hans Havermann08/2020
9592(2^291357+5)/684787704Lelio R Paula01/2013
9593(2^291280+462)/287684Stefano Morozzi01/2020
959420749^16816+16816^2074987680Hans Havermann08/2020
959593^44541-287679Lelio R Paula09/2013
95962^291261-10956187679Enzo Doria04/2014
9597(4*10^87669+149)/987669Robert Price03/2017
95982^291217+425787666Lelio R Paula10/2013
959922748^7137+7137^2274887660Hans Havermann08/2020
96002*12^81214-5^8121487645Mike Oakes12/2010
9601(85*10^87637-139)/987638Robert Price08/2021
9602(5005^23689-1)/500487632Serge Batalov08/2020
9603(5*10^87622-473)/987622Robert Price12/2017
960412^81188+8587617Lelio R Paula11/2015
9605(2^291030+3462)/287609Stefano Morozzi01/2020
9606(21*2^290980-1)/587595Lelio R Paula02/2014
9607(2^290980+1150)/287594Stefano Morozzi01/2020
96082^290958+12787588Lelio R Paula09/2012
960978531!4-887580Robert Price11/2019
96102^290923-6787577Lelio R Paula09/2012
96113*10^87573-9787574Robert Price08/2017
9612(13*10^87565+11)/387566Robert Price05/2015
9613(2^290881+1022)/287564Stefano Morozzi01/2020
9614(2^290857-7)/5587555Lelio R Paula01/2013
9615(2^290808+1498)/287542Stefano Morozzi01/2020
96162^290802+8287587541Lelio R Paula10/2013
9617(509203*2^290792-1)/756098787536Lelio R Paula04/2015
96183^183441+23687524Lelio R Paula12/2015
96194*10^87513-6987514Robert Price01/2022
96202^290618-3387485Lelio R Paula09/2012
9621(184*10^87473-1)/387475Robert Price02/2017
96222^290534-11515187460Enzo Doria06/2015
96232^290512-10975787453Enzo Doria04/2014
9624(32*10^87448-41)/987449Robert Price05/2015
9625(2^290493+3074)/287447Stefano Morozzi01/2020
9626(2^290491+9)/317987444Lelio R Paula01/2013
9627(25*2^290489-1)/5180987443Lelio R Paula02/2014
96282^290426+8287587427Lelio R Paula11/2013
96293*2^290415-787425Lelio R Paula08/2014
963110^87408+5787409Robert Price03/2011
96302^290366+7477987409Enzo Doria04/2016
963222284^8365+8365^2228487409Hans Havermann08/2020
963310^87408-12356987408Patrick De Geest07/2013
963421517^11536+11536^2151787404Hans Havermann08/2020
96356*10^87396+7787397Robert Price06/2020
9636(2^290268+3882)/287380Stefano Morozzi01/2020
96372^290265+5890587379Lelio R Paula10/2013
96387^103391+1687376Lelio R Paula10/2015
9639(115*10^87368-7)/987370Robert Price11/2017
9640(92^44491-1)/9187369Paul Bourdelais08/2017
96418*7^103379+387367Lelio R Paula10/2014
9642(2^290226+7)/7187365Lelio R Paula01/2013
9643(29*10^87355-89)/387356Robert Price01/2022
9644(3216^24907-1)/321587354Serge Batalov08/2020
9645(2^290160+2686)/287347Stefano Morozzi01/2020
964613^78407-3087341Lelio R Paula11/2015
96474*10^87337-9987338Robert Price12/2016
96487*10^87319+3987320Robert Price07/2016
96493*5^124921+287317Lelio R Paula10/2014
965078315!4-1687316Robert Price11/2019
96513^182984+8887306Lelio R Paula12/2015
9652(10^87323-1)/(9*33909262597306826117)87303Alfred Reich02/2019
9653(10^87323-1)/30518336337576143505387303Anonymous10/2020
9654(2^290008+958)/287301Stefano Morozzi01/2020
9655(10536^21701-1)/1053587293Serge Batalov08/2020
96564*10^87287-9987288Robert Price12/2016
965811^83813-186087283Enzo Doria12/2012
9657(3068^25033-1)/306787283Serge Batalov08/2020
9659734^30453+30453^73487270Norbert Schneider04/2017
966012^80855+2987258Lelio R Paula11/2015
966122209^8482+8482^2220987249Hans Havermann08/2020
96623*6^112119-587247Lelio R Paula10/2014
966312^80806+7987205Lelio R Paula11/2015
966491382^9+9^9138287201Andrey Kulsha11/2004
9665(21181*2^289657+1)/8187198Lelio R Paula06/2014
96666^112054-4787195Lelio R Paula12/2015
9667(55459*2^289632+1)/5587191Lelio R Paula06/2014
966815^74131-6887185Lelio R Paula11/2015
96692^289583-74187174Lelio R Paula10/2013
96707^103146+1287169Lelio R Paula10/2015
9671(2^289562+2182)/287167Stefano Morozzi01/2020
96725*2^289556-387166Lelio R Paula08/2014
