PRP Records

Probable Primes Top 10000

(255244 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 ?
550112^80806+7987205Lelio R Paula11/2015
550291382^9+9^9138287201Andrey Kulsha11/2004
5503(21181*2^289657+1)/8187198Lelio R Paula06/2014
55046^112054-4787195Lelio R Paula12/2015
5505(55459*2^289632+1)/5587191Lelio R Paula06/2014
550615^74131-6887185Lelio R Paula11/2015
55072^289583-74187174Lelio R Paula10/2013
55087^103146+1287169Lelio R Paula10/2015
55095*2^289556-387166Lelio R Paula08/2014
55102^289543-11273587162Enzo Doria06/2014
55118*3^182655-787150Lelio R Paula08/2014
55122*10^87144+8187145Robert Price01/2017
55137^103106+2*3^10310687135Mike Oakes08/2010
55148*3^182614+787130Lelio R Paula08/2014
5515(2^289368-509203)/987108Lelio R Paula01/2013
55163^182566+1487107Robert Price09/2013
5517(3^182385-5)/287020Lelio R Paula01/2013
551811^83534-886992Lelio R Paula11/2015
55194^144479-1426786986Mike Oakes03/2011
5520(145*10^86982-1)/986984Serge Batalov12/2014
5521(151*10^86963-1)/386965Robert Price04/2017
552215^73940-5886961Lelio R Paula11/2015
55232^288761-11314386926Enzo Doria07/2014
55242^288747+308386922Yves Minet03/2011
552530^58842+2986917Norbert Schneider03/2017
5526(10^86906-13)/386906Robert Price02/2017
55272^288692-11002786905Enzo Doria04/2014
5528(2^288682+7)/25989544986894Lelio R Paula01/2013
5529(2^288636+47)/129386885Lelio R Paula01/2013
55303^182089-3486879Robert Price11/2013
55312^288543-10980186861Enzo Doria04/2014
553260^48847-5986858Norbert Schneider10/2014
55332^288470-6487586839Lelio R Paula10/2013
553410^86816+3299786817Patrick De Geest07/2013
553510^86816-9986816Robert Price05/2011
5536(89*10^86802-539)/986803Robert Price11/2017
553741487!2+25686786Robert Price01/2015
5538(5*2^288301-1)/99986785Lelio R Paula02/2014
55392^288243+7604386770Enzo Doria04/2016
5540(29*2^288232+1)/1586767Lelio R Paula01/2013
55419*6^111495+586761Lelio R Paula10/2014
5542(5*2^288202+1)/8186757Lelio R Paula01/2013
55439*7^102654-286754Lelio R Paula10/2014
55442^288122-11284186734Enzo Doria06/2014
55455^124062-6886716Lelio R Paula10/2015
5546(2^288007-3)/12586697Lelio R Paula01/2013
5547379*10^86691+986694Arkadiusz Wesolowski10/2011
55487^102555+4886670Lelio R Paula10/2015
55492^287902-496186668Yves Minet05/2019
555077779!4+286660Robert Price08/2017
55512^287809-11135586640Enzo Doria05/2014
5552(47*2^287795+1)/786636Lelio R Paula04/2015
55539*7^102504+886627Lelio R Paula10/2014
55543^181551+3286622Robert Price11/2013
55552^287735-52134786617Paul Bourdelais05/2013
5556(1017*2^287600-1)/9186578Lelio R Paula04/2015
55572^287540-11296786559Enzo Doria06/2014
55583^181407+2086554Robert Price10/2013
5559(13*10^86546+83)/386547Robert Price09/2016
55602^287482-471586541Yves Minet05/2019
55613^181378-2^(181378-1)86540Robert Price01/2016
556283^45080-286513Lelio R Paula08/2013
5563(78557*2^287351+1)/61186504Lelio R Paula06/2014
556425*29^59147+2093686498Curtis Bright05/2015
55652^287298+187135986486Enzo Doria05/2016
5566118^41740-11786481Norbert Schneider08/2018
55673*10^86478+8986479Robert Price03/2017
55682^287272-7904986478Paul Bourdelais02/2012
5569906705*2*((10^86453-1)/9)+186459Danilo Nitsche01/2016
5570811824*2*((10^86453-1)/9)+186459Danilo Nitsche01/2016
5571779064*2*((10^86453-1)/9)+186459Danilo Nitsche01/2016
5572768385*2*((10^86453-1)/9)+186459Danilo Nitsche01/2016
5573700891*2*((10^86453-1)/9)+186459Danilo Nitsche01/2016
5574652320*2*((10^86453-1)/9)+186459Danilo Nitsche01/2016
5575377920*2*((10^86453-1)/9)+186458Danilo Nitsche01/2016
5576255060*2*((10^86453-1)/9)+186458Danilo Nitsche01/2016
5577187111*2*((10^86453-1)/9)+186458Danilo Nitsche01/2016
5578(10^86453-1)/986453Lew Baxter10/2000
557987^44563-86^4456386431Robert Price05/2015
55806^111057+6186420Lelio R Paula12/2015
55812^287057-10990986413Enzo Doria04/2014
55825^123608+2286399Lelio R Paula10/2015
