PRP Records

Probable Primes Top 10000

(205869 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 ?
45013^182566+1487107Robert Price09/2013
4502(3^182385-5)/287020Lelio R Paula01/2013
450311^83534-886992Lelio R Paula11/2015
45044^144479-1426786986Mike Oakes03/2011
4505(145*10^86982-1)/986984Serge Batalov12/2014
4506(151*10^86963-1)/386965Robert Price04/2017
450715^73940-5886961Lelio R Paula11/2015
45082^288761-11314386926Enzo Doria07/2014
45092^288747+308386922Yves Minet03/2011
451030^58842+2986917Norbert Schneider03/2017
4511(10^86906-13)/386906Robert Price02/2017
45122^288692-11002786905Enzo Doria04/2014
4513(2^288682+7)/25989544986894Lelio R Paula01/2013
4514(2^288636+47)/129386885Lelio R Paula01/2013
45153^182089-3486879Robert Price11/2013
45162^288543-10980186861Enzo Doria04/2014
451760^48847-5986858Norbert Schneider10/2014
45182^288470-6487586839Lelio R Paula10/2013
451910^86816+3299786817Patrick De Geest07/2013
452010^86816-9986816Robert Price05/2011
4521(89*10^86802-539)/986803Robert Price11/2017
452241487!2+25686786Robert Price01/2015
4523(5*2^288301-1)/99986785Lelio R Paula02/2014
45242^288243+7604386770Enzo Doria04/2016
4525(29*2^288232+1)/1586767Lelio R Paula01/2013
45269*6^111495+586761Lelio R Paula10/2014
4527(5*2^288202+1)/8186757Lelio R Paula01/2013
45289*7^102654-286754Lelio R Paula10/2014
45292^288122-11284186734Enzo Doria06/2014
45305^124062-6886716Lelio R Paula10/2015
4531(2^288007-3)/12586697Lelio R Paula01/2013
4532379*10^86691+986694Arkadiusz Wesolowski10/2011
45337^102555+4886670Lelio R Paula10/2015
453477779!4+286660Robert Price08/2017
45352^287809-11135586640Enzo Doria05/2014
4536(47*2^287795+1)/786636Lelio R Paula04/2015
45379*7^102504+886627Lelio R Paula10/2014
45383^181551+3286622Robert Price11/2013
45392^287735-52134786617Paul Bourdelais05/2013
4540(1017*2^287600-1)/9186578Lelio R Paula04/2015
45412^287540-11296786559Enzo Doria06/2014
45423^181407+2086554Robert Price10/2013
4543(13*10^86546+83)/386547Robert Price09/2016
45443^181378-2^(181378-1)86540Robert Price01/2016
454583^45080-286513Lelio R Paula08/2013
4546(78557*2^287351+1)/61186504Lelio R Paula06/2014
454725*29^59147+2093686498Curtis Bright05/2015
45482^287298+187135986486Enzo Doria05/2016
45493*10^86478+8986479Robert Price03/2017
45502^287272-7904986478Paul Bourdelais02/2012
4551906705*2*((10^86453-1)/9)+186459Danilo Nitsche01/2016
4552811824*2*((10^86453-1)/9)+186459Danilo Nitsche01/2016
4553779064*2*((10^86453-1)/9)+186459Danilo Nitsche01/2016
4554768385*2*((10^86453-1)/9)+186459Danilo Nitsche01/2016
4555700891*2*((10^86453-1)/9)+186459Danilo Nitsche01/2016
4556652320*2*((10^86453-1)/9)+186459Danilo Nitsche01/2016
4557377920*2*((10^86453-1)/9)+186458Danilo Nitsche01/2016
4558255060*2*((10^86453-1)/9)+186458Danilo Nitsche01/2016
4559187111*2*((10^86453-1)/9)+186458Danilo Nitsche01/2016
4560(10^86453-1)/986453Lew Baxter10/2000
456187^44563-86^4456386431Robert Price05/2015
45626^111057+6186420Lelio R Paula12/2015
45632^287057-10990986413Enzo Doria04/2014
45645^123608+2286399Lelio R Paula10/2015
4565(31*10^86364-121)/986365Robert Price06/2016
45662^286859+7166386354Enzo Doria04/2016
45672^286740+2983586318Lelio R Paula10/2013
45682*10^86310+9^8631086311Mike Oakes05/2011
456911^82878-186086309Enzo Doria12/2012
45702^286547+1609586260Lelio R Paula10/2013
4571(58*10^86242+329)/986243Robert Price11/2017
45722^286455-11042786232Enzo Doria05/2014
4573(37*10^86230+53)/986231Robert Price05/2015
45748*3^180700+586217Lelio R Paula08/2014
45753^180697-4086215Lelio R Paula12/2015
4576(13*2^286318-1)/1325786188Lelio R Paula02/2014
45772^286165+7786145Lelio R Paula08/2012
45789*2^286140+786138Lelio R Paula08/2014
4579(29*2^286108-1)/200236786123Lelio R Paula02/2014
458010^86110+16111386111Patrick De Geest07/2013
458110^86110-6986110Robert Price05/2011
