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 ?
87512^169555-15951042Lelio R Paula01/2011
875291^26054-251041Lelio R Paula08/2013
8753Phi(101775,10)/162840151034Makoto Kamada05/2015
875497*10^51027-351029Robert Price01/2017
87552^169499-264751025Yves Minet07/2014
87565*6^65567+751022Lelio R Paula09/2014
875714763^2858+2858^1476351022Hans Havermann08/2015
875824^36966-147751021Enzo Doria03/2013
8759(78557*2^169464+1)/16052751014Lelio R Paula06/2014
8760(34*10^51008-43)/951009Ray Chandler09/2010
876110^51004+12842751005Patrick De Geest08/2009
876310^51004-11351004Milton L. Brown12/2008
876210^51003+1695151004Patrick De Geest08/2009
876410^51003-7960151003Milton L. Brown12/2008
876510^51003-8083151003Milton L. Brown12/2008
876610^51002+887751003Patrick De Geest08/2009
876810^51002-1054151002Milton L. Brown11/2008
876710^51001+5205151002Patrick De Geest08/2009
876910^51001-15868751001Milton L. Brown10/2008
87702*10^51000+9351001Robert Price07/2016
8772(2^169416+5)/350999Lelio R Paula01/2012
8773(49*10^50998+41)/950999Robert Price07/2015
877113292^6867+6867^1329250999Hans Havermann02/2016
8774(35*10^50997-71)/950998Robert Price05/2015
877529^34871-28^3487150996Robert Price09/2012
877676^27112-7550993Norbert Schneider11/2012
8777(12451^12451+1345)/2^2/19/89/139/697750980Makoto Morimoto07/2016
877810736^12645-12645^1073650971Norbert Schneider12/2016
8780(1017*2^169315-1)/971550968Lelio R Paula03/2015
87797^60309-6^(60309+1)50968Robert Price06/2016
87822^169267+9950955Lelio R Paula07/2009
87815*2^169264+350955Lelio R Paula02/2014
8783t(192517)50950Robert Price08/2014
878410^50943+62445150944Robert Price03/2015
878510^50943+5440950944Patrick De Geest02/2016
878610^50943-10055950943Patrick De Geest03/2016
87872^169206-364550937Lelio R Paula05/2009
87882^169196-11257750934Enzo Doria06/2014
878920^39146-348350931Enzo Doria03/2013
879010^50929+1684950930Patrick De Geest01/2012
879210^50929-5150929Robert Price05/2011
87917^60264+4850929Lelio R Paula10/2012
87932^169167+129950925Lelio R Paula05/2009
879410103^12717-10050925Enzo Doria07/2012
87953^106721-13050919Lelio R Paula07/2012
879718225^622+622^1822550917Anatoly F. Selevich11/2006
8796(10223*2^169138+1)/111350917Lelio R Paula05/2014
87987*2^169125+950913Lelio R Paula02/2014
8799(47*2^169123+1)/2950912Lelio R Paula03/2015
880020^39131+9350911Lelio R Paula01/2013
8801(21*27^35567-94921)/2650910Curtis Bright05/2015
8802(7*2^169124-1)/954950909Lelio R Paula01/2014
8803(12433^12433+809)/2/3/1150907Makoto Morimoto07/2016
880413693^5212+5212^1369350897Hans Havermann02/2016
88057*5^72813+650895Lelio R Paula09/2014
88063^106656-1202850888Enzo Doria02/2013
8807(2^169028+3)/25950881Lelio R Paula01/2012
88082^169000-112750875Yves Minet05/2013
880919^39780+1650869Lelio R Paula01/2013
8810(19*2^168960+1)/550863Lelio R Paula07/2012
8811(-lucasV(1,2,337937)-2)/(3^2*11)50863Mike Oakes02/2017
881311^48840+4650862Lelio R Paula01/2013
8812(5*10^50861-107)/350862Robert Price01/2017
881420^39087-420350854Enzo Doria03/2013
