PRP Records

Probable Primes Top 10000

(201620 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*10^85703+1185704Robert Price11/2017
4502(6883*2^284668-1)/385697Lelio R Paula04/2015
450320^65855+8385680Lelio R Paula01/2016
45046^110105+5385679Lelio R Paula12/2015
4505(10^85666-97)/385666Robert Kinser10/2017
45062^284567-760585664Lelio R Paula09/2013
45079*5^122555-285664Lelio R Paula10/2014
45085^122554-1485662Lelio R Paula10/2015
45099*5^122543+485655Lelio R Paula10/2014
45103^179489-2^(179489-1)85639Robert Price01/2016
45112^284429+17785622Lelio R Paula08/2012
45122*3^179452+585621Lelio R Paula07/2014
4513(19^66919+3^66919)/2285572Robert Price07/2013
451466^47023-6585561Norbert Schneider11/2014
45156^109943+1385553Lelio R Paula12/2015
4516(2^284167-509203)/3456477585536Lelio R Paula01/2013
45172^284133-385533M. Frind & P. Underwood07/2002
45182^284113+31585527Lelio R Paula09/2013
4519(28*10^85500+149)/385501Robert Price10/2017
4520(16*10^85495-19)/385496Robert Price03/2016
45212^284004+17785494Lelio R Paula08/2012
4522(16*10^85473-91)/385474Robert Price06/2016
45233^179120+2285462Robert Price12/2013
45242^283872-279224985454Enzo Doria03/2016
4525(29*10^85438+259)/985439Robert Price04/2017
45262^283817+8287585438Lelio R Paula09/2013
4527(2^283815-5)/20185435Lelio R Paula01/2013
45282^283796-12585432Lelio R Paula08/2012
4529(29*2^283784-1)/1385428Lelio R Paula02/2014
453015^72592-2885375Lelio R Paula11/2015
45312^283604-5869585374Lelio R Paula09/2013
4532(44*10^85370-503)/985371Robert Price10/2017
4533496^31671+31671^49685369Norbert Schneider07/2017
4534(15*2^283583-1)/10305185364Lelio R Paula02/2014
453515^72572+9285352Lelio R Paula11/2015
45362^283473-161585334Lelio R Paula09/2013
45372^283466-1585332Lelio R Paula08/2012
453811^81916-702085307Enzo Doria02/2013
45396^109626-785306Lelio R Paula11/2014
45402^283374-11032785305Enzo Doria05/2014
454133*10^85297+785299Robert Price07/2016
454218^67933+4185275Lelio R Paula11/2015
45432^283271-10934185274Enzo Doria04/2014
4544(25*10^85249-73)/385250Robert Price09/2016
45452*5^121959+385246Lelio R Paula10/2014
454619834^19834+894785235Henri Lifchitz11/2004
45472^283140+191585234Lelio R Paula09/2013
45483*10^85227-9785228Robert Price08/2017
4549(16*10^85221-31)/385222Robert Price03/2016
45502^283083+186938385217Enzo Doria05/2016
4551(24737*2^283051+1)/1785211Lelio R Paula06/2014
4552(2^283032+78557)/385201Lelio R Paula01/2013
45532^283026-10989385200Enzo Doria04/2014
4554(2^283012+78557)/12985193Lelio R Paula01/2013
4555(10^(2*42589+1)+72*10^42589-1)/985179Robert Price09/2017
45562^282860-10972785150Enzo Doria04/2014
45572^282819+186941385138Enzo Doria05/2016
45583^178428+285132Ray Chandler07/2011
4559(22699*2^282742+1)/7385117Lelio R Paula06/2014
4560(16^70687+5^70687)/2185115Robert Price07/2013
4561(3^178352-2)/785095Lelio R Paula12/2012
456211^81699-279085081Enzo Doria12/2012
45632^282612-9585075Lelio R Paula08/2012
456475^45366-285065Lelio R Paula08/2013
45652^282511+6985045Lelio R Paula08/2012
456669^46249+285045Lelio R Paula06/2013
45673^178226+1085036Robert Price10/2013
4568(182*10^85017+43)/985019Robert Price11/2017
4569(14*10^85010+73)/385011Robert Price04/2016
45709*2^282338-784994Lelio R Paula08/2014
4571(9913*2^282330-1)/157800384988Lelio R Paula04/2015
45722^282203+584952Lelio R Paula08/2012
45732^282184+1384946Lelio R Paula08/2012
457411^81568-240084945Enzo Doria12/2012
457511^81562-234084939Enzo Doria12/2012
4576(41*10^84927+31)/984928Robert Price05/2015
4577(2*10^84904-17)/384904Robert Price08/2014
4578(4^141017+23)/384901Robert Price02/2017
45796^109100-1865384897Enzo Doria03/2013
45802^281973+102584883Lelio R Paula09/2013
45812^281951-10965184876Enzo Doria04/2014
458211^81491-543084865Enzo Doria01/2013
4583((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
45842^281825-186148384838Enzo Doria03/2016