45822^286036-86968810586106Lelio R Paula07/2016
4583(77*10^86072+31)/986073Robert Price10/2015
45842^285923+34586072Lelio R Paula09/2013
458513^77266-9086070Lelio R Paula11/2015
45862^285910-45890386068Enzo Doria04/2015
45872^285904-12586066Lelio R Paula08/2012
45882^285836+6583586046Lelio R Paula09/2013
4589(2^285766+78557)/386024Lelio R Paula01/2013
4590(5*10^86011-107)/386012Robert Price01/2017
45916^110522+16386003Lelio R Paula12/2015
459241^53323-40^5332385999Robert Price07/2012
45932^285678-10961785998Enzo Doria04/2014
45946^110506-1667385991Enzo Doria02/2013
45962^285569-74185965Lelio R Paula09/2013
4595(32*10^85964+31)/985965Robert Price05/2015
45976*10^85910-785911Dmitry Domanov11/2010
4598(412*10^85897-7)/985899Robert Price10/2017
45994*10^85881+6385882Robert Price06/2016
4600(10^85864+53)/985864Robert Price01/2015
46012^285230+34585863Lelio R Paula09/2013
4602(5*10^85855-473)/985855Robert Price12/2017
46032^285199+7568385854Enzo Doria04/2016
4604(76*10^85847-211)/985848Robert Price10/2017
4605p(17832)#/2+51285845Robert Price05/2017
4606(16*10^85839+167)/385840Robert Price10/2017
460711^82426-123085838Enzo Doria11/2012
46082^285113-10988185828Enzo Doria04/2014
46095^122746-9285796Lelio R Paula10/2015
46102^285001-11346185794Enzo Doria08/2014
4611(11*10^85782-131)/385783Robert Price02/2017
46122^284913-11049185768Enzo Doria05/2014
46136^110220+4785768Lelio R Paula12/2015
46143*6^110202-585755Lelio R Paula10/2014
4615(157^39047-1)/15685742Alexander Zhirkov06/2016
4616(3^179705+7)/25085739Lelio R Paula12/2012
46172^284734-655585714Lelio R Paula09/2013
4618(10^85712+53)/985712Robert Price01/2015
46193*10^85703+1185704Robert Price11/2017
4620(6883*2^284668-1)/385697Lelio R Paula04/2015
462120^65855+8385680Lelio R Paula01/2016
46226^110105+5385679Lelio R Paula12/2015
4623(10^85666-97)/385666Robert Kinser10/2017
46252^284567-760585664Lelio R Paula09/2013
46249*5^122555-285664Lelio R Paula10/2014
46265^122554-1485662Lelio R Paula10/2015
46279*5^122543+485655Lelio R Paula10/2014
46283^179489-2^(179489-1)85639Robert Price01/2016
46292^284429+17785622Lelio R Paula08/2012
46302*3^179452+585621Lelio R Paula07/2014
4631(19^66919+3^66919)/2285572Robert Price07/2013
463266^47023-6585561Norbert Schneider11/2014
46336^109943+1385553Lelio R Paula12/2015
4634(2^284167-509203)/3456477585536Lelio R Paula01/2013
46352^284133-385533M. Frind & P. Underwood07/2002
46362^284113+31585527Lelio R Paula09/2013
4637(28*10^85500+149)/385501Robert Price10/2017
4638(16*10^85495-19)/385496Robert Price03/2016
46392^284004+17785494Lelio R Paula08/2012
4640(16*10^85473-91)/385474Robert Price06/2016
46413^179120+2285462Robert Price12/2013
46422^283872-279224985454Enzo Doria03/2016
4643(29*10^85438+259)/985439Robert Price04/2017
46442^283817+8287585438Lelio R Paula09/2013
4645(2^283815-5)/20185435Lelio R Paula01/2013
46462^283796-12585432Lelio R Paula08/2012
4647(29*2^283784-1)/1385428Lelio R Paula02/2014
464815^72592-2885375Lelio R Paula11/2015
46492^283604-5869585374Lelio R Paula09/2013
4650(44*10^85370-503)/985371Robert Price10/2017
4651496^31671+31671^49685369Norbert Schneider07/2017
4652(15*2^283583-1)/10305185364Lelio R Paula02/2014
465315^72572+9285352Lelio R Paula11/2015
46542^283473-161585334Lelio R Paula09/2013
46552^283466-1585332Lelio R Paula08/2012
465611^81916-702085307Enzo Doria02/2013
46576^109626-785306Lelio R Paula11/2014
46582^283374-11032785305Enzo Doria05/2014
465933*10^85297+785299Robert Price07/2016
466018^67933+4185275Lelio R Paula11/2015
46612^283271-10934185274Enzo Doria04/2014
4662(25*10^85249-73)/385250Robert Price09/2016
46632*5^121959+385246Lelio R Paula10/2014
466419834^19834+894785235Henri Lifchitz11/2004
46652^283140+191585234Lelio R Paula09/2013
46663*10^85227-9785228Robert Price08/2017
4667(16*10^85221-31)/385222Robert Price03/2016
46682^283083+186938385217Enzo Doria05/2016
