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 ?
5751(13*10^87565+11)/387566Robert Price05/2015
5752(2^290881+1022)/287564Stefano Morozzi01/2020
5753(2^290857-7)/5587555Lelio R Paula01/2013
5754(2^290808+1498)/287542Stefano Morozzi01/2020
57552^290802+8287587541Lelio R Paula10/2013
5756(509203*2^290792-1)/756098787536Lelio R Paula04/2015
57573^183441+23687524Lelio R Paula12/2015
57582^290618-3387485Lelio R Paula09/2012
5759(184*10^87473-1)/387475Robert Price02/2017
57602^290534-11515187460Enzo Doria06/2015
57612^290512-10975787453Enzo Doria04/2014
5762(32*10^87448-41)/987449Robert Price05/2015
5763(2^290493+3074)/287447Stefano Morozzi01/2020
5764(2^290491+9)/317987444Lelio R Paula01/2013
5765(25*2^290489-1)/5180987443Lelio R Paula02/2014
57662^290426+8287587427Lelio R Paula11/2013
57673*2^290415-787425Lelio R Paula08/2014
576910^87408+5787409Robert Price03/2011
57682^290366+7477987409Enzo Doria04/2016
577010^87408-12356987408Patrick De Geest07/2013
5771(2^290268+3882)/287380Stefano Morozzi01/2020
57722^290265+5890587379Lelio R Paula10/2013
57737^103391+1687376Lelio R Paula10/2015
5774(115*10^87368-7)/987370Robert Price11/2017
5775(92^44491-1)/9187369Paul Bourdelais08/2017
57768*7^103379+387367Lelio R Paula10/2014
5777(2^290226+7)/7187365Lelio R Paula01/2013
5778(2^290160+2686)/287347Stefano Morozzi01/2020
577913^78407-3087341Lelio R Paula11/2015
57804*10^87337-9987338Robert Price12/2016
57817*10^87319+3987320Robert Price07/2016
57823*5^124921+287317Lelio R Paula10/2014
578378315!4-1687316Robert Price11/2019
57843^182984+8887306Lelio R Paula12/2015
5785(10^87323-1)/(9*33909262597306826117)87303Alfred Reich02/2019
5786(2^290008+958)/287301Stefano Morozzi01/2020
57874*10^87287-9987288Robert Price12/2016
578811^83813-186087283Enzo Doria12/2012
5789734^30453+30453^73487270Norbert Schneider04/2017
579012^80855+2987258Lelio R Paula11/2015
57913*6^112119-587247Lelio R Paula10/2014
579212^80806+7987205Lelio R Paula11/2015
579391382^9+9^9138287201Andrey Kulsha11/2004
5794(21181*2^289657+1)/8187198Lelio R Paula06/2014
57956^112054-4787195Lelio R Paula12/2015
5796(55459*2^289632+1)/5587191Lelio R Paula06/2014
579715^74131-6887185Lelio R Paula11/2015
57982^289583-74187174Lelio R Paula10/2013
57997^103146+1287169Lelio R Paula10/2015
5800(2^289562+2182)/287167Stefano Morozzi01/2020
58015*2^289556-387166Lelio R Paula08/2014
58022^289543-11273587162Enzo Doria06/2014
58038*3^182655-787150Lelio R Paula08/2014
58042*10^87144+8187145Robert Price01/2017
58057^103106+2*3^10310687135Mike Oakes08/2010
58068*3^182614+787130Lelio R Paula08/2014
5807(2^289368-509203)/987108Lelio R Paula01/2013
58083^182566+1487107Robert Price09/2013
5809(3^182385-5)/287020Lelio R Paula01/2013
581011^83534-886992Lelio R Paula11/2015
58114^144479-1426786986Mike Oakes03/2011
5812(145*10^86982-1)/986984Serge Batalov12/2014
5813(151*10^86963-1)/386965Robert Price04/2017
5814(2^288892+826)/286965Stefano Morozzi01/2020