96732^289543-11273587162Enzo Doria06/2014
967410890^21589-21589^1089087156Norbert Schneider01/2022
967520204^20243-20243^2020487155Norbert Schneider04/2020
96768*3^182655-787150Lelio R Paula08/2014
96772*10^87144+8187145Robert Price01/2017
967820541^17468+17468^2054187140Hans Havermann07/2020
96807^103106+2*3^10310687135Mike Oakes08/2010
9679(65*10^87134-29)/987135Robert Price01/2021
96818*3^182614+787130Lelio R Paula08/2014
96823*10^87121-7387122Robert Price02/2021
9683(4982^23563-1)/498187119Serge Batalov08/2020
9684(2^289368-509203)/987108Lelio R Paula01/2013
96853^182566+1487107Robert Price09/2013
96861738^26881+26881^173887096Norbert Schneider04/2020
968724290^3849+3849^2429087089Hans Havermann08/2020
9688(10^87038+7)/43/53/75187032Alfred Reich06/2021
9689(3^182385-5)/287020Lelio R Paula01/2013
969011^83534-886992Lelio R Paula11/2015
96914^144479-1426786986Mike Oakes03/2011
9692(145*10^86982-1)/986984Serge Batalov12/2014
9693(151*10^86963-1)/386965Robert Price04/2017
9694(2^288892+826)/286965Stefano Morozzi01/2020
969515^73940-5886961Lelio R Paula11/2015
9696(11*10^86951-71)/386952Robert Price04/2022
96972^288761-11314386926Enzo Doria07/2014
969824440^3603+3603^2444086925Hans Havermann08/2020
97002^288747+308386922Yves Minet03/2011
9699(2^288749+3102)/286922Stefano Morozzi01/2020
970130^58842+2986917Norbert Schneider03/2017
9702(2^288705+2186)/286909Stefano Morozzi01/2020
9703(10^86906-13)/386906Robert Price02/2017
97042^288692-11002786905Enzo Doria04/2014
9705(2^288682+7)/25989544986894Lelio R Paula01/2013
9706(26*10^86885+79)/386886Robert Price09/2020
9707(2^288636+47)/129386885Lelio R Paula01/2013
97083^182089-3486879Robert Price11/2013
9709(2^288571+1698)/286869Stefano Morozzi01/2020
97102^288543-10980186861Enzo Doria04/2014
971160^48847-5986858Norbert Schneider10/2014
9712(2^288484+3186)/286843Stefano Morozzi01/2020
97132^288470-6487586839Lelio R Paula10/2013
971410^86816+3299786817Patrick De Geest07/2013
971510^86816-9986816Robert Price05/2011
9716(89*10^86802-539)/986803Robert Price11/2017
971720272^19123+19123^2027286796Hans Havermann07/2020
9718(2^288316+1530)/286792Stefano Morozzi01/2020
9719(2^288316+2218)/286792Stefano Morozzi01/2020
972041487!2+25686786Robert Price01/2015
9721(5*2^288301-1)/99986785Lelio R Paula02/2014
9722(2^288278+1750)/286781Stefano Morozzi01/2020
97232^288243+7604386770Enzo Doria04/2016
9724(29*2^288232+1)/1586767Lelio R Paula01/2013
97259*6^111495+586761Lelio R Paula10/2014
9726(5*2^288202+1)/8186757Lelio R Paula01/2013
97279*7^102654-286754Lelio R Paula10/2014
9728(2^288155+1154)/286743Stefano Morozzi01/2020
97292^288122-11284186734Enzo Doria06/2014
97305^124062-6886716Lelio R Paula10/2015
9731(2^288007-3)/12586697Lelio R Paula01/2013
9732379*10^86691+986694Arkadiusz Wesolowski10/2011
97337^102555+4886670Lelio R Paula10/2015
97342^287902-496186668Yves Minet05/2019
973577779!4+286660Robert Price08/2017
9736(2^287842+3250)/286649Stefano Morozzi01/2020
97372^287809-11135586640Enzo Doria05/2014
9738(47*2^287795+1)/786636Lelio R Paula04/2015
97399*7^102504+886627Lelio R Paula10/2014
97403^181551+3286622Robert Price11/2013
97412^287735-52134786617Paul Bourdelais05/2013
974221912^8953+8953^2191286596Hans Havermann08/2020
9743(1017*2^287600-1)/9186578Lelio R Paula04/2015
9744(2^287552+1302)/286562Stefano Morozzi01/2020
97452^287540-11296786559Enzo Doria06/2014
97463^181407+2086554Robert Price10/2013
9747(28*10^86550+101)/386551Robert Price09/2020
9749(13*10^86546+83)/386547Robert Price09/2016
9748(2^287502+2238)/286547Stefano Morozzi01/2020
97502^287482-471586541Yves Minet05/2019


Find by discoverer :


Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: June, 23 2022 21:24 (Time in France)

Go back
Valid XHTML 1.0!    Valid CSS!