PRP Records

Probable Primes Top 10000

(202632 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 ?
95012^170609-11314351359Enzo Doria07/2014
9502760^17827-759^1782751357Jean-Louis Charton12/2010
9503(22699*2^170592+1)/443551355Lelio R Paula05/2014
95048*7^60767+351355Lelio R Paula09/2014
95055^73452-2064651341Enzo Doria03/2013
95062^170531-23040751335Gary Barnes08/2009
950735^33243-211251330Enzo Doria03/2013
9508(1845768^8192+1)/6553751328Lelio R Paula06/2013
950913^46072+4251322Lelio R Paula01/2013
951014^44778-9551322Lelio R Paula01/2013
951111008^12697+12697^1100851318Norbert Schneider01/2016
9512t(180039)51312Robert Price09/2014
95132^170444-44351309Yves Minet05/2013
9514(-lucasV(1,2,340915)+2)/(340913*4220189*8187163)51294Mike Oakes03/2017
9515(2*10^51285-71)/351285Robert Price01/2017
9516(23*10^51283-47)/351284Robert Price10/2017
9517(1819288^8192+1)/6553751277Lelio R Paula06/2013
95188907^12982-12982^890751276Norbert Schneider06/2017
95195^73350+2851270Lelio R Paula10/2012
95203^107450+251267Mike Oakes11/2009
95212^170296+253351265Henri Lifchitz07/2004
95222^170293+7648151264Enzo Doria05/2016
952311835^12584+12584^1183551257Norbert Schneider11/2015
9524(12511^12511+193)/2^5/3937151256Makoto Morimoto07/2016
952612^47489+47489^1251250Serge Batalov02/2012
952514637^3172+3172^1463751250Hans Havermann04/2016
9527(2^170245+7)/951248Lelio R Paula02/2012
95285^73308-1992651241Enzo Doria03/2013
95298966^12963-12963^896651238Norbert Schneider06/2017
95303*2^170203+551237Lelio R Paula02/2014
95315^73300+4651235Lelio R Paula10/2012
95322^170167+7151226Lelio R Paula01/2011
95332^170140-1507751218Enzo Doria04/2013
953415^43542-4651210Lelio R Paula01/2013
95362^170111-101751209Lelio R Paula06/2008
95354*10^51208-8751209Robert Price03/2017
953714^44679+8351208Lelio R Paula01/2013
953810^51207+10014751208Patrick De Geest06/2016
953910^51207-80151207Robert Price04/2016
9540t(170300)51191Robert Price03/2015
954111966^12553-12553^1196651191Norbert Schneider11/2016
954214670^3083+3083^1467051184Hans Havermann04/2016
954399^25644-9851177Norbert Schneider07/2013
954413211^7468+7468^1321151169Hans Havermann04/2016
9545(2^169969-1017)/3551165Lelio R Paula01/2012
95465*10^51163-751164Dmitry Domanov11/2010
9547(73*10^51162-1)/951163Robert Price01/2015
9548L(244779)+P(244779)51156Robert Price12/2017
9549(22*10^51154+383)/951155Robert Price11/2017
95502^169899+6351145Lelio R Paula05/2009
95512^169898+51351145Lelio R Paula05/2009
95533^107186-1238851141Enzo Doria02/2013
9552(299*10^51139+1)/351141Robert Price11/2017
9554(12487^12487+173)/2^2/3/2917/3463/4448351140Makoto Morimoto07/2016
95553*6^65715-751137Lelio R Paula09/2014
9556116^24768+11551133Norbert Schneider10/2013
955735^33113-402651129Enzo Doria03/2013
9558(13*2^169830-1)/8447751121Lelio R Paula01/2014
9559(46*10^51111-1)/951112Serge Batalov10/2014
956015^43452-3451104Lelio R Paula01/2013
95612^169750-13751100Lelio R Paula01/2011
95622^169739+9406551097Lelio R Paula10/2011
956415^43442-2651092Lelio R Paula01/2013
