PRP Records

Probable Primes Top 10000

(180278 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 ?
72522^203642+3961303Lelio R Paula08/2011
7251floor(Pi*10^61382)%(10^61303)61303Serge Batalov07/2012
725311^58849-604061285Enzo Doria02/2013
725443694!3-361264Robert Price10/2014
725558*(10^(3*20420)-1)/111-161260Robert Price10/2014
72562^203490+1290961257Lelio R Paula10/2011
7257(16*10^61251-31)/361252Robert Price03/2016
725820^47077-570361249Enzo Doria03/2013
72592^203434-11308161240Enzo Doria07/2014
72605^87606+461234Wojciech Florek11/2005
72612^203412-16761234Lelio R Paula08/2011
72622^203402+108961231Lelio R Paula10/2011
7263(8*10^61230+67)/361231Robert Price01/2017
7264(2^203408+lucasV(1,2,203408)+1)/(2*32993)61228Mike Oakes11/2016
72651265^19732+19732^126561211Serge Batalov05/2014
72662^203330+14561209Lelio R Paula08/2011
72676^78647-13761200Lelio R Paula04/2013
726885^31718+8461198Norbert Schneider10/2015
726911^58763-27061196Enzo Doria07/2012
72702^203285-11232161195Enzo Doria06/2014
72712^203253-99514361186Paul Bourdelais11/2012
727215319^9862+9862^1531961184Hans Havermann07/2016
72737^72395-4461181Lelio R Paula04/2013
72745*2^203176-761163Lelio R Paula04/2014
72767^72358+5461150Lelio R Paula04/2013
72752^203133-11177561150Enzo Doria05/2014
7277(lucasV(1,2,406356)+2)/(3^2*5*11*19*31*583697*9671743)61145Mike Oakes01/2017
72782^203112-1800961143Enzo Doria05/2013
727943607!3+72961129Robert Price09/2014
72802^203065-11485361129Enzo Doria05/2015
72813^128111+19661125Lelio R Paula04/2013
7282128^29007+29007^12861124Serge Batalov05/2014
72834*10^61119+4961120Robert Price08/2017
728422355*2^203009-361117Donovan Johnson03/2004
72852^203018+3361115Lelio R Paula08/2011
72862^203017-161561115Lelio R Paula10/2011
728716697^4570+4570^1669761110Hans Havermann12/2016
72882^202998-1724161109Enzo Doria05/2013
728920^46964+9361102Lelio R Paula06/2013
7290(55*10^61097-1)/961098Ray Chandler02/2012
729120^46960-546361097Enzo Doria03/2013
7292(11*10^61095+49)/361096Robert Price05/2016
72932^202934-595561090Lelio R Paula10/2011
729419^47772-6861089Lelio R Paula05/2013
72952^202877-49942361073Paul Bourdelais03/2013
72962^202763-1712561038Enzo Doria05/2013
7297(23*2^202756+1)/961037Lelio R Paula03/2012
729814788^13355+13355^1478861011Hans Havermann12/2016
729916069^6258+6258^1606961005Hans Havermann12/2016
73005^87276-1433661004Enzo Doria02/2013
730150^35899-49^3589960992Robert Price12/2012
73022^202599-304960989Yves Minet10/2014
73032^202535-11157160970Enzo Doria05/2014
730410^60959+5760960Patrick De Geest12/2008
730610^60959-6095960959Henri Lifchitz08/2002
730510^60959-2917760959Patrick De Geest08/2008
73075^87206+4^(87206+1)60955Robert Price07/2016
73082^202476-1590960952Enzo Doria04/2013
73092^202472-1751360951Enzo Doria05/2013
731014858^12651+12651^1485860950Hans Havermann12/2016
73112^202389-5869560926Lelio R Paula09/2011
73123^127597-3460880Lelio R Paula04/2013
