PRP Records

Probable Primes Top 10000

(247113 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 ?
825110^60776+360777Robert Price01/2011
825210^60776-1481960776Patrick De Geest12/2012
825355*10^60772+760774Robert Price10/2017
8254(6883*2^201869-1)/3560771Lelio R Paula04/2015
8255(27*2^201841-1)/4360760Lelio R Paula01/2014
82562^201822-17760755Lelio R Paula08/2011
8257(13*10^60744+17)/360745Robert Price06/2015
8258(31*2^201754-1)/9960734Lelio R Paula01/2014
8259(26*10^60717-71)/960718Robert Price03/2015
826037^38712-260709Lelio R Paula08/2013
82612^201657-11200360705Enzo Doria05/2014
8262(10^60703+3^60703)/1360702Robert Price01/2013
82632^201622-11281760695Enzo Doria06/2014
82642^201620-1717760694Enzo Doria05/2013
8265(2^201615-3)*6-760693Gilbert Mozzo05/2016
82662^201609-4978960691Henri Lifchitz03/2005
82672^201582-1906160683Enzo Doria05/2013
826843316!3+2760679Robert Price09/2014
8269(509203*2^201564-1)/506760679Lelio R Paula04/2015
82702^201560+10560676Lelio R Paula08/2011
8271(27*2^201584-1)/64675548645760673Lelio R Paula01/2014
82722^201545-1802160672Enzo Doria05/2013
82732^201543+1171560671Lelio R Paula09/2011
82742^201512-11175560662Enzo Doria05/2014
8275p(13013)#/2+6460662Robert Price03/2017
827611^58248+1660660Lelio R Paula05/2013
82772^201496-2760657Lelio R Paula08/2011
82785*10^60655+5760656Robert Price11/2017
8279(7*10^60643+197)/360644Robert Price07/2017
82802^201426-1609760636Enzo Doria04/2013
8281(17*10^60631-11)/360632Robert Price07/2015
82826^77916-7760631Lelio R Paula04/2013
8283(27*2^201410-1)/49160630Lelio R Paula01/2014
82845^86727+9860620Lelio R Paula04/2013
828517^49266-2660620Lelio R Paula05/2013
828620^46589-3360614Lelio R Paula05/2013
82876^77889+6560610Lelio R Paula04/2013
8288139901#+14838760595Nicolas PALAU09/2016
82892^201285-11172360593Enzo Doria05/2014
829046199*2^201268+12964760593Paul Vanderveen11/2016
82923^126991-10060591Lelio R Paula04/2013
82912^201278-11162360591Enzo Doria05/2014
82935^86682-1600460589Enzo Doria05/2014
8294(865*10^60583-1)/960585Robert Price11/2017
8295(58*10^60579+221)/960580Robert Price02/2017
82969*2^201231-560578Lelio R Paula04/2014
82974*10^60572-8960573Robert Price08/2017
8298(78557*2^201207+1)/1306760571Lelio R Paula06/2014
82992^201186-6694560564Lelio R Paula09/2011
83002^201186-9439560564Lelio R Paula09/2011
830165^33403+3260557Lelio R Paula01/2016
8302103^30079+10260545Norbert Schneider10/2016
8303(1000159^10091+1)/100016060541Faysal YAtim08/2008
83042^201098-1771760537Enzo Doria05/2013
8305(3^126881+8)/482960534Lelio R Paula03/2012
83062^201074+7504960530Enzo Doria04/2016
830711^58111-129060517Enzo Doria11/2012
8308(509203*2^201012-1)/960516Lelio R Paula04/2015
83092^200911+571160481Lelio R Paula10/2011
8310(2^200912-3)/2360480Lelio R Paula03/2012
831118^48179-17^4817960478Jean-Louis Charton12/2010
831338^38281-37^3828160476Robert Price09/2012
83124*7^71560-360476Lelio R Paula09/2014