581515^73940-5886961Lelio R Paula11/2015
58162^288761-11314386926Enzo Doria07/2014
58182^288747+308386922Yves Minet03/2011
5817(2^288749+3102)/286922Stefano Morozzi01/2020
581930^58842+2986917Norbert Schneider03/2017
5820(2^288705+2186)/286909Stefano Morozzi01/2020
5821(10^86906-13)/386906Robert Price02/2017
58222^288692-11002786905Enzo Doria04/2014
5823(2^288682+7)/25989544986894Lelio R Paula01/2013
5824(2^288636+47)/129386885Lelio R Paula01/2013
58253^182089-3486879Robert Price11/2013
5826(2^288571+1698)/286869Stefano Morozzi01/2020
58272^288543-10980186861Enzo Doria04/2014
582860^48847-5986858Norbert Schneider10/2014
5829(2^288484+3186)/286843Stefano Morozzi01/2020
58302^288470-6487586839Lelio R Paula10/2013
583110^86816+3299786817Patrick De Geest07/2013
583210^86816-9986816Robert Price05/2011
5833(89*10^86802-539)/986803Robert Price11/2017
5834(2^288316+1530)/286792Stefano Morozzi01/2020
5835(2^288316+2218)/286792Stefano Morozzi01/2020
583641487!2+25686786Robert Price01/2015
5837(5*2^288301-1)/99986785Lelio R Paula02/2014
5838(2^288278+1750)/286781Stefano Morozzi01/2020
58392^288243+7604386770Enzo Doria04/2016
5840(29*2^288232+1)/1586767Lelio R Paula01/2013
58419*6^111495+586761Lelio R Paula10/2014
5842(5*2^288202+1)/8186757Lelio R Paula01/2013
58439*7^102654-286754Lelio R Paula10/2014
5844(2^288155+1154)/286743Stefano Morozzi01/2020
58452^288122-11284186734Enzo Doria06/2014
58465^124062-6886716Lelio R Paula10/2015
5847(2^288007-3)/12586697Lelio R Paula01/2013
5848379*10^86691+986694Arkadiusz Wesolowski10/2011
58497^102555+4886670Lelio R Paula10/2015
58502^287902-496186668Yves Minet05/2019
585177779!4+286660Robert Price08/2017
5852(2^287842+3250)/286649Stefano Morozzi01/2020
58532^287809-11135586640Enzo Doria05/2014
5854(47*2^287795+1)/786636Lelio R Paula04/2015
58559*7^102504+886627Lelio R Paula10/2014
58563^181551+3286622Robert Price11/2013
58572^287735-52134786617Paul Bourdelais05/2013
5858(1017*2^287600-1)/9186578Lelio R Paula04/2015
5859(2^287552+1302)/286562Stefano Morozzi01/2020
58602^287540-11296786559Enzo Doria06/2014
58613^181407+2086554Robert Price10/2013
5863(13*10^86546+83)/386547Robert Price09/2016
5862(2^287502+2238)/286547Stefano Morozzi01/2020
58642^287482-471586541Yves Minet05/2019
58653^181378-2^(181378-1)86540Robert Price01/2016
586683^45080-286513Lelio R Paula08/2013
5867(2^287367+2570)/286506Stefano Morozzi01/2020
5869(78557*2^287351+1)/61186504Lelio R Paula06/2014
5868(2^287360+1006)/286504Stefano Morozzi01/2020
587025*29^59147+2093686498Curtis Bright05/2015
58712^287298+187135986486Enzo Doria05/2016
5872118^41740-11786481Norbert Schneider08/2018
58733*10^86478+8986479Robert Price03/2017
58742^287272-7904986478Paul Bourdelais02/2012
5875(2^287259+2846)/286474Stefano Morozzi01/2020
5876906705*2*((10^86453-1)/9)+186459Danilo Nitsche01/2016
5877811824*2*((10^86453-1)/9)+186459Danilo Nitsche01/2016
5878779064*2*((10^86453-1)/9)+186459Danilo Nitsche01/2016