45852^281809-9730584833Lelio R Paula09/2013
45862^281780-11489384825Enzo Doria05/2015
45873^177719+6484794Lelio R Paula12/2015
45892^281675-19984793Lelio R Paula08/2012
45882^281673-11122384793Enzo Doria05/2014
4590(4*10^84779+149)/984779Robert Price03/2017
4591(72*10^84772-27)/984773Ray Chandler01/2011
459211^81398-63084768Enzo Doria11/2012
4593(25*2^281577-1)/2384764Lelio R Paula02/2014
45942^281500-45584740Yves Minet03/2012
459510^84725+114514191984726Marisa Kirisame03/2015
459610^84725+14204184726Patrick De Geest10/2015
459710^84725-13867784725Patrick De Geest02/2016
459876^45044+7584720Norbert Schneider02/2015
459954^48897-5384709Norbert Schneider08/2014
4600(9913*2^281377-1)/6584706Lelio R Paula04/2015
4601Phi(171124,10)/29946701/7761329021/5856034404184700Maksym Voznyy11/2015
46022^281337-11122384691Enzo Doria05/2014
46032^281308+5461584683Lelio R Paula09/2013
46047*5^121144-684677Lelio R Paula10/2014
4605(2^281252+47)/384665Lelio R Paula01/2013
460611^81297-315084663Enzo Doria12/2012
46072^281208-30384653Yves Minet02/2012
4608197^36892-284648Lelio R Paula10/2017
4609(21*2^281187+1)/248384644Lelio R Paula01/2013
461011^81247-8484611Lelio R Paula10/2015
461117^68747-6484590Lelio R Paula11/2015
46125^121018-1559684588Enzo Doria02/2013
46136^108702+784587Lelio R Paula11/2014
461410^84582+10067784583Patrick De Geest05/2016
461510^84582-800184582Robert Price03/2016
46163*5^121004-884579Lelio R Paula10/2014
46175^120996-8484573Lelio R Paula10/2015
4618(10223*2^280881+1)/6841984553Lelio R Paula06/2014
46192^280852+9768184545Yves Minet08/2004
46202^280848-120384544Lelio R Paula09/2013
46215^120946-2484538Lelio R Paula10/2015
46222^280810-211184533Yves Minet08/2013
462311^81161-516084521Enzo Doria01/2013
46242^280737-9384511Lelio R Paula08/2012
46252^280698+31584499Lelio R Paula09/2013
46263^177099-34084498Lelio R Paula12/2015
4627(5*10^84469-107)/384470Robert Price01/2017
4628(3^177002+7)/669602227216174484436Lelio R Paula12/2012
4629(2^280500-1017)/82384436Lelio R Paula01/2013
463014^73660-584424Lelio R Paula11/2015
4631(19*10^84409-61)/384410Robert Price04/2017
46322^280388+11784406Lelio R Paula08/2012
46332^280389-56653384406Paul Bourdelais03/2013
4634(141584^16384+1)/6553784390Syoichiro Yamada06/2008
46352^280240-17384361Lelio R Paula08/2012
4636(184*10^84348-1)/384350Robert Price02/2017
46374*10^84346+9384347Robert Price01/2017
46387*2^280156-584337Lelio R Paula08/2014
46398*7^99782-384327Lelio R Paula10/2014
46402^280116+13384324Lelio R Paula08/2012
46412^280118+5461584324Lelio R Paula09/2013
4642(509203*2^280090-1)/384321Lelio R Paula04/2015
46436^108354+4784316Lelio R Paula12/2015
464410^84305+14196384306Patrick De Geest07/2013
464510^84305-5784305Robert Price05/2011
46469^88339+3*8^88339-2*4^88339-3*2^8833984297Mike Oakes01/2011
46473^176648-11280484283Enzo Doria06/2014
46486^108310+11584282Lelio R Paula12/2015
4649(11*2^279968-1)/584280Lelio R Paula02/2014
46506^108288-1664384265Enzo Doria02/2013
46512^279917-5869584264Lelio R Paula08/2013
465265^46477+3684259Lelio R Paula01/2016
46532^279866-190784249Yves Minet05/2013
4654(3^176580-5)/2807684246Lelio R Paula12/2012
4655(p(17530)#+4)/284246Robert Price09/2017
4656(2*10^84239+1)/384239Serge Batalov07/2009
465718^67103-4184233Lelio R Paula11/2015
465820^64743-4384233Lelio R Paula01/2016
4659143^39070+39070^14384209Serge Batalov05/2014
466011^80857-540084204Enzo Doria01/2013
4661(13*10^84179+161)/384180Robert Price04/2017
46622^279634-11040584179Enzo Doria05/2014
4663(74*10^84170+313)/984171Robert Price11/2017
46642^279582-101784163Lelio R Paula08/2013
4665(22*10^84159-19)/384160Robert Price02/2017
4666p(17513)#/2+51284156Robert Price05/2017
4667(19*10^84144-43)/384145Robert Price10/2017
4668(9*2^279507-1)/13784139Lelio R Paula02/2014
466911^80792-81084137Enzo Doria11/2012
