PRP Records

Probable Primes Top 10000

(172213 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 (> 30000) Who ? When ?
40014*10^87337-9987338Robert Price12/2016
40027*10^87319+3987320Robert Price07/2016
40033*5^124921+287317Lelio R Paula10/2014
40043^182984+8887306Lelio R Paula12/2015
40054*10^87287-9987288Robert Price12/2016
400611^83813-186087283Enzo Doria12/2012
400712^80855+2987258Lelio R Paula11/2015
40083*6^112119-587247Lelio R Paula10/2014
400912^80806+7987205Lelio R Paula11/2015
401091382^9+9^9138287201Andrey Kulsha11/2004
4011(21181*2^289657+1)/8187198Lelio R Paula06/2014
40126^112054-4787195Lelio R Paula12/2015
4013(55459*2^289632+1)/5587191Lelio R Paula06/2014
401415^74131-6887185Lelio R Paula11/2015
40152^289583-74187174Lelio R Paula10/2013
40167^103146+1287169Lelio R Paula10/2015
40175*2^289556-387166Lelio R Paula08/2014
40182^289543-11273587162Enzo Doria06/2014
40198*3^182655-787150Lelio R Paula08/2014
40202*10^87144+8187145Robert Price01/2017
40217^103106+2*3^10310687135Mike Oakes08/2010
40228*3^182614+787130Lelio R Paula08/2014
4023(2^289368-509203)/987108Lelio R Paula01/2013
40243^182566+1487107Robert Price09/2013
4025(3^182385-5)/287020Lelio R Paula01/2013
402611^83534-886992Lelio R Paula11/2015
40274^144479-1426786986Mike Oakes03/2011
4028(145*10^86982-1)/986984Serge Batalov12/2014
402915^73940-5886961Lelio R Paula11/2015
40302^288761-11314386926Enzo Doria07/2014
40312^288747+308386922Yves Minet03/2011
4032(10^86906-13)/386906Robert Price02/2017
40332^288692-11002786905Enzo Doria04/2014
4034(2^288682+7)/25989544986894Lelio R Paula01/2013
4035(2^288636+47)/129386885Lelio R Paula01/2013
40363^182089-3486879Robert Price11/2013
40372^288543-10980186861Enzo Doria04/2014
403860^48847-5986858Norbert Schneider10/2014
40392^288470-6487586839Lelio R Paula10/2013
404010^86816+3299786817Patrick De Geest07/2013
404110^86816-9986816Robert Price05/2011
404241487!2+25686786Robert Price01/2015
4043(5*2^288301-1)/99986785Lelio R Paula02/2014
40442^288243+7604386770Enzo Doria04/2016
4045(29*2^288232+1)/1586767Lelio R Paula01/2013
40469*6^111495+586761Lelio R Paula10/2014
4047(5*2^288202+1)/8186757Lelio R Paula01/2013
40489*7^102654-286754Lelio R Paula10/2014
40492^288122-11284186734Enzo Doria06/2014
40505^124062-6886716Lelio R Paula10/2015
4051(2^288007-3)/12586697Lelio R Paula01/2013
4052379*10^86691+986694Arkadiusz Wesolowski10/2011
40537^102555+4886670Lelio R Paula10/2015
40542^287809-11135586640Enzo Doria05/2014
4055(47*2^287795+1)/786636Lelio R Paula04/2015
40569*7^102504+886627Lelio R Paula10/2014
40573^181551+3286622Robert Price11/2013
40582^287735-52134786617Paul Bourdelais05/2013
4059(1017*2^287600-1)/9186578Lelio R Paula04/2015
40602^287540-11296786559Enzo Doria06/2014
40613^181407+2086554Robert Price10/2013
4062(13*10^86546+83)/386547Robert Price09/2016
40633^181378-2^(181378-1)86540Robert Price01/2016
406483^45080-286513Lelio R Paula08/2013
4065(78557*2^287351+1)/61186504Lelio R Paula06/2014
406625*29^59147+2093686498Curtis Bright05/2015
40672^287298+187135986486Enzo Doria05/2016
40683*10^86478+8986479Robert Price03/2017
40692^287272-7904986478Paul Bourdelais02/2012
4070906705*2*((10^86453-1)/9)+186459Danilo Nitsche01/2016
4071811824*2*((10^86453-1)/9)+186459Danilo Nitsche01/2016
4072779064*2*((10^86453-1)/9)+186459Danilo Nitsche01/2016
4073768385*2*((10^86453-1)/9)+186459Danilo Nitsche01/2016
4074700891*2*((10^86453-1)/9)+186459Danilo Nitsche01/2016
4075652320*2*((10^86453-1)/9)+186459Danilo Nitsche01/2016
4076377920*2*((10^86453-1)/9)+186458Danilo Nitsche01/2016
4077255060*2*((10^86453-1)/9)+186458Danilo Nitsche01/2016
4078187111*2*((10^86453-1)/9)+186458Danilo Nitsche01/2016
4079(10^86453-1)/986453Lew Baxter10/2000
408087^44563-86^4456386431Robert Price05/2015
40816^111057+6186420Lelio R Paula12/2015