731315088^10831+10831^1508860876Hans Havermann12/2016
73142^202198-11326160868Enzo Doria07/2014
73152^202182+13560863Lelio R Paula08/2011
73162^202176+8560862Lelio R Paula08/2011
73175183^16384+5182^1638460860Henri Lifchitz01/2007
7318(31*2^202163+1)/360859Lelio R Paula03/2012
731914708^13707+13707^1470860847Hans Havermann12/2016
73202^202112+202112^2-160842Robert Price04/2014
7321(13*2^202142-1)/40598427425760841Lelio R Paula01/2014
732264743*10^60832+(6^78175-11)/560837Gilbert Mozzo05/2012
7323(19*2^202098-1)/679560836Lelio R Paula01/2014
7324(6^78175-11)/560832Paul Bourdelais11/2011
73252^202063+160560828Lelio R Paula09/2011
73262^202058+85960826Lelio R Paula09/2011
73271576^19021+19021^157660821Serge Batalov05/2014
7328(2^202009+3)/600560807Lelio R Paula03/2012
732910^60776+360777Robert Price01/2011
733010^60776-1481960776Patrick De Geest12/2012
7331(6883*2^201869-1)/3560771Lelio R Paula04/2015
7332(27*2^201841-1)/4360760Lelio R Paula01/2014
73332^201822-17760755Lelio R Paula08/2011
7334(13*10^60744+17)/360745Robert Price06/2015
7335(31*2^201754-1)/9960734Lelio R Paula01/2014
7336(26*10^60717-71)/960718Robert Price03/2015
733737^38712-260709Lelio R Paula08/2013
73382^201657-11200360705Enzo Doria05/2014
7339(10^60703+3^60703)/1360702Robert Price01/2013
73402^201622-11281760695Enzo Doria06/2014
73412^201620-1717760694Enzo Doria05/2013
7342(2^201615-3)*6-760693Gilbert Mozzo05/2016
73432^201609-4978960691Henri Lifchitz03/2005
73442^201582-1906160683Enzo Doria05/2013
734543316!3+2760679Robert Price09/2014
7346(509203*2^201564-1)/506760679Lelio R Paula04/2015
73472^201560+10560676Lelio R Paula08/2011
7348(27*2^201584-1)/64675548645760673Lelio R Paula01/2014
73492^201545-1802160672Enzo Doria05/2013
73502^201543+1171560671Lelio R Paula09/2011
73522^201512-11175560662Enzo Doria05/2014
7351p(13013)#/2+6460662Robert Price03/2017
735311^58248+1660660Lelio R Paula05/2013
73542^201496-2760657Lelio R Paula08/2011
7355(7*10^60643+197)/360644Robert Price07/2017
73562^201426-1609760636Enzo Doria04/2013
7357(17*10^60631-11)/360632Robert Price07/2015
73586^77916-7760631Lelio R Paula04/2013
7359(27*2^201410-1)/49160630Lelio R Paula01/2014
73605^86727+9860620Lelio R Paula04/2013
736117^49266-2660620Lelio R Paula05/2013
736220^46589-3360614Lelio R Paula05/2013
73636^77889+6560610Lelio R Paula04/2013
7364139901#+14838760595Nicolas PALAU09/2016
73652^201285-11172360593Enzo Doria05/2014
736646199*2^201268+12964760593Paul Vanderveen11/2016
73683^126991-10060591Lelio R Paula04/2013
73672^201278-11162360591Enzo Doria05/2014
73695^86682-1600460589Enzo Doria05/2014
7370(58*10^60579+221)/960580Robert Price02/2017
73719*2^201231-560578Lelio R Paula04/2014
73724*10^60572-8960573Robert Price08/2017
7373(78557*2^201207+1)/1306760571Lelio R Paula06/2014
73742^201186-6694560564Lelio R Paula09/2011
73752^201186-9439560564Lelio R Paula09/2011
737665^33403+3260557Lelio R Paula01/2016