4670(97*10^84134-1)/384136Serge Batalov12/2014
4671p(17507)#/2+3284125Robert Price12/2016
467221485^8224+8224^2148584116Hans Havermann04/2017
46733^176294-34084114Lelio R Paula12/2015
4674(3^176287+4)/219184107Lelio R Paula12/2012
46752^279388-71984105Yves Minet05/2012
4676(22699*2^279378+1)/22184104Lelio R Paula06/2014
46772^279332-11044784088Enzo Doria05/2014
46782^279320+784084Lelio R Paula06/2012
4679127^39966-284081Lelio R Paula10/2017
4680(11*2^279240-1)/9584059Lelio R Paula02/2014
46812^279218-11134784053Enzo Doria05/2014
468235^54435+284052Lelio R Paula05/2013
4683(31*2^279191-1)/1251152384040Lelio R Paula02/2014
468420996^10059+10059^2099684038Hans Havermann05/2017
468597*10^84033-384035Robert Price01/2017
468621234^9067+9067^2123484033Hans Havermann05/2017
46872^279095-10971784016Enzo Doria04/2014
468814^73282-9983991Lelio R Paula11/2015
468921457^8200+8200^2145783979Hans Havermann06/2017
469089*10^83976-783978Robert Price03/2017
46912^278955+17383974Lelio R Paula06/2012
4692(7*2^278851+1)/3983942Lelio R Paula12/2012
4693(9913*2^278844-1)/4080383940Lelio R Paula04/2015
46945^120076-1484683930Enzo Doria02/2013
4695(85*10^83921-1)/383923Robert Price07/2017
4696(2^278770-3)/2383917Lelio R Paula12/2012
4697(10^83916+449)/983916Serge Batalov12/2014
46982^278715+9983902Lelio R Paula06/2012
469940235!2-2^4023583899Robert Price09/2015
47002^278698-17183897Lelio R Paula06/2012
4701(19*10^83894-43)/383895Robert Price10/2017
47026^107802+2583887Lelio R Paula12/2015
47038*10^83880+3983881Robert Price01/2017
4704(58*10^83878+23)/983879Robert Price09/2015
47057^99244-9083871Lelio R Paula10/2015
47062^278554+425783854Lelio R Paula08/2013
47072^278504-10961983839Enzo Doria04/2014
47082^278499+187043383837Enzo Doria05/2016
4709105^41475+10483829Norbert Schneider11/2016
471015^71276-6883828Lelio R Paula11/2015
47112^278464-21641383827Enzo Doria04/2013
4712(76*10^83816-211)/983817Robert Price10/2017
4713(8*10^83811-101)/383812Robert Price10/2017
47142^278400+4075583807Lelio R Paula08/2013
4715(9*2^278381-1)/783802Lelio R Paula02/2014
47163*9^87813+6^87813+2*4^8781383796Mike Oakes12/2010
471719551^19268+19268^1955183773Hans Havermann05/2017
471820625^11522+11522^2062583770Hans Havermann05/2017
4719(44*10^83768-791)/983769Robert Price10/2017
4720(87^43189+1)/8883764Paul Bourdelais08/2017
47212^278235-4983758Lelio R Paula06/2012
472223543^3610+3610^2354383755Hans Havermann05/2017
472418^66711-9183741Lelio R Paula11/2015
47234*10^83740-8983741Robert Price08/2017
4725(3*2^278172-1)/1183738Lelio R Paula02/2014
4726(15*29^57251+2561)/2883724Curtis Bright05/2015
47274*7^99059-983716Lelio R Paula10/2014
4728(2^278128-3)/12684472414983714Lelio R Paula12/2012
47292^278077+186721183710Enzo Doria03/2016
47302^278059-2783705Lelio R Paula06/2012
4731214^35917+35917^21483702Norbert Schneider12/2014
4732(23*10^83693+7)/383694Robert Price10/2015
473385^43375-283689Lelio R Paula09/2013
47345*3^175360+483669Lelio R Paula07/2014
4735(23^61441-1)/2283665Robert Price01/2012
473620091^14596+14596^2009183664Hans Havermann03/2017
47372^277907-11062983659Enzo Doria05/2014
473819522^19283+19283^1952283656Hans Havermann04/2017
47398*5^119664-383643Lelio R Paula10/2014
47408*3^175299-783640Lelio R Paula07/2014
4741(26*10^83638-413)/983639Robert Price10/2017
47423^175250+2283616Robert Price12/2013
474411^80285+3083609Lelio R Paula10/2015
474326870^1293+1293^2687083609Hans Havermann03/2017
47452^277691+187442383594Enzo Doria06/2016
474613^75022-6083571Lelio R Paula11/2015
474714^72905-5183559Lelio R Paula11/2015
4748(17*2^277565-1)/54383554Lelio R Paula02/2014
47495^119532-1283550Lelio R Paula10/2015
47506^107358-1625383541Enzo Doria02/2013


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: January, 21 2018 09:45 (Time in France)

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