40822^287057-10990986413Enzo Doria04/2014
40835^123608+2286399Lelio R Paula10/2015
4084(31*10^86364-121)/986365Robert Price06/2016
40852^286859+7166386354Enzo Doria04/2016
40862^286740+2983586318Lelio R Paula10/2013
40872*10^86310+9^8631086311Mike Oakes05/2011
408811^82878-186086309Enzo Doria12/2012
40892^286547+1609586260Lelio R Paula10/2013
40902^286455-11042786232Enzo Doria05/2014
4091(37*10^86230+53)/986231Robert Price05/2015
40928*3^180700+586217Lelio R Paula08/2014
40933^180697-4086215Lelio R Paula12/2015
4094(13*2^286318-1)/1325786188Lelio R Paula02/2014
40952^286165+7786145Lelio R Paula08/2012
40969*2^286140+786138Lelio R Paula08/2014
4097(29*2^286108-1)/200236786123Lelio R Paula02/2014
409810^86110+16111386111Patrick De Geest07/2013
409910^86110-6986110Robert Price05/2011
41002^286036-86968810586106Lelio R Paula07/2016
4101(77*10^86072+31)/986073Robert Price10/2015
41022^285923+34586072Lelio R Paula09/2013
410313^77266-9086070Lelio R Paula11/2015
41042^285910-45890386068Enzo Doria04/2015
41052^285904-12586066Lelio R Paula08/2012
41062^285836+6583586046Lelio R Paula09/2013
4107(2^285766+78557)/386024Lelio R Paula01/2013
4108(5*10^86011-107)/386012Robert Price01/2017
41096^110522+16386003Lelio R Paula12/2015
411041^53323-40^5332385999Robert Price07/2012
41112^285678-10961785998Enzo Doria04/2014
41126^110506-1667385991Enzo Doria02/2013
41142^285569-74185965Lelio R Paula09/2013
4113(32*10^85964+31)/985965Robert Price05/2015
41156*10^85910-785911Dmitry Domanov11/2010
41164*10^85881+6385882Robert Price06/2016
4117(10^85864+53)/985864Robert Price01/2015
41182^285230+34585863Lelio R Paula09/2013
41192^285199+7568385854Enzo Doria04/2016
412011^82426-123085838Enzo Doria11/2012
41212^285113-10988185828Enzo Doria04/2014
41225^122746-9285796Lelio R Paula10/2015
41232^285001-11346185794Enzo Doria08/2014
4124(11*10^85782-131)/385783Robert Price02/2017
41252^284913-11049185768Enzo Doria05/2014
41266^110220+4785768Lelio R Paula12/2015
41273*6^110202-585755Lelio R Paula10/2014
4128(157^39047-1)/15685742Alexander Zhirkov06/2016
4129(3^179705+7)/25085739Lelio R Paula12/2012
41302^284734-655585714Lelio R Paula09/2013
4131(10^85712+53)/985712Robert Price01/2015
4132(6883*2^284668-1)/385697Lelio R Paula04/2015
413320^65855+8385680Lelio R Paula01/2016
41346^110105+5385679Lelio R Paula12/2015
41362^284567-760585664Lelio R Paula09/2013
41359*5^122555-285664Lelio R Paula10/2014
41375^122554-1485662Lelio R Paula10/2015
41389*5^122543+485655Lelio R Paula10/2014
41393^179489-2^(179489-1)85639Robert Price01/2016
41402^284429+17785622Lelio R Paula08/2012
41412*3^179452+585621Lelio R Paula07/2014
4142(19^66919+3^66919)/2285572Robert Price07/2013
414366^47023-6585561Norbert Schneider11/2014
41446^109943+1385553Lelio R Paula12/2015
4145(2^284167-509203)/3456477585536Lelio R Paula01/2013
41462^284133-385533M. Frind & P. Underwood07/2002
41472^284113+31585527Lelio R Paula09/2013
4148(16*10^85495-19)/385496Robert Price03/2016
41492^284004+17785494Lelio R Paula08/2012
4150(16*10^85473-91)/385474Robert Price06/2016
41513^179120+2285462Robert Price12/2013
41522^283872-279224985454Enzo Doria03/2016
41532^283817+8287585438Lelio R Paula09/2013
4154(2^283815-5)/20185435Lelio R Paula01/2013
41552^283796-12585432Lelio R Paula08/2012
4156(29*2^283784-1)/1385428Lelio R Paula02/2014
415715^72592-2885375Lelio R Paula11/2015
41582^283604-5869585374Lelio R Paula09/2013
4159(15*2^283583-1)/10305185364Lelio R Paula02/2014
416015^72572+9285352Lelio R Paula11/2015
41612^283473-161585334Lelio R Paula09/2013
41622^283466-1585332Lelio R Paula08/2012
416311^81916-702085307Enzo Doria02/2013
41646^109626-785306Lelio R Paula11/2014
41652^283374-11032785305Enzo Doria05/2014
416633*10^85297+785299Robert Price07/2016
416718^67933+4185275Lelio R Paula11/2015
41682^283271-10934185274Enzo Doria04/2014