7377103^30079+10260545Norbert Schneider10/2016
7378(1000159^10091+1)/100016060541Faysal YAtim08/2008
73792^201098-1771760537Enzo Doria05/2013
7380(3^126881+8)/482960534Lelio R Paula03/2012
73812^201074+7504960530Enzo Doria04/2016
738211^58111-129060517Enzo Doria11/2012
7383(509203*2^201012-1)/960516Lelio R Paula04/2015
73842^200911+571160481Lelio R Paula10/2011
7385(2^200912-3)/2360480Lelio R Paula03/2012
738618^48179-17^4817960478Jean-Louis Charton12/2010
738838^38281-37^3828160476Robert Price09/2012
73874*7^71560-360476Lelio R Paula09/2014
7389(10^(2*30232+1)+15*10^30232-1)/360465Robert Price04/2016
7390lucasV(1,2,401712)+260464Mike Oakes01/2017
73912^200833-1849360457Enzo Doria05/2013
739220^46465-504360453Enzo Doria03/2013
73932^200810-1825760450Enzo Doria05/2013
73945^86466-1433660438Enzo Doria02/2013
7395Phi(145558,10)/103928413/161714939/14779231531/36075385837/24241141985360432Maksym Voznyy10/2011
7396(29*2^200703-1)/23160417Lelio R Paula01/2014
73972^200682-101683160412Paul Bourdelais11/2012
73982^200617-1788160392Enzo Doria05/2013
7399(25^43201+1)/2660391Robert Price06/2013
74012^200609-13360390Lelio R Paula08/2011
74002^200608-1283760390Enzo Doria10/2012
74022^200607-1712160389Enzo Doria05/2013
740311^57975-162060375Enzo Doria11/2012
7404(9913*2^200538-1)/380160369Lelio R Paula04/2015
74055^86342+6460351Lelio R Paula04/2013
7406(14*10^60346-23)/960347Robert Price04/2015
74072^200457-829560344Lelio R Paula09/2011
74086^77546+11360343Lelio R Paula04/2013
741037^38461-36^3846160315Robert Price06/2012
74092^200361-1759360315Enzo Doria05/2013
741110103^15059-10660304Enzo Doria07/2012
74122^200301-1740160297Enzo Doria05/2013
7413(37*10^60290+71)/960291Robert Price04/2015
74142^200266-9439560287Lelio R Paula09/2011
74152^200261-11161360285Enzo Doria05/2014
741646^36238-4560256Norbert Schneider07/2014
741713^54091+9460255Lelio R Paula05/2013
7418311^24171-15460253Enzo Doria07/2012
74192^200120-8108960243Paul Bourdelais01/2012
74203^126262+868060243Lelio R Paula04/2013
742143031!3-5904960239Robert Price12/2015
74222^200100-11126960237Enzo Doria05/2014
7423(29*2^200069-1)/537360225Lelio R Paula01/2014
742420^46283-192360216Enzo Doria03/2013
74252^200011-11207560210Enzo Doria05/2014
74262^200002+7453960207Enzo Doria04/2016
7427(38602791*2^200026-1)/(577849*2645749*3427009)60203Jens K. Andersen09/2007
74282^199872+9360168Donovan Johnson06/2008
74296^77321+7760168Lelio R Paula04/2013
7430(86*10^60165-77)/960166Robert Price05/2016
7431(2^199868+78557)/2337360162Lelio R Paula05/2012
74327^71180+8260155Lelio R Paula04/2013
74332^199814-11229560151Enzo Doria06/2014
743442964!3-8160135Robert Price09/2014
74352^199709-5160119Lelio R Paula05/2011
74362^199700-11162360116Enzo Doria05/2014
7437(15185*2^199681-1)/15960112Lelio R Paula04/2015
74382^199672+253360108Henri Lifchitz09/2004
743920^46198-1160105Lelio R Paula04/2013
74402^199657+9325760103Yves Minet03/2010