8314(10^(2*30232+1)+15*10^30232-1)/360465Robert Price04/2016
8315lucasV(1,2,401712)+260464Mike Oakes01/2017
83162^200833-1849360457Enzo Doria05/2013
831720^46465-504360453Enzo Doria03/2013
83182^200810-1825760450Enzo Doria05/2013
8319((2)^(2*100400-1)+(2)^(100400-1)+1)+2667260447Faysal YAtim04/2018
83205^86466-1433660438Enzo Doria02/2013
8321Phi(145558,10)/103928413/161714939/14779231531/36075385837/24241141985360432Maksym Voznyy10/2011
8322(29*2^200703-1)/23160417Lelio R Paula01/2014
83232^200682-101683160412Paul Bourdelais11/2012
83242^200617-1788160392Enzo Doria05/2013
8325(25^43201+1)/2660391Robert Price06/2013
83272^200609-13360390Lelio R Paula08/2011
83262^200608-1283760390Enzo Doria10/2012
83282^200607-1712160389Enzo Doria05/2013
832911^57975-162060375Enzo Doria11/2012
8330(9913*2^200538-1)/380160369Lelio R Paula04/2015
83315^86342+6460351Lelio R Paula04/2013
8332(14*10^60346-23)/960347Robert Price04/2015
83332^200457-829560344Lelio R Paula09/2011
83346^77546+11360343Lelio R Paula04/2013
833637^38461-36^3846160315Robert Price06/2012
83352^200361-1759360315Enzo Doria05/2013
833710103^15059-10660304Enzo Doria07/2012
83382^200301-1740160297Enzo Doria05/2013
8339(37*10^60290+71)/960291Robert Price04/2015
83402^200266-9439560287Lelio R Paula09/2011
83412^200261-11161360285Enzo Doria05/2014
834246^36238-4560256Norbert Schneider07/2014
834313^54091+9460255Lelio R Paula05/2013
8344311^24171-15460253Enzo Doria07/2012
83452^200120-8108960243Paul Bourdelais01/2012
83463^126262+868060243Lelio R Paula04/2013
834743031!3-5904960239Robert Price12/2015
83482^200100-11126960237Enzo Doria05/2014
8349(29*2^200069-1)/537360225Lelio R Paula01/2014
835020^46283-192360216Enzo Doria03/2013
83512^200011-11207560210Enzo Doria05/2014
83522^200002+7453960207Enzo Doria04/2016
8353(38602791*2^200026-1)/(577849*2645749*3427009)60203Jens K. Andersen09/2007
8354(28*10^60180+149)/360181Robert Price10/2017
83552^199872+9360168Donovan Johnson06/2008
83566^77321+7760168Lelio R Paula04/2013
8357(86*10^60165-77)/960166Robert Price05/2016
8358(2^199868+78557)/2337360162Lelio R Paula05/2012
83597^71180+8260155Lelio R Paula04/2013
83612^199814-11229560151Enzo Doria06/2014
8360(51^35227-1)/5060151Paul Bourdelais08/2017
836242964!3-8160135Robert Price09/2014
83632^199709-5160119Lelio R Paula05/2011
83642^199700-11162360116Enzo Doria05/2014
8365(15185*2^199681-1)/15960112Lelio R Paula04/2015
83662^199672+253360108Henri Lifchitz09/2004
836720^46198-1160105Lelio R Paula04/2013
83682^199657+9325760103Yves Minet03/2010
83693^125967-11060102Lelio R Paula10/2012
83702^199654-1881360102Enzo Doria05/2013
8371(29*10^60100+19)/360101Robert Price01/2017
83722^199615-2*199615+160091Robert Price04/2018
8373129^28468+28468^12960085Serge Batalov05/2014
83742^199572-1587360078Enzo Doria04/2013
83759*2^199559+760075Lelio R Paula03/2014
83762^199527-11191960064Enzo Doria05/2014
83772^199522+8287560063Lelio R Paula10/2012
83785^85928-7260062Lelio R Paula10/2012