5879768385*2*((10^86453-1)/9)+186459Danilo Nitsche01/2016
5880700891*2*((10^86453-1)/9)+186459Danilo Nitsche01/2016
5881652320*2*((10^86453-1)/9)+186459Danilo Nitsche01/2016
5882377920*2*((10^86453-1)/9)+186458Danilo Nitsche01/2016
5883255060*2*((10^86453-1)/9)+186458Danilo Nitsche01/2016
5884187111*2*((10^86453-1)/9)+186458Danilo Nitsche01/2016
5885(10^86453-1)/986453Lew Baxter10/2000
5886(2^287172+658)/286448Stefano Morozzi01/2020
5887(2^287146+2542)/286440Stefano Morozzi01/2020
5888(2^287136+1726)/286437Stefano Morozzi01/2020
5889(2^287128+958)/286434Stefano Morozzi01/2020
589087^44563-86^4456386431Robert Price05/2015
58916^111057+6186420Lelio R Paula12/2015
58922^287057-10990986413Enzo Doria04/2014
58935^123608+2286399Lelio R Paula10/2015
5894(2^286970+618)/286387Stefano Morozzi01/2020
5895(2^286916+2646)/286371Stefano Morozzi01/2020
5896(2^286907+3690)/286368Stefano Morozzi01/2020
5897(31*10^86364-121)/986365Robert Price06/2016
5898(2^286868+2686)/286356Stefano Morozzi01/2020
58992^286859+7166386354Enzo Doria04/2016
5900(2^286845+1866)/286349Stefano Morozzi01/2020
59012^286740+2983586318Lelio R Paula10/2013
59022*10^86310+9^8631086311Mike Oakes05/2011
590311^82878-186086309Enzo Doria12/2012
59042223^25780+25780^222386285Norbert Schneider12/2019
59052^286547+1609586260Lelio R Paula10/2013
5906(58*10^86242+329)/986243Robert Price11/2017
59072^286455-11042786232Enzo Doria05/2014
5908(37*10^86230+53)/986231Robert Price05/2015
59098*3^180700+586217Lelio R Paula08/2014
59103^180697-4086215Lelio R Paula12/2015
5911(2^286383+3386)/286210Stefano Morozzi01/2020
5912(13*2^286318-1)/1325786188Lelio R Paula02/2014
5913(2^286295+1934)/286184Stefano Morozzi01/2020
5914(2^286251+3974)/286170Stefano Morozzi01/2020
59152^286165+7786145Lelio R Paula08/2012
59169*2^286140+786138Lelio R Paula08/2014
5917(2^286128+1762)/286133Stefano Morozzi01/2020
5918(29*2^286108-1)/200236786123Lelio R Paula02/2014
5919(2^286077+1122)/286118Stefano Morozzi01/2020
592010^86110+16111386111Patrick De Geest07/2013
592110^86110-6986110Robert Price05/2011
59222^286036-86968810586106Lelio R Paula07/2016
5923(2^285946+2358)/286079Stefano Morozzi01/2020
5925(77*10^86072+31)/986073Robert Price10/2015
5924(2^285926+3382)/286073Stefano Morozzi01/2020
59262^285923+34586072Lelio R Paula09/2013
592713^77266-9086070Lelio R Paula11/2015
59282^285910-45890386068Enzo Doria04/2015
59292^285904-12586066Lelio R Paula08/2012
5930(2^285882+2830)/286059Stefano Morozzi01/2020
59312^285836+6583586046Lelio R Paula09/2013
5932(2^285766+78557)/386024Lelio R Paula01/2013
5933(2^285732+2682)/286014Stefano Morozzi01/2020
5934(5*10^86011-107)/386012Robert Price01/2017
59356^110522+16386003Lelio R Paula12/2015
593641^53323-40^5332385999Robert Price07/2012
59372^285678-10961785998Enzo Doria04/2014
59386^110506-1667385991Enzo Doria02/2013
59392^285569-74185965Lelio R Paula09/2013
5940(32*10^85964+31)/985965Robert Price05/2015