4669(24737*2^283051+1)/1785211Lelio R Paula06/2014
4670(2^283032+78557)/385201Lelio R Paula01/2013
46712^283026-10989385200Enzo Doria04/2014
4672(2^283012+78557)/12985193Lelio R Paula01/2013
4673(10^(2*42589+1)+72*10^42589-1)/985179Robert Price09/2017
46742^282860-10972785150Enzo Doria04/2014
46752^282819+186941385138Enzo Doria05/2016
46763^178428+285132Ray Chandler07/2011
4677(22699*2^282742+1)/7385117Lelio R Paula06/2014
4678(16^70687+5^70687)/2185115Robert Price07/2013
4679(3^178352-2)/785095Lelio R Paula12/2012
468011^81699-279085081Enzo Doria12/2012
46812^282612-9585075Lelio R Paula08/2012
46822^282609-406985074Yves Minet02/2018
468375^45366-285065Lelio R Paula08/2013
46842^282511+6985045Lelio R Paula08/2012
468569^46249+285045Lelio R Paula06/2013
46863^178226+1085036Robert Price10/2013
4687(182*10^85017+43)/985019Robert Price11/2017
4688(14*10^85010+73)/385011Robert Price04/2016
46899*2^282338-784994Lelio R Paula08/2014
4690(9913*2^282330-1)/157800384988Lelio R Paula04/2015
46912^282203+584952Lelio R Paula08/2012
46922^282184+1384946Lelio R Paula08/2012
469311^81568-240084945Enzo Doria12/2012
469411^81562-234084939Enzo Doria12/2012
4695(41*10^84927+31)/984928Robert Price05/2015
4696(2*10^84904-17)/384904Robert Price08/2014
4697(4^141017+23)/384901Robert Price02/2017
46986^109100-1865384897Enzo Doria03/2013
46992^281973+102584883Lelio R Paula09/2013
47002^281951-10965184876Enzo Doria04/2014
470111^81491-543084865Enzo Doria01/2013
4702((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
47032^281825-186148384838Enzo Doria03/2016
47042^281809-9730584833Lelio R Paula09/2013
47052^281780-11489384825Enzo Doria05/2015
47063^177719+6484794Lelio R Paula12/2015
47082^281675-19984793Lelio R Paula08/2012
47072^281673-11122384793Enzo Doria05/2014
4709(4*10^84779+149)/984779Robert Price03/2017
4710(72*10^84772-27)/984773Ray Chandler01/2011
471111^81398-63084768Enzo Doria11/2012
4712(25*2^281577-1)/2384764Lelio R Paula02/2014
47132^281500-45584740Yves Minet03/2012
471410^84725+114514191984726Marisa Kirisame03/2015
471510^84725+14204184726Patrick De Geest10/2015
471610^84725-13867784725Patrick De Geest02/2016
471776^45044+7584720Norbert Schneider02/2015
471854^48897-5384709Norbert Schneider08/2014
4719(9913*2^281377-1)/6584706Lelio R Paula04/2015
4720Phi(171124,10)/29946701/7761329021/5856034404184700Maksym Voznyy11/2015
47212^281337-11122384691Enzo Doria05/2014
47222^281308+5461584683Lelio R Paula09/2013
47237*5^121144-684677Lelio R Paula10/2014
4724(2^281252+47)/384665Lelio R Paula01/2013
472511^81297-315084663Enzo Doria12/2012
47262^281208-30384653Yves Minet02/2012
4727197^36892-284648Lelio R Paula10/2017
4728(21*2^281187+1)/248384644Lelio R Paula01/2013
472911^81247-8484611Lelio R Paula10/2015
473017^68747-6484590Lelio R Paula11/2015
47315^121018-1559684588Enzo Doria02/2013
47326^108702+784587Lelio R Paula11/2014
473310^84582+10067784583Patrick De Geest05/2016
473410^84582-800184582Robert Price03/2016
47353*5^121004-884579Lelio R Paula10/2014
47365^120996-8484573Lelio R Paula10/2015
4737(10223*2^280881+1)/6841984553Lelio R Paula06/2014
47382^280852+9768184545Yves Minet08/2004
47392^280848-120384544Lelio R Paula09/2013
47405^120946-2484538Lelio R Paula10/2015
47412^280810-211184533Yves Minet08/2013
474211^81161-516084521Enzo Doria01/2013
47432^280737-9384511Lelio R Paula08/2012
47442^280698+31584499Lelio R Paula09/2013
47453^177099-34084498Lelio R Paula12/2015
4746(5*10^84469-107)/384470Robert Price01/2017
4747(3^177002+7)/669602227216174484436Lelio R Paula12/2012
4748(2^280500-1017)/82384436Lelio R Paula01/2013
474914^73660-584424Lelio R Paula11/2015
4750(19*10^84409-61)/384410Robert Price04/2017


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: April, 22 2018 09:48 (Time in France)

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