8815(12421^12421+1339)/2^4/5/43/15750848Makoto Morimoto07/2016
88162^168907-54444750847Paul Bourdelais11/2012
881719312^429+429^1931250839Anatoly F. Selevich12/2006
88185^72716-1322650827Enzo Doria02/2013
88192^168823+102550821Lelio R Paula01/2009
88207*10^50818-8950819Robert Price01/2017
88222^168811+15015*16881150818Henri Lifchitz02/2005
88212^168813-283350818Yves Minet09/2014
8823(12413^12413+3221)/2/8950816Makoto Morimoto07/2016
88242^168795+538550813Lelio R Paula05/2009
88254*3^106483+550806Lelio R Paula03/2014
882613^45606+450803Lelio R Paula01/2013
882713^45606-3850803Lelio R Paula01/2013
88282^168746+5890550798Lelio R Paula05/2009
8829(16*10^50795-43)/950796Robert Price02/2015
8830gcd(V(615445),5*F(123089)*(F(123089)-1)+1)50794Serge Batalov04/2015
88317*10^50789-4750790Robert Price02/2017
88322^168717-72952350789Paul Bourdelais11/2012
8833(12409^12409+136)/5^2/13/5647/47327950788Makoto Morimoto07/2016
8834(21*2^168652-1)/21550769Lelio R Paula01/2014
88352^168629+1290950763Lelio R Paula01/2011
88369328^12787+12787^932850762Norbert Schneider01/2016
88372^168627+7311350762Enzo Doria04/2016
88382^168623+4733350761Yves Minet02/2010
8839(12401^12401+154)/3^2/5/31/59/67/97/761/863/1214350745Makoto Morimoto07/2016
8840(lucasV(1,2,337126)+2)/(5*11)50739Mike Oakes02/2017
8841(17^41221+1)/1850720Paul Bourdelais03/2010
884210^50711+750712Jason Earls12/2007
884310^50711-31796950711Patrick De Geest04/2009
8845(17^41213+3^41213)/2050710Robert Price08/2013
8844(12391^12391+58)/59/211/782350710Makoto Morimoto07/2016
88472^168431-15950703Lelio R Paula01/2011
8846(7*10^50702-1)/350703Erik Branger03/2014
8848117216#-p(117216)50700Henri Lifchitz03/2007
8849(1543550^8192+1)/6553750692Syoichiro Yamada06/2008
8850(13*2^168352-1)/47750678Lelio R Paula01/2014
88518*10^50675+3950676Robert Price01/2017
8852(lucasV(1,2,336840)+2)/(113*337*23609*70589*125621*144481)50676Mike Oakes02/2017
885314415^3274+3274^1441550670Hans Havermann05/2016
8854(12379^12379+282)/1750663Makoto Morimoto07/2016
88565^72480-1712650662Enzo Doria02/2013
8855(34*10^50667-7)/9/3^3/13627750662Makoto Morimoto04/2016
88573^106143+250644Mike Oakes11/2009
88589178^12777-12777^917850633Norbert Schneider02/2017
8859(2*10^50603-41)/350603Robert Price01/2017
8860(12^46889-1)/1150601Paul Bourdelais09/2008
88612^168068-189350594Yves Minet09/2012
88622^168057+841550591Lelio R Paula11/2011
88634*10^50579+950580Robert Price05/2015
88642^168019-9439550579Lelio R Paula07/2011
88652^168019+7421350579Enzo Doria04/2016
88663^106002+7050576Lelio R Paula07/2012
88675*2^167970-950565Lelio R Paula02/2014
8868(58*10^50558-13)/950559Robert Price09/2015
886988*10^50547+750549Robert Price11/2016
88702^167910-11262550546Enzo Doria06/2014
8871(1476500^8192+1)/6553750534Syoichiro Yamada06/2008
88722^167866+1171550533Lelio R Paula05/2009
8873gcd(V(621415),5*F(124283)*(F(124283)+1)+1)50528Serge Batalov04/2015
88742^167847-13550527Lelio R Paula01/2011
8875-lucasV(-1,2,335684)50526Mike Oakes01/2017
8876(-lucasV(1,2,335677)+2)/(3*226777)50519Mike Oakes02/2017
