PRP Records

Probable Primes Top 10000

(191107 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 (> 30000) Who ? When ?
4251(265*10^88077+11)/388079Robert Price03/2017
425291^44959-90^4495988077Robert Price07/2015
42536^113177-5^11317788069Jean-Louis Charton01/2009
4254(10^88020+101)/388020Robert Price04/2016
4255(10^(2*43982+1)-6*10^43982-1)/387965Robert Price02/2016
4256p(18225)#/2+12887929Robert Price04/2017
42574*6^112977+787914Lelio R Paula10/2014
425814^76677+6987882Lelio R Paula11/2015
4259(22*10^87863-1)/387864Robert Price12/2014
42602^291822-279781187848Enzo Doria04/2016
42612^291716-11138987816Enzo Doria05/2014
4262(782*10^87809-71)/987811Robert Price06/2017
42633^184039+182087809Lelio R Paula12/2015
426412^81356+4187798Lelio R Paula11/2015
42656^112792-1898387770Enzo Doria03/2013
42663*6^112787-587766Lelio R Paula10/2014
42677^103848+8287762Lelio R Paula10/2015
4268(19*2^291534-1)/17869639587754Lelio R Paula02/2014
4269(3^183915+5)/12887748Lelio R Paula01/2013
427019^68619+2487747Lelio R Paula12/2015
42722^291480+118587745Lelio R Paula10/2013
42712^291482+186736987745Enzo Doria03/2016
42732^291467-93787741Yves Minet05/2013
4274(25*10^87726+161)/387727Robert Price01/2017
427511^84239-285087726Enzo Doria12/2012
427610^87720+21554187721Patrick De Geest01/2011
427710^87720-387720Markus Tervooren07/2010
4278(2^291357+5)/684787704Lelio R Paula01/2013
427993^44541-287679Lelio R Paula09/2013
42802^291261-10956187679Enzo Doria04/2014
4281(4*10^87669+149)/987669Robert Price03/2017
42822^291217+425787666Lelio R Paula10/2013
42832*12^81214-5^8121487645Mike Oakes12/2010
428412^81188+8587617Lelio R Paula11/2015
4285(21*2^290980-1)/587595Lelio R Paula02/2014
42862^290958+12787588Lelio R Paula09/2012
42872^290923-6787577Lelio R Paula09/2012
42883*10^87573-9787574Robert Price08/2017
4289(13*10^87565+11)/387566Robert Price05/2015
4290(2^290857-7)/5587555Lelio R Paula01/2013
42912^290802+8287587541Lelio R Paula10/2013
4292(509203*2^290792-1)/756098787536Lelio R Paula04/2015
42933^183441+23687524Lelio R Paula12/2015
42942^290618-3387485Lelio R Paula09/2012
4295(184*10^87473-1)/387475Robert Price02/2017
42962^290534-11515187460Enzo Doria06/2015
42972^290512-10975787453Enzo Doria04/2014
4298(32*10^87448-41)/987449Robert Price05/2015
4299(2^290491+9)/317987444Lelio R Paula01/2013
4300(25*2^290489-1)/5180987443Lelio R Paula02/2014
43012^290426+8287587427Lelio R Paula11/2013
43023*2^290415-787425Lelio R Paula08/2014
430310^87408+5787409Robert Price03/2011
43042^290366+7477987409Enzo Doria04/2016
430510^87408-12356987408Patrick De Geest07/2013
43062^290265+5890587379Lelio R Paula10/2013
43077^103391+1687376Lelio R Paula10/2015
4308(115*10^87368-7)/987370Robert Price11/2017
4309(92^44491-1)/9187369Paul Bourdelais08/2017
43108*7^103379+387367Lelio R Paula10/2014
4311(2^290226+7)/7187365Lelio R Paula01/2013
431213^78407-3087341Lelio R Paula11/2015
43134*10^87337-9987338Robert Price12/2016
43147*10^87319+3987320Robert Price07/2016
43153*5^124921+287317Lelio R Paula10/2014
43163^182984+8887306Lelio R Paula12/2015
43174*10^87287-9987288Robert Price12/2016
431811^83813-186087283Enzo Doria12/2012
4319734^30453+30453^73487270Norbert Schneider04/2017
432012^80855+2987258Lelio R Paula11/2015
43213*6^112119-587247Lelio R Paula10/2014
432212^80806+7987205Lelio R Paula11/2015
432391382^9+9^9138287201Andrey Kulsha11/2004
4324(21181*2^289657+1)/8187198Lelio R Paula06/2014
43256^112054-4787195Lelio R Paula12/2015
4326(55459*2^289632+1)/5587191Lelio R Paula06/2014
432715^74131-6887185Lelio R Paula11/2015
43282^289583-74187174Lelio R Paula10/2013
43297^103146+1287169Lelio R Paula10/2015
43305*2^289556-387166Lelio R Paula08/2014
43312^289543-11273587162Enzo Doria06/2014
43328*3^182655-787150Lelio R Paula08/2014
43332*10^87144+8187145Robert Price01/2017
43347^103106+2*3^10310687135Mike Oakes08/2010