4169(25*10^85249-73)/385250Robert Price09/2016
41702*5^121959+385246Lelio R Paula10/2014
417119834^19834+894785235Henri Lifchitz11/2004
41722^283140+191585234Lelio R Paula09/2013
4173(16*10^85221-31)/385222Robert Price03/2016
41742^283083+186938385217Enzo Doria05/2016
4175(24737*2^283051+1)/1785211Lelio R Paula06/2014
4176(2^283032+78557)/385201Lelio R Paula01/2013
41772^283026-10989385200Enzo Doria04/2014
4178(2^283012+78557)/12985193Lelio R Paula01/2013
41792^282860-10972785150Enzo Doria04/2014
41802^282819+186941385138Enzo Doria05/2016
41813^178428+285132Ray Chandler07/2011
4182(22699*2^282742+1)/7385117Lelio R Paula06/2014
4183(16^70687+5^70687)/2185115Robert Price07/2013
4184(3^178352-2)/785095Lelio R Paula12/2012
418511^81699-279085081Enzo Doria12/2012
41862^282612-9585075Lelio R Paula08/2012
418775^45366-285065Lelio R Paula08/2013
41882^282511+6985045Lelio R Paula08/2012
418969^46249+285045Lelio R Paula06/2013
41903^178226+1085036Robert Price10/2013
4191(14*10^85010+73)/385011Robert Price04/2016
41929*2^282338-784994Lelio R Paula08/2014
4193(9913*2^282330-1)/157800384988Lelio R Paula04/2015
41942^282203+584952Lelio R Paula08/2012
41952^282184+1384946Lelio R Paula08/2012
419611^81568-240084945Enzo Doria12/2012
419711^81562-234084939Enzo Doria12/2012
4198(41*10^84927+31)/984928Robert Price05/2015
4199(2*10^84904-17)/384904Robert Price08/2014
4200(4^141017+23)/384901Robert Price02/2017
42016^109100-1865384897Enzo Doria03/2013
42022^281973+102584883Lelio R Paula09/2013
42032^281951-10965184876Enzo Doria04/2014
420411^81491-543084865Enzo Doria01/2013
4205((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
42062^281825-186148384838Enzo Doria03/2016
42072^281809-9730584833Lelio R Paula09/2013
42082^281780-11489384825Enzo Doria05/2015
42093^177719+6484794Lelio R Paula12/2015
42112^281675-19984793Lelio R Paula08/2012
42102^281673-11122384793Enzo Doria05/2014
4212(72*10^84772-27)/984773Ray Chandler01/2011
421311^81398-63084768Enzo Doria11/2012
4214(25*2^281577-1)/2384764Lelio R Paula02/2014
42152^281500-45584740Yves Minet03/2012
421610^84725+114514191984726Marisa Kirisame03/2015
421710^84725+14204184726Patrick De Geest10/2015
421810^84725-13867784725Patrick De Geest02/2016
421976^45044+7584720Norbert Schneider02/2015
422054^48897-5384709Norbert Schneider08/2014
4221(9913*2^281377-1)/6584706Lelio R Paula04/2015
4222Phi(171124,10)/29946701/7761329021/5856034404184700Maksym Voznyy11/2015
42232^281337-11122384691Enzo Doria05/2014
42242^281308+5461584683Lelio R Paula09/2013
42257*5^121144-684677Lelio R Paula10/2014
4226(2^281252+47)/384665Lelio R Paula01/2013
422711^81297-315084663Enzo Doria12/2012
42282^281208-30384653Yves Minet02/2012
4229(21*2^281187+1)/248384644Lelio R Paula01/2013
423011^81247-8484611Lelio R Paula10/2015
423117^68747-6484590Lelio R Paula11/2015
42325^121018-1559684588Enzo Doria02/2013
42336^108702+784587Lelio R Paula11/2014
423410^84582+10067784583Patrick De Geest05/2016
423510^84582-800184582Robert Price03/2016
42363*5^121004-884579Lelio R Paula10/2014
42375^120996-8484573Lelio R Paula10/2015
4238(10223*2^280881+1)/6841984553Lelio R Paula06/2014
42392^280852+9768184545Yves Minet08/2004
42402^280848-120384544Lelio R Paula09/2013
42415^120946-2484538Lelio R Paula10/2015
42422^280810-211184533Yves Minet08/2013
424311^81161-516084521Enzo Doria01/2013
42442^280737-9384511Lelio R Paula08/2012
42452^280698+31584499Lelio R Paula09/2013
42463^177099-34084498Lelio R Paula12/2015
4247(5*10^84469-107)/384470Robert Price01/2017
4248(3^177002+7)/669602227216174484436Lelio R Paula12/2012
4249(2^280500-1017)/82384436Lelio R Paula01/2013
425014^73660-584424Lelio R Paula11/2015


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: March, 26 2017 17:51 (Time in France)

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