5583(31*10^86364-121)/986365Robert Price06/2016
55842^286859+7166386354Enzo Doria04/2016
55852^286740+2983586318Lelio R Paula10/2013
55862*10^86310+9^8631086311Mike Oakes05/2011
558711^82878-186086309Enzo Doria12/2012
55882^286547+1609586260Lelio R Paula10/2013
5589(58*10^86242+329)/986243Robert Price11/2017
55902^286455-11042786232Enzo Doria05/2014
5591(37*10^86230+53)/986231Robert Price05/2015
55928*3^180700+586217Lelio R Paula08/2014
55933^180697-4086215Lelio R Paula12/2015
5594(13*2^286318-1)/1325786188Lelio R Paula02/2014
55952^286165+7786145Lelio R Paula08/2012
55969*2^286140+786138Lelio R Paula08/2014
5597(29*2^286108-1)/200236786123Lelio R Paula02/2014
559810^86110+16111386111Patrick De Geest07/2013
559910^86110-6986110Robert Price05/2011
56002^286036-86968810586106Lelio R Paula07/2016
5601(77*10^86072+31)/986073Robert Price10/2015
56022^285923+34586072Lelio R Paula09/2013
560313^77266-9086070Lelio R Paula11/2015
56042^285910-45890386068Enzo Doria04/2015
56052^285904-12586066Lelio R Paula08/2012
56062^285836+6583586046Lelio R Paula09/2013
5607(2^285766+78557)/386024Lelio R Paula01/2013
5608(5*10^86011-107)/386012Robert Price01/2017
56096^110522+16386003Lelio R Paula12/2015
561041^53323-40^5332385999Robert Price07/2012
56112^285678-10961785998Enzo Doria04/2014
56126^110506-1667385991Enzo Doria02/2013
56132^285569-74185965Lelio R Paula09/2013
5614(32*10^85964+31)/985965Robert Price05/2015
5615133^40466+13285944Norbert Schneider02/2019
56166*10^85910-785911Dmitry Domanov11/2010
5617(412*10^85897-7)/985899Robert Price10/2017
56184*10^85881+6385882Robert Price06/2016
5619(10^85864+53)/985864Robert Price01/2015
56202^285230+34585863Lelio R Paula09/2013
5621(5*10^85855-473)/985855Robert Price12/2017
56222^285199+7568385854Enzo Doria04/2016
5623(76*10^85847-211)/985848Robert Price10/2017
5624p(17832)#/2+51285845Robert Price05/2017
5625(16*10^85839+167)/385840Robert Price10/2017
562611^82426-123085838Enzo Doria11/2012
56272^285113-10988185828Enzo Doria04/2014
56285^122746-9285796Lelio R Paula10/2015
56292^285001-11346185794Enzo Doria08/2014
5630(11*10^85782-131)/385783Robert Price02/2017
56322^284913-11049185768Enzo Doria05/2014
56316^110220+4785768Lelio R Paula12/2015
56333*6^110202-585755Lelio R Paula10/2014
5634(157^39047-1)/15685742Alexander Zhirkov06/2016
5635(3^179705+7)/25085739Lelio R Paula12/2012
56362^284734-655585714Lelio R Paula09/2013
5637(10^85712+53)/985712Robert Price01/2015
56383*10^85703+1185704Robert Price11/2017
5639(6883*2^284668-1)/385697Lelio R Paula04/2015
564020^65855+8385680Lelio R Paula01/2016
56416^110105+5385679Lelio R Paula12/2015
5642(10^85666-97)/385666Robert Kinser10/2017
56442^284567-760585664Lelio R Paula09/2013
56439*5^122555-285664Lelio R Paula10/2014
56455^122554-1485662Lelio R Paula10/2015
56469*5^122543+485655Lelio R Paula10/2014
56473^179489-2^(179489-1)85639Robert Price01/2016
56482^284429+17785622Lelio R Paula08/2012
56492*3^179452+585621Lelio R Paula07/2014
5650(19^66919+3^66919)/2285572Robert Price07/2013
565166^47023-6585561Norbert Schneider11/2014
56526^109943+1385553Lelio R Paula12/2015
56532^284183-474785548Yves Minet05/2019
5654(2^284167-509203)/3456477585536Lelio R Paula01/2013
56552^284133-385533M. Frind & P. Underwood07/2002
56562^284113+31585527Lelio R Paula09/2013
5657(28*10^85500+149)/385501Robert Price10/2017
5658(16*10^85495-19)/385496Robert Price03/2016
56592^284004+17785494Lelio R Paula08/2012
5660(16*10^85473-91)/385474Robert Price06/2016
56613^179120+2285462Robert Price12/2013
56622^283872-279224985454Enzo Doria03/2016
5663(29*10^85438+259)/985439Robert Price04/2017
56642^283817+8287585438Lelio R Paula09/2013
5665(2^283815-5)/20185435Lelio R Paula01/2013
56662^283796-12585432Lelio R Paula08/2012
5667(29*2^283784-1)/1385428Lelio R Paula02/2014
566815^72592-2885375Lelio R Paula11/2015
56692^283604-5869585374Lelio R Paula09/2013