43358*3^182614+787130Lelio R Paula08/2014
4336(2^289368-509203)/987108Lelio R Paula01/2013
43373^182566+1487107Robert Price09/2013
4338(3^182385-5)/287020Lelio R Paula01/2013
433911^83534-886992Lelio R Paula11/2015
43404^144479-1426786986Mike Oakes03/2011
4341(145*10^86982-1)/986984Serge Batalov12/2014
4342(151*10^86963-1)/386965Robert Price04/2017
434315^73940-5886961Lelio R Paula11/2015
43442^288761-11314386926Enzo Doria07/2014
43452^288747+308386922Yves Minet03/2011
434630^58842+2986917Norbert Schneider03/2017
4347(10^86906-13)/386906Robert Price02/2017
43482^288692-11002786905Enzo Doria04/2014
4349(2^288682+7)/25989544986894Lelio R Paula01/2013
4350(2^288636+47)/129386885Lelio R Paula01/2013
43513^182089-3486879Robert Price11/2013
43522^288543-10980186861Enzo Doria04/2014
435360^48847-5986858Norbert Schneider10/2014
43542^288470-6487586839Lelio R Paula10/2013
435510^86816+3299786817Patrick De Geest07/2013
435610^86816-9986816Robert Price05/2011
4357(89*10^86802-539)/986803Robert Price11/2017
435841487!2+25686786Robert Price01/2015
4359(5*2^288301-1)/99986785Lelio R Paula02/2014
43602^288243+7604386770Enzo Doria04/2016
4361(29*2^288232+1)/1586767Lelio R Paula01/2013
43629*6^111495+586761Lelio R Paula10/2014
4363(5*2^288202+1)/8186757Lelio R Paula01/2013
43649*7^102654-286754Lelio R Paula10/2014
43652^288122-11284186734Enzo Doria06/2014
43665^124062-6886716Lelio R Paula10/2015
4367(2^288007-3)/12586697Lelio R Paula01/2013
4368379*10^86691+986694Arkadiusz Wesolowski10/2011
43697^102555+4886670Lelio R Paula10/2015
437077779!4+286660Robert Price08/2017
43712^287809-11135586640Enzo Doria05/2014
4372(47*2^287795+1)/786636Lelio R Paula04/2015
43739*7^102504+886627Lelio R Paula10/2014
43743^181551+3286622Robert Price11/2013
43752^287735-52134786617Paul Bourdelais05/2013
4376(1017*2^287600-1)/9186578Lelio R Paula04/2015
43772^287540-11296786559Enzo Doria06/2014
43783^181407+2086554Robert Price10/2013
4379(13*10^86546+83)/386547Robert Price09/2016
43803^181378-2^(181378-1)86540Robert Price01/2016
438183^45080-286513Lelio R Paula08/2013
4382(78557*2^287351+1)/61186504Lelio R Paula06/2014
438325*29^59147+2093686498Curtis Bright05/2015
43842^287298+187135986486Enzo Doria05/2016
43853*10^86478+8986479Robert Price03/2017
43862^287272-7904986478Paul Bourdelais02/2012
4387906705*2*((10^86453-1)/9)+186459Danilo Nitsche01/2016
4388811824*2*((10^86453-1)/9)+186459Danilo Nitsche01/2016
4389779064*2*((10^86453-1)/9)+186459Danilo Nitsche01/2016
4390768385*2*((10^86453-1)/9)+186459Danilo Nitsche01/2016
4391700891*2*((10^86453-1)/9)+186459Danilo Nitsche01/2016
4392652320*2*((10^86453-1)/9)+186459Danilo Nitsche01/2016
4393377920*2*((10^86453-1)/9)+186458Danilo Nitsche01/2016
4394255060*2*((10^86453-1)/9)+186458Danilo Nitsche01/2016
4395187111*2*((10^86453-1)/9)+186458Danilo Nitsche01/2016
4396(10^86453-1)/986453Lew Baxter10/2000
439787^44563-86^4456386431Robert Price05/2015
43986^111057+6186420Lelio R Paula12/2015
43992^287057-10990986413Enzo Doria04/2014
44005^123608+2286399Lelio R Paula10/2015
4401(31*10^86364-121)/986365Robert Price06/2016
44022^286859+7166386354Enzo Doria04/2016
44032^286740+2983586318Lelio R Paula10/2013
44042*10^86310+9^8631086311Mike Oakes05/2011
440511^82878-186086309Enzo Doria12/2012
44062^286547+1609586260Lelio R Paula10/2013
4407(58*10^86242+329)/986243Robert Price11/2017
44082^286455-11042786232Enzo Doria05/2014
4409(37*10^86230+53)/986231Robert Price05/2015
44108*3^180700+586217Lelio R Paula08/2014
44113^180697-4086215Lelio R Paula12/2015
4412(13*2^286318-1)/1325786188Lelio R Paula02/2014
44132^286165+7786145Lelio R Paula08/2012
44149*2^286140+786138Lelio R Paula08/2014
4415(29*2^286108-1)/200236786123Lelio R Paula02/2014
441610^86110+16111386111Patrick De Geest07/2013
441710^86110-6986110Robert Price05/2011