5941133^40466+13285944Norbert Schneider02/2019
59426*10^85910-785911Dmitry Domanov11/2010
5943(412*10^85897-7)/985899Robert Price10/2017
59444*10^85881+6385882Robert Price06/2016
5945(2^285257+1514)/285871Stefano Morozzi01/2020
5946(2^285248+3738)/285868Stefano Morozzi01/2020
5947(10^85864+53)/985864Robert Price01/2015
59482^285230+34585863Lelio R Paula09/2013
5949(5*10^85855-473)/985855Robert Price12/2017
59502^285199+7568385854Enzo Doria04/2016
5951(76*10^85847-211)/985848Robert Price10/2017
5952p(17832)#/2+51285845Robert Price05/2017
5953(16*10^85839+167)/385840Robert Price10/2017
595411^82426-123085838Enzo Doria11/2012
59552^285113-10988185828Enzo Doria04/2014
5956(2^285033+1670)/285804Stefano Morozzi01/2020
5957(2^285033+3854)/285804Stefano Morozzi01/2020
5958(2^285035+3194)/285804Stefano Morozzi01/2020
59595^122746-9285796Lelio R Paula10/2015
59602^285001-11346185794Enzo Doria08/2014
5961(11*10^85782-131)/385783Robert Price02/2017
5962(2^284963+2778)/285783Stefano Morozzi01/2020
5963(2^284960+3570)/285782Stefano Morozzi01/2020
5964(2^284937+1706)/285775Stefano Morozzi01/2020
59652^284913-11049185768Enzo Doria05/2014
59666^110220+4785768Lelio R Paula12/2015
59673*6^110202-585755Lelio R Paula10/2014
5968(157^39047-1)/15685742Alexander Zhirkov06/2016
5969(3^179705+7)/25085739Lelio R Paula12/2012
59702^284734-655585714Lelio R Paula09/2013
5971(10^85712+53)/985712Robert Price01/2015
59723*10^85703+1185704Robert Price11/2017
5973(6883*2^284668-1)/385697Lelio R Paula04/2015
597420^65855+8385680Lelio R Paula01/2016
59756^110105+5385679Lelio R Paula12/2015
5976(10^85666-97)/385666Robert Kinser10/2017
59782^284567-760585664Lelio R Paula09/2013
59779*5^122555-285664Lelio R Paula10/2014
59795^122554-1485662Lelio R Paula10/2015
59809*5^122543+485655Lelio R Paula10/2014
59823^179489-2^(179489-1)85639Robert Price01/2016
5981(2^284487+1970)/285639Stefano Morozzi01/2020
5983(2^284477+1614)/285636Stefano Morozzi01/2020
598419690^19941+19941^1969085632Norbert Schneider03/2020
59852^284429+17785622Lelio R Paula08/2012
59862*3^179452+585621Lelio R Paula07/2014
5988(19^66919+3^66919)/2285572Robert Price07/2013
5987(2^284265+602)/285572Stefano Morozzi01/2020
599166^47023-6585561Norbert Schneider11/2014
5989(2^284226+3802)/285561Stefano Morozzi01/2020
5990(2^284228+2170)/285561Stefano Morozzi01/2020
59926^109943+1385553Lelio R Paula12/2015
59932^284183-474785548Yves Minet05/2019
5994(2^284167-509203)/3456477585536Lelio R Paula01/2013
5995(2^284136+2262)/285534Stefano Morozzi01/2020
59962^284133-385533M. Frind & P. Underwood07/2002
59972^284113+31585527Lelio R Paula09/2013
5998(2^284098+3082)/285522Stefano Morozzi01/2020
5999(2^284070+1482)/285514Stefano Morozzi01/2020
6000(2^284068+2866)/285513Stefano Morozzi01/2020


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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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