95655^73096-1700651092Enzo Doria02/2013
956310^51091+7160151092Patrick De Geest07/2017
956610^51091-70151091Robert Price06/2017
9567(-lucasV(1,2,339439)-2)/(79*83)51088Mike Oakes03/2017
95682^169706-27055151087Gary Barnes08/2009
9569(2^169696+5)/2151083Lelio R Paula01/2012
9570(1722520^8192+1)/6553751082Syoichiro Yamada01/2009
957111^49051-876051082Enzo Doria02/2013
9572(24737*2^169672+1)/2751080Lelio R Paula05/2014
9573(14*10^51079+229)/951080Robert Price11/2017
95742^169677+1609551078Lelio R Paula05/2009
95752^169659-13551073Lelio R Paula01/2011
95762^169638-11318351067Enzo Doria07/2014
9577(29*2^169622-1)/234653118551054Lelio R Paula01/2014
9578(10^51054+17)/951054Robert Price10/2014
95798329^13022-13022^832951054Norbert Schneider07/2017
9580(24737*2^169577+1)/551052Lelio R Paula05/2014
958111^49021-7851051Lelio R Paula01/2013
958218^40669+6151051Lelio R Paula01/2013
958314038^4327+4327^1403851045Hans Havermann02/2016
95842^169555-15951042Lelio R Paula01/2011
958591^26054-251041Lelio R Paula08/2013
9586Phi(101775,10)/162840151034Makoto Kamada05/2015
95877559^13158-13158^755951033Norbert Schneider11/2017
958897*10^51027-351029Robert Price01/2017
95892^169499-264751025Yves Minet07/2014
95905*6^65567+751022Lelio R Paula09/2014
959114763^2858+2858^1476351022Hans Havermann08/2015
959224^36966-147751021Enzo Doria03/2013
9593(78557*2^169464+1)/16052751014Lelio R Paula06/2014
9594(34*10^51008-43)/951009Ray Chandler09/2010
959510^51004+12842751005Patrick De Geest08/2009
959710^51004-11351004Milton L. Brown12/2008
959610^51003+1695151004Patrick De Geest08/2009
959810^51003-7960151003Milton L. Brown12/2008
959910^51003-8083151003Milton L. Brown12/2008
960010^51002+887751003Patrick De Geest08/2009
960210^51002-1054151002Milton L. Brown11/2008
960110^51001+5205151002Patrick De Geest08/2009
960310^51001-15868751001Milton L. Brown10/2008
96042*10^51000+9351001Robert Price07/2016
960510^51000+18825151001Patrick De Geest10/2017
960610^51000-3128951000Patrick De Geest10/2017
9609(2^169416+5)/350999Lelio R Paula01/2012
9608(49*10^50998+41)/950999Robert Price07/2015
960713292^6867+6867^1329250999Hans Havermann02/2016
9610(35*10^50997-71)/950998Robert Price05/2015
96116^65536+2*97878-150997Jiahao He05/2017
961229^34871-28^3487150996Robert Price09/2012
961376^27112-7550993Norbert Schneider11/2012
9614(70^27631-1)/6950981Richard Fischer08/2017
9615(12451^12451+1345)/2^2/19/89/139/697750980Makoto Morimoto07/2016
961610736^12645-12645^1073650971Norbert Schneider12/2016
9617(1017*2^169315-1)/971550968Lelio R Paula03/2015
96187^60309-6^(60309+1)50968Robert Price06/2016
96192^169267+9950955Lelio R Paula07/2009
96205*2^169264+350955Lelio R Paula02/2014
9621t(192517)50950Robert Price08/2014
962210^50943+62445150944Robert Price03/2015
962310^50943+5440950944Patrick De Geest02/2016
962410^50943-10055950943Patrick De Geest03/2016
96252^169206-364550937Lelio R Paula05/2009
96262^169196-11257750934Enzo Doria06/2014
962720^39146-348350931Enzo Doria03/2013
962810^50929+1684950930Patrick De Geest01/2012