44182^286036-86968810586106Lelio R Paula07/2016
4419(77*10^86072+31)/986073Robert Price10/2015
44202^285923+34586072Lelio R Paula09/2013
442113^77266-9086070Lelio R Paula11/2015
44222^285910-45890386068Enzo Doria04/2015
44232^285904-12586066Lelio R Paula08/2012
44242^285836+6583586046Lelio R Paula09/2013
4425(2^285766+78557)/386024Lelio R Paula01/2013
4426(5*10^86011-107)/386012Robert Price01/2017
44276^110522+16386003Lelio R Paula12/2015
442841^53323-40^5332385999Robert Price07/2012
44292^285678-10961785998Enzo Doria04/2014
44306^110506-1667385991Enzo Doria02/2013
44322^285569-74185965Lelio R Paula09/2013
4431(32*10^85964+31)/985965Robert Price05/2015
44336*10^85910-785911Dmitry Domanov11/2010
4434(412*10^85897-7)/985899Robert Price10/2017
44354*10^85881+6385882Robert Price06/2016
4436(10^85864+53)/985864Robert Price01/2015
44372^285230+34585863Lelio R Paula09/2013
44382^285199+7568385854Enzo Doria04/2016
4439(76*10^85847-211)/985848Robert Price10/2017
4440p(17832)#/2+51285845Robert Price05/2017
4441(16*10^85839+167)/385840Robert Price10/2017
444211^82426-123085838Enzo Doria11/2012
44432^285113-10988185828Enzo Doria04/2014
44445^122746-9285796Lelio R Paula10/2015
44452^285001-11346185794Enzo Doria08/2014
4446(11*10^85782-131)/385783Robert Price02/2017
44472^284913-11049185768Enzo Doria05/2014
44486^110220+4785768Lelio R Paula12/2015
44493*6^110202-585755Lelio R Paula10/2014
4450(157^39047-1)/15685742Alexander Zhirkov06/2016
4451(3^179705+7)/25085739Lelio R Paula12/2012
44522^284734-655585714Lelio R Paula09/2013
4453(10^85712+53)/985712Robert Price01/2015
4454(6883*2^284668-1)/385697Lelio R Paula04/2015
445520^65855+8385680Lelio R Paula01/2016
44566^110105+5385679Lelio R Paula12/2015
4457(10^85666-97)/385666Robert Kinser10/2017
44592^284567-760585664Lelio R Paula09/2013
44589*5^122555-285664Lelio R Paula10/2014
44605^122554-1485662Lelio R Paula10/2015
44619*5^122543+485655Lelio R Paula10/2014
44623^179489-2^(179489-1)85639Robert Price01/2016
44632^284429+17785622Lelio R Paula08/2012
44642*3^179452+585621Lelio R Paula07/2014
4465(19^66919+3^66919)/2285572Robert Price07/2013
446666^47023-6585561Norbert Schneider11/2014
44676^109943+1385553Lelio R Paula12/2015
4468(2^284167-509203)/3456477585536Lelio R Paula01/2013
44692^284133-385533M. Frind & P. Underwood07/2002
44702^284113+31585527Lelio R Paula09/2013
4471(28*10^85500+149)/385501Robert Price10/2017
4472(16*10^85495-19)/385496Robert Price03/2016
44732^284004+17785494Lelio R Paula08/2012
4474(16*10^85473-91)/385474Robert Price06/2016
44753^179120+2285462Robert Price12/2013
44762^283872-279224985454Enzo Doria03/2016
4477(29*10^85438+259)/985439Robert Price04/2017
44782^283817+8287585438Lelio R Paula09/2013
4479(2^283815-5)/20185435Lelio R Paula01/2013
44802^283796-12585432Lelio R Paula08/2012
4481(29*2^283784-1)/1385428Lelio R Paula02/2014
448215^72592-2885375Lelio R Paula11/2015
44832^283604-5869585374Lelio R Paula09/2013
4484(44*10^85370-503)/985371Robert Price10/2017
4485496^31671+31671^49685369Norbert Schneider07/2017
4486(15*2^283583-1)/10305185364Lelio R Paula02/2014
448715^72572+9285352Lelio R Paula11/2015
44882^283473-161585334Lelio R Paula09/2013
44892^283466-1585332Lelio R Paula08/2012
449011^81916-702085307Enzo Doria02/2013
44916^109626-785306Lelio R Paula11/2014
44922^283374-11032785305Enzo Doria05/2014
449333*10^85297+785299Robert Price07/2016
449418^67933+4185275Lelio R Paula11/2015
44952^283271-10934185274Enzo Doria04/2014
4496(25*10^85249-73)/385250Robert Price09/2016
44972*5^121959+385246Lelio R Paula10/2014
449819834^19834+894785235Henri Lifchitz11/2004
44992^283140+191585234Lelio R Paula09/2013
45003*10^85227-9785228Robert Price08/2017


Find by discoverer :


Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: November, 22 2017 23:29 (Time in France)

Go back
Valid XHTML 1.0!    Valid CSS!