8877(12347^12347+1567)/2/3^2/550517Makoto Morimoto07/2016
88792^167807+7550515Lelio R Paula08/2010
88782^167805+7627750515Enzo Doria04/2016
88808335^12882+12882^833550510Norbert Schneider03/2016
88817*2^167777+950507Lelio R Paula02/2014
888214162^3681+3681^1416250502Hans Havermann05/2016
8883(17*10^50495-11)/350496Robert Price07/2015
88842^167682+8550478Lelio R Paula08/2010
88852^167667-92742750473Paul Bourdelais11/2012
88869737^12654+12654^973750470Norbert Schneider01/2016
8887(9179*2^167644-1)/1750469Lelio R Paula03/2015
888813386^5891+5891^1338650468Hans Havermann05/2016
8889(lucasV(1,2,335347)+2)/(3*5*11*302287*439661)50462Mike Oakes02/2017
88905003^13637-15650447Enzo Doria07/2012
88916^64826-2672350445Enzo Doria03/2013
8892(3^105718+7)/3250439Lelio R Paula03/2012
8893(1436724^8192+1)/6553750437Syoichiro Yamada06/2008
889417^40989+5650435Lelio R Paula01/2013
8895(12329^12329+1652)/42150435Makoto Morimoto07/2016
88962*5^72153+750434Lelio R Paula09/2014
8897(3126^14431-1)/312550433Richard Fischer03/2015
889839^31694+3850428Norbert Schneider05/2014
88992^167460+218750411Lelio R Paula11/2011
8900(12323^12323+2709)/2^450409Makoto Morimoto07/2016
890111^48400-771050404Enzo Doria02/2013
89022^167432+5461550403Lelio R Paula05/2009
8903(23*2^167430-1)/416950400Lelio R Paula01/2014
890419^39404+2250389Lelio R Paula01/2013
890535^32629-783450382Enzo Doria03/2013
89066^64744+16350381Lelio R Paula06/2012
8907116447#+17465950381Nicolas PALAU09/2016
89082^167353+12950379Lelio R Paula05/2009
890920^38722-113350379Enzo Doria03/2013
89103^105567-1650369Lelio R Paula07/2012
89112^167321-11284950369Enzo Doria06/2014
8912(28*10^50362-43)/350363Robert Price04/2016
891311421^12410-12410^1142150357Norbert Schneider08/2013
89142^167278-206350356Yves Minet03/2013
8915181^22300+22300^18150347Serge Batalov05/2014
89169932^12595-12595^993250343Norbert Schneider12/2016
89178993^12732-12732^899350342Norbert Schneider02/2017
89183*5^72018-450339Lelio R Paula09/2014
89192^167207-11268750335Enzo Doria06/2014
89206^64674-3750327Lelio R Paula06/2012
89212^167177+7480150326Enzo Doria04/2016
892213739^4600+4600^1373950323Hans Havermann10/2015
892311508^12391+12391^1150850320Norbert Schneider06/2014
89242^167132-216350312Yves Minet08/2013
89257^59527-6250307Lelio R Paula06/2012
8926(310027^9161+1)/31002850302Faysal YAtim04/2008
8927(12301^12301+74)/3^2/5^3/11/17/115150302Makoto Morimoto07/2016
89282^167083-11251950297Enzo Doria06/2014
8929272^20659-20659^27250296Norbert Schneider09/2015
893025337!!-1650290Robert Price06/2015
89319722^12611-12611^972250290Norbert Schneider12/2016
8933(15*2^167013+1)/64950275Lelio R Paula07/2012
893219^39315-1250275Lelio R Paula01/2013
89345^71925-3650274Lelio R Paula06/2012
89352^167002+279913950273Enzo Doria04/2016
893610957^12444-12444^1095750270Norbert Schneider07/2013
89378*10^50253-9950254Robert Price02/2017
89385^71894-5450252Lelio R Paula06/2012
893918^40028-550247Lelio R Paula01/2013
8940(3*2^166904+1)/127950241Lelio R Paula07/2012
894124^36397+2350236Norbert Schneider12/2013