963010^50929-5150929Robert Price05/2011
96297^60264+4850929Lelio R Paula10/2012
96322^169167+129950925Lelio R Paula05/2009
963110103^12717-10050925Enzo Doria07/2012
96333^106721-13050919Lelio R Paula07/2012
963518225^622+622^1822550917Anatoly F. Selevich11/2006
9634(10223*2^169138+1)/111350917Lelio R Paula05/2014
96367*2^169125+950913Lelio R Paula02/2014
9637(47*2^169123+1)/2950912Lelio R Paula03/2015
963820^39131+9350911Lelio R Paula01/2013
9639(21*27^35567-94921)/2650910Curtis Bright05/2015
9640(7*2^169124-1)/954950909Lelio R Paula01/2014
9641(12433^12433+809)/2/3/1150907Makoto Morimoto07/2016
964213693^5212+5212^1369350897Hans Havermann02/2016
96437*5^72813+650895Lelio R Paula09/2014
96445*10^50890-8150891Robert Price04/2017
96453^106656-1202850888Enzo Doria02/2013
9646(2^169028+3)/25950881Lelio R Paula01/2012
96472^169000-112750875Yves Minet05/2013
964819^39780+1650869Lelio R Paula01/2013
9649(19*2^168960+1)/550863Lelio R Paula07/2012
9650(-lucasV(1,2,337937)-2)/(3^2*11)50863Mike Oakes02/2017
965211^48840+4650862Lelio R Paula01/2013
9651(5*10^50861-107)/350862Robert Price01/2017
965320^39087-420350854Enzo Doria03/2013
9654(12421^12421+1339)/2^4/5/43/15750848Makoto Morimoto07/2016
96552^168907-54444750847Paul Bourdelais11/2012
965619312^429+429^1931250839Anatoly F. Selevich12/2006
96575^72716-1322650827Enzo Doria02/2013
96582^168823+102550821Lelio R Paula01/2009
96597*10^50818-8950819Robert Price01/2017
96612^168811+15015*16881150818Henri Lifchitz02/2005
96602^168813-283350818Yves Minet09/2014
9663(12413^12413+3221)/2/8950816Makoto Morimoto07/2016
96627022^13211-13211^702250816Norbert Schneider12/2017
96642^168795+538550813Lelio R Paula05/2009
96657670^13079-13079^767050810Norbert Schneider09/2017
96664*3^106483+550806Lelio R Paula03/2014
966713^45606+450803Lelio R Paula01/2013
966813^45606-3850803Lelio R Paula01/2013
96692^168746+5890550798Lelio R Paula05/2009
9670(16*10^50795-43)/950796Robert Price02/2015
9671gcd(V(615445),5*F(123089)*(F(123089)-1)+1)50794Serge Batalov04/2015
96727*10^50789-4750790Robert Price02/2017
96732^168717-72952350789Paul Bourdelais11/2012
9674(12409^12409+136)/5^2/13/5647/47327950788Makoto Morimoto07/2016
9675(21*2^168652-1)/21550769Lelio R Paula01/2014
96762^168629+1290950763Lelio R Paula01/2011
96779328^12787+12787^932850762Norbert Schneider01/2016
96782^168627+7311350762Enzo Doria04/2016
96792^168623+4733350761Yves Minet02/2010
9680(8*10^50750-101)/350751Robert Price10/2017
9681(12401^12401+154)/3^2/5/31/59/67/97/761/863/1214350745Makoto Morimoto07/2016
9682(lucasV(1,2,337126)+2)/(5*11)50739Mike Oakes02/2017
96833*10^50727-3150728Robert Price10/2017
96848544^12901-12901^854450723Norbert Schneider05/2017
9685(17^41221+1)/1850720Paul Bourdelais03/2010
968610^50711+750712Jason Earls12/2007
968710^50711-31796950711Patrick De Geest04/2009
9688(17^41213+3^41213)/2050710Robert Price08/2013
9689(12391^12391+58)/59/211/782350710Makoto Morimoto07/2016
969047779!4+102450708Robert Price08/2017
96912^168431-15950703Lelio R Paula01/2011