5670(44*10^85370-503)/985371Robert Price10/2017
5671496^31671+31671^49685369Norbert Schneider07/2017
5672(15*2^283583-1)/10305185364Lelio R Paula02/2014
567315^72572+9285352Lelio R Paula11/2015
56742^283473-161585334Lelio R Paula09/2013
56752^283466-1585332Lelio R Paula08/2012
567611^81916-702085307Enzo Doria02/2013
56776^109626-785306Lelio R Paula11/2014
56782^283374-11032785305Enzo Doria05/2014
567933*10^85297+785299Robert Price07/2016
568018^67933+4185275Lelio R Paula11/2015
56812^283271-10934185274Enzo Doria04/2014
5682(25*10^85249-73)/385250Robert Price09/2016
56832*5^121959+385246Lelio R Paula10/2014
568419834^19834+894785235Henri Lifchitz11/2004
56852^283140+191585234Lelio R Paula09/2013
56863*10^85227-9785228Robert Price08/2017
5687(16*10^85221-31)/385222Robert Price03/2016
56882^283083+186938385217Enzo Doria05/2016
5689(24737*2^283051+1)/1785211Lelio R Paula06/2014
5690(2^283032+78557)/385201Lelio R Paula01/2013
56912^283026-10989385200Enzo Doria04/2014
5692(2^283012+78557)/12985193Lelio R Paula01/2013
5693(10^(2*42589+1)+72*10^42589-1)/985179Robert Price09/2017
56942^282860-10972785150Enzo Doria04/2014
56952^282819+186941385138Enzo Doria05/2016
56963^178428+285132Ray Chandler07/2011
5697(22699*2^282742+1)/7385117Lelio R Paula06/2014
5698(16^70687+5^70687)/2185115Robert Price07/2013
5699(3^178352-2)/785095Lelio R Paula12/2012
570011^81699-279085081Enzo Doria12/2012
57012^282612-9585075Lelio R Paula08/2012
57022^282609-406985074Yves Minet02/2018
570375^45366-285065Lelio R Paula08/2013
57042^282511+6985045Lelio R Paula08/2012
570569^46249+285045Lelio R Paula06/2013
57063^178226+1085036Robert Price10/2013
5707(182*10^85017+43)/985019Robert Price11/2017
5708(14*10^85010+73)/385011Robert Price04/2016
57099*2^282338-784994Lelio R Paula08/2014
5710(9913*2^282330-1)/157800384988Lelio R Paula04/2015
57112^282203+584952Lelio R Paula08/2012
57122^282184+1384946Lelio R Paula08/2012
571311^81568-240084945Enzo Doria12/2012
571411^81562-234084939Enzo Doria12/2012
5715(41*10^84927+31)/984928Robert Price05/2015
5716(2*10^84904-17)/384904Robert Price08/2014
5717(4^141017+23)/384901Robert Price02/2017
57186^109100-1865384897Enzo Doria03/2013
57192^281973+102584883Lelio R Paula09/2013
57202^281951-10965184876Enzo Doria04/2014
572111^81491-543084865Enzo Doria01/2013
5722((1+sqrt(3)+sqrt(2))^79357-1)*((1+sqrt(3)-sqrt(2))^79357-1)*((1-sqrt(3)+sqrt(2))^79357-1)*((1-sqrt(384849Mike Oakes04/2009
57232^281825-186148384838Enzo Doria03/2016
57242^281809-9730584833Lelio R Paula09/2013
57252^281780-11489384825Enzo Doria05/2015
57263^177719+6484794Lelio R Paula12/2015
57282^281675-19984793Lelio R Paula08/2012
57272^281673-11122384793Enzo Doria05/2014
5729(4*10^84779+149)/984779Robert Price03/2017
5730129^40167-12884777Norbert Schneider01/2019
5731(72*10^84772-27)/984773Ray Chandler01/2011
573211^81398-63084768Enzo Doria11/2012
5733(25*2^281577-1)/2384764Lelio R Paula02/2014
57342^281500-45584740Yves Minet03/2012
573510^84725+114514191984726Marisa Kirisame03/2015
573610^84725+14204184726Patrick De Geest10/2015
573710^84725-13867784725Patrick De Geest02/2016
573876^45044+7584720Norbert Schneider02/2015
573954^48897-5384709Norbert Schneider08/2014
5740(9913*2^281377-1)/6584706Lelio R Paula04/2015
5741Phi(171124,10)/29946701/7761329021/5856034404184700Maksym Voznyy11/2015
57422^281337-11122384691Enzo Doria05/2014
57432^281308+5461584683Lelio R Paula09/2013
57447*5^121144-684677Lelio R Paula10/2014
5745(2^281252+47)/384665Lelio R Paula01/2013
574611^81297-315084663Enzo Doria12/2012
57472^281208-30384653Yves Minet02/2012
5748197^36892-284648Lelio R Paula10/2017
5749(21*2^281187+1)/248384644Lelio R Paula01/2013
575011^81247-8484611Lelio R Paula10/2015


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: November, 10 2019 12:07 (Time in France)

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