837939^37749+3860062Norbert Schneider05/2014
83806^77182-14360060Lelio R Paula10/2012
83812^199502-214560057Lelio R Paula06/2011
83822^199493+425760054Lelio R Paula06/2011
83832^199488+4075560052Lelio R Paula06/2011
8384(2^199451+9)/2561960037Lelio R Paula02/2012
83852^199425-6160033Lelio R Paula05/2011
8386(85*10^60026+23)/960027Robert Price11/2015
838765^33107+6260021Lelio R Paula01/2016
83882^199362-121560014Lelio R Paula06/2011
83892^199362-11163360014Enzo Doria05/2014
83901537^18832+18832^153760012Serge Batalov05/2014
83912^199324-1743360003Enzo Doria05/2013
839310^60000+20433160001Milton L. Brown04/2006
839410^60000+8712960001Milton L. Brown04/2006
8392143^27838-260001Lelio R Paula10/2017
839510^59999+6519760000Patrick De Geest04/2005
840910^60000-3252960000Patrick De Geest08/2009
8410(10^60000+2249)/960000Makoto Morimoto09/2016
8411((2^43112609)/10^24296)%10^6000060000Michael Vang10/2016
8412(2^57885161/10^105090)%10^6000060000Michael Vang10/2016
8413(2^42643801/10^58945)%10^6000060000Michael Vang10/2016
8396(2^37156667/10^243655)%10^6000060000Michael Vang10/2016
8397(2^30402457/10^69028)%10^6000060000Michael Vang11/2016
8398(2^32582657/10^248088)%10^6000060000Michael Vang11/2016
8399(2^32582657/10^238942)%10^6000060000Michael Vang11/2016
8400(2^24036583/10^13547)%10^6000060000Michael Vang11/2016
8401(2^20996011/10^131008)%10^6000060000Michael Vang11/2016
8402(2^13466917/10^79774)%10^6000060000Michael Vang11/2016
8403(2^13466917/10^102581)%10^6000060000Michael Vang11/2016
8404(2^6972593/10^339640)%10^6000060000Michael Vang11/2016
8405(2^2976221/10^65464)%10^6000060000Michael Vang12/2016
8406(2^1398269/10^61138)%10^6000060000Michael Vang12/2016
8407(2^3021377/10^418881)%10^6000060000Michael Vang12/2016
8408(2^1257787/10^164080)%10^6000060000Michael Vang12/2016
841610^59999-51626759999Patrick De Geest06/2009
841720^46116-4159999Lelio R Paula03/2013
8414(2^74207281/10^184638)%10^6000059999Michael Vang10/2016
8415(2^25964951/10^135429)%10^6000059999Michael Vang11/2016
84186^77100-5559996Lelio R Paula10/2012
8420(19*2^199274+1)/16159987Lelio R Paula07/2012
8419(23^44053+1)/2459987Robert Price06/2013
84219^62848+6^62848-2^6284859973Mike Oakes08/2010
842215852^6061+6061^1585259961Hans Havermann08/2016
842319^46880-2059948Lelio R Paula03/2013
84242^199107-1773759938Enzo Doria05/2013
8425(13*10^59928+83)/359929Robert Price09/2016
842610^59913+10893143159914Marisa Kirisame02/2015
842710^59913+4861959914Patrick De Geest04/2016
842810^59913-7412359913Patrick De Geest03/2016
8429t(199528)59890Robert Price01/2015
84302^198903-1790159876Enzo Doria05/2013
84319*10^59862-1959863Robert Price10/2017
8432gcd(V(776555),5*F(155311)*(F(155311)+1)+1)59858Serge Batalov04/2015
8433(3^125447+7)/259854Lelio R Paula04/2012
84345^85630+4^(85630-1)59853Robert Price03/2016
84352^198824-213559852Yves Minet06/2013
8436(124^28591-1)/12359851Richard Fischer10/2017