9692(7*10^50702-1)/350703Erik Branger03/2014
9693117216#-p(117216)50700Henri Lifchitz03/2007
9694(1543550^8192+1)/6553750692Syoichiro Yamada06/2008
9695(13*2^168352-1)/47750678Lelio R Paula01/2014
96968*10^50675+3950676Robert Price01/2017
9697(lucasV(1,2,336840)+2)/(113*337*23609*70589*125621*144481)50676Mike Oakes02/2017
969814415^3274+3274^1441550670Hans Havermann05/2016
9699(12379^12379+282)/1750663Makoto Morimoto07/2016
97015^72480-1712650662Enzo Doria02/2013
9700(34*10^50667-7)/9/3^3/13627750662Makoto Morimoto04/2016
97023^106143+250644Mike Oakes11/2009
97039178^12777-12777^917850633Norbert Schneider02/2017
9704(2*10^50603-41)/350603Robert Price01/2017
9705(12^46889-1)/1150601Paul Bourdelais09/2008
97062^168068-189350594Yves Minet09/2012
97072^168057+841550591Lelio R Paula11/2011
97084*10^50579+950580Robert Price05/2015
97092^168019-9439550579Lelio R Paula07/2011
97102^168019+7421350579Enzo Doria04/2016
9711(47*10^50578+493)/950579Robert Price11/2017
97123^106002+7050576Lelio R Paula07/2012
97135*2^167970-950565Lelio R Paula02/2014
9714(58*10^50558-13)/950559Robert Price09/2015
971588*10^50547+750549Robert Price11/2016
97162^167910-11262550546Enzo Doria06/2014
9717(1476500^8192+1)/6553750534Syoichiro Yamada06/2008
97182^167866+1171550533Lelio R Paula05/2009
9719gcd(V(621415),5*F(124283)*(F(124283)+1)+1)50528Serge Batalov04/2015
97202^167847-13550527Lelio R Paula01/2011
9721-lucasV(-1,2,335684)50526Mike Oakes01/2017
9722(-lucasV(1,2,335677)+2)/(3*226777)50519Mike Oakes02/2017
9723(12347^12347+1567)/2/3^2/550517Makoto Morimoto07/2016
97252^167807+7550515Lelio R Paula08/2010
97242^167805+7627750515Enzo Doria04/2016
97268335^12882+12882^833550510Norbert Schneider03/2016
97277*2^167777+950507Lelio R Paula02/2014
972814162^3681+3681^1416250502Hans Havermann05/2016
9729(17*10^50495-11)/350496Robert Price07/2015
97302^167682+8550478Lelio R Paula08/2010
97312^167667-92742750473Paul Bourdelais11/2012
97329737^12654+12654^973750470Norbert Schneider01/2016
9733(9179*2^167644-1)/1750469Lelio R Paula03/2015
973413386^5891+5891^1338650468Hans Havermann05/2016
9735(10^50467-97)/350467Robert Kinser10/2017
9736(lucasV(1,2,335347)+2)/(3*5*11*302287*439661)50462Mike Oakes02/2017
97375003^13637-15650447Enzo Doria07/2012
97386^64826-2672350445Enzo Doria03/2013
9739(3^105718+7)/3250439Lelio R Paula03/2012
9740(1436724^8192+1)/6553750437Syoichiro Yamada06/2008
974117^40989+5650435Lelio R Paula01/2013
9742(12329^12329+1652)/42150435Makoto Morimoto07/2016
97432*5^72153+750434Lelio R Paula09/2014
9744(3126^14431-1)/312550433Richard Fischer03/2015
97458078^12907-12907^807850432Norbert Schneider05/2017
974639^31694+3850428Norbert Schneider05/2014
9747(7*10^50414-151)/950414Robert Price09/2017
97482^167460+218750411Lelio R Paula11/2011
9749(12323^12323+2709)/2^450409Makoto Morimoto07/2016
975011^48400-771050404Enzo Doria02/2013


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: February, 20 2018 10:36 (Time in France)

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