89427984*29^34345+2150230Curtis Bright05/2015
89433^105248-1352850217Enzo Doria02/2013
89446^64532-6550216Lelio R Paula06/2012
89455^71834-2061650210Enzo Doria03/2013
8946(31*2^166778-1)/365150204Lelio R Paula01/2014
89472^166752-11239750198Enzo Doria06/2014
8948(12277^12277+1746)/17/37/15150197Makoto Morimoto07/2016
894911^48199-93050195Enzo Doria11/2012
89503*10^50194-750195Erik Branger11/2013
89519992^12549+12549^999250192Norbert Schneider10/2015
89522^166708+15750185Lelio R Paula01/2011
8953(1338272^8192+1)/6553750184Syoichiro Yamada06/2008
89547*2^166685+350179Lelio R Paula02/2014
89557*2^166671-950174Lelio R Paula02/2014
89569*2^166670+750174Lelio R Paula02/2014
89572^166670-11254150173Enzo Doria06/2014
89582^166657+46550169Lelio R Paula11/2011
895917^40768-2050163Lelio R Paula01/2013
89602^166596-7879550151Lelio R Paula07/2011
8961135^23541+13450151Norbert Schneider04/2015
896224^36335-67350150Enzo Doria03/2013
8963(12269^12269+291)/2^8/5/7/19/41/109/1042634950150Makoto Morimoto07/2016
8964(28*10^50147-97)/350148Robert Price07/2016
8965263^20718-20718^26350137Norbert Schneider09/2015
8966t(167020)50133Robert Price01/2015
8967(12263^12263+1442)/127/547950133Makoto Morimoto07/2016
89682868*(2340*(29023#-29527)*(2340*(29023#-29527)+3)+1)*(2868*(2340*(29023#-29527)*(2340*(29023#-29527)50129Pierre CAMI06/2008
896912^46445-1950123Lelio R Paula12/2012
89702^166501-1459350122Enzo Doria04/2013
8971(31*2^166509-1)/368407750120Lelio R Paula01/2014
89722^166483-16950117Lelio R Paula01/2011
89739^52515+2*6^52515-4^5251550113Mike Oakes04/2010
8974(23*2^166487-1)/3377049950112Lelio R Paula01/2014
89752*5^71689-950109Lelio R Paula09/2014
897613495^5154+5154^1349550096Hans Havermann04/2016
89776^64369-11950089Lelio R Paula06/2012
89789224^12633-12633^922450089Norbert Schneider12/2016
89792^166370-11254150083Enzo Doria06/2014
8980(12253^12253+1454)/3^3/251/947/29242750081Makoto Morimoto07/2016
89812^166339-11232150074Enzo Doria06/2014
89825^71637-2250073Lelio R Paula06/2012
8983Phi(50131,10)/89010999409/9123691040118653/18020045580157867/3062191531806380194750068Maksym Voznyy01/2013
89845^71618-1382650059Enzo Doria02/2013
898515^42563-250058Lelio R Paula11/2012
89861943^15222+15222^194350058Serge Batalov05/2014
898711641^12310+12310^1164150053Norbert Schneider04/2014
898813537!-2^13537+150052Joe McLean06/2006
89892^166227-16446750040Gary Barnes08/2009
899012241^12241+475650039Makoto Morimoto07/2016
8991(106*10^50035-1)/350037Serge Batalov12/2014
899211^48044-81050033Enzo Doria11/2012
899315^42539+8850030Lelio R Paula11/2012
8994524^18397-523^1839750028Jean-Louis Charton10/2009
89952^166159-1449750019Enzo Doria04/2013
89962^166155+8785550018Lelio R Paula01/2009
89972^166138-1165550013Lelio R Paula07/2011
89982^166104-11262550003Enzo Doria06/2014
89992^166100+19901550002Lelio R Paula05/2008
900010^50000+6585950001Milton L. Brown02/2006


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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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