84372^198799-1611759845Enzo Doria04/2013
84387^70811+6^(70811+1)59843Robert Price07/2016
84392^198774-1594559837Enzo Doria04/2013
84402^198753-1587359831Enzo Doria04/2013
8441(31*2^198748-1)/4559829Lelio R Paula01/2014
84422^198725+6959823Lelio R Paula04/2011
8443(68*10^59821+31)/959822Robert Price10/2015
8444(37*25^42785+1867)/859812Curtis Bright05/2015
84453^125354+266059810Lelio R Paula10/2012
8446105^29591-10459810Norbert Schneider08/2013
84474*5^85565-359808Lelio R Paula09/2014
844813963842222*Bern(19550)/5572727559803Thomas Ritschel03/2014
8450125330^3+3^12533059798Anatoly F. Selevich06/2010
84492^198643-318959798Yves Minet10/2014
8451(13*10^59797+191)/359798Robert Price08/2017
8452(7*10^59796-1)/359797Erik Branger03/2014
84532^198595+15359784Lelio R Paula04/2011
8454(19*10^59766+161)/959767Robert Price07/2016
84552^198510-196559758Lelio R Paula06/2011
84562^198506-1907759757Enzo Doria05/2013
84572^198484-1600559750Enzo Doria04/2013
84582^198473-1682159747Enzo Doria05/2013
8459(2^198481-5)/2831159745Lelio R Paula02/2012
84602^198400-18959725Lelio R Paula04/2011
84612^198384-1283759720Enzo Doria10/2012
846242694!3-72959719Robert Price09/2014
84632^198320-1871759701Enzo Doria05/2013
846420^45881-118359693Enzo Doria03/2013
84652^198224-685559672Lelio R Paula05/2011
84662^198181-1910159659Enzo Doria05/2013
84675*10^59650+4159651Robert Price08/2017
84682^198149-11221359649Enzo Doria06/2014
84692^198138+7369959646Enzo Doria04/2016
84702^198129-5559643Lelio R Paula04/2011
84715^85318-1463659635Enzo Doria02/2013
8472(2^198119+47)/156093559634Lelio R Paula02/2012
84732^198090-1609759632Enzo Doria04/2013
84749*10^59617+8959618Robert Price11/2016
847542625!3+8159612Robert Price09/2014
84765^85277-8459607Lelio R Paula10/2012
8477(871*10^59599-7)/959601Robert Price11/2017
84782^197984-1824559600Enzo Doria05/2013
84792^197951-213759590Yves Minet06/2013
8480(38*10^59589+187)/959590Robert Price11/2017
848166^32749-65^3274959589Robert Price09/2013
84825*10^59586-359587Dmitry Domanov11/2010
8483(35*10^59584-197)/959585Robert Kinser10/2017
84842^197932-395959584Yves Minet04/2017
84852^197909-1896159577Enzo Doria05/2013
8486(3^124871+2)/4503159574Lelio R Paula04/2012
84872^197872+8159566Henri Lifchitz10/2005
84882^197873-1846959566Enzo Doria05/2013
8489(22*10^59558-31)/959559Robert Price04/2015
84912^197840-46559556Lelio R Paula05/2011
8490(31*2^197856-1)/388960559556Lelio R Paula01/2014
84922^197808-1780559547Enzo Doria05/2013
84932^197781-1790559539Enzo Doria05/2013
84942^197777-1747359537Enzo Doria05/2013
84956^76507-14959535Lelio R Paula10/2012
8497Phi(61456,109)59526Enzo Doria05/2012
849618^47420+2359526Lelio R Paula03/2013
8498(59^33613+1)/6059522Paul Bourdelais08/2017
84993^124747+9459520Lelio R Paula10/2012
850017^48370+1859517Lelio R Paula03/2013


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: December, 11 2018 05:54 (Time in France)

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