74413^125967-11060102Lelio R Paula10/2012
74422^199654-1881360102Enzo Doria05/2013
7443(29*10^60100+19)/360101Robert Price01/2017
7444129^28468+28468^12960085Serge Batalov05/2014
74452^199572-1587360078Enzo Doria04/2013
74469*2^199559+760075Lelio R Paula03/2014
74472^199527-11191960064Enzo Doria05/2014
74482^199522+8287560063Lelio R Paula10/2012
74495^85928-7260062Lelio R Paula10/2012
745039^37749+3860062Norbert Schneider05/2014
74516^77182-14360060Lelio R Paula10/2012
74522^199502-214560057Lelio R Paula06/2011
74532^199493+425760054Lelio R Paula06/2011
74542^199488+4075560052Lelio R Paula06/2011
7455(2^199451+9)/2561960037Lelio R Paula02/2012
74562^199425-6160033Lelio R Paula05/2011
7457(85*10^60026+23)/960027Robert Price11/2015
745865^33107+6260021Lelio R Paula01/2016
74602^199362-121560014Lelio R Paula06/2011
74592^199362-11163360014Enzo Doria05/2014
74611537^18832+18832^153760012Serge Batalov05/2014
74622^199324-1743360003Enzo Doria05/2013
746310^60000+20433160001Milton L. Brown04/2006
746410^60000+8712960001Milton L. Brown04/2006
746510^59999+6519760000Patrick De Geest04/2005
746610^60000-3252960000Patrick De Geest08/2009
7467(10^60000+2249)/960000Makoto Morimoto09/2016
7468((2^43112609)/10^24296)%10^6000060000Michael Vang10/2016
7469(2^57885161/10^105090)%10^6000060000Michael Vang10/2016
7470(2^42643801/10^58945)%10^6000060000Michael Vang10/2016
7471(2^37156667/10^243655)%10^6000060000Michael Vang10/2016
7472(2^30402457/10^69028)%10^6000060000Michael Vang11/2016
7473(2^32582657/10^248088)%10^6000060000Michael Vang11/2016
7474(2^32582657/10^238942)%10^6000060000Michael Vang11/2016
7475(2^24036583/10^13547)%10^6000060000Michael Vang11/2016
7476(2^20996011/10^131008)%10^6000060000Michael Vang11/2016
7477(2^13466917/10^79774)%10^6000060000Michael Vang11/2016
7478(2^13466917/10^102581)%10^6000060000Michael Vang11/2016
7479(2^6972593/10^339640)%10^6000060000Michael Vang11/2016
7480(2^2976221/10^65464)%10^6000060000Michael Vang12/2016
7481(2^1398269/10^61138)%10^6000060000Michael Vang12/2016
7482(2^3021377/10^418881)%10^6000060000Michael Vang12/2016
7483(2^1257787/10^164080)%10^6000060000Michael Vang12/2016
748610^59999-51626759999Patrick De Geest06/2009
748520^46116-4159999Lelio R Paula03/2013
7487(2^74207281/10^184638)%10^6000059999Michael Vang10/2016
7484(2^25964951/10^135429)%10^6000059999Michael Vang11/2016
74886^77100-5559996Lelio R Paula10/2012
7490(19*2^199274+1)/16159987Lelio R Paula07/2012
7489(23^44053+1)/2459987Robert Price06/2013
74919^62848+6^62848-2^6284859973Mike Oakes08/2010
749215852^6061+6061^1585259961Hans Havermann08/2016
749319^46880-2059948Lelio R Paula03/2013
74942^199107-1773759938Enzo Doria05/2013
7495(13*10^59928+83)/359929Robert Price09/2016
749610^59913+10893143159914Marisa Kirisame02/2015
749710^59913+4861959914Patrick De Geest04/2016
749810^59913-7412359913Patrick De Geest03/2016
7499t(199528)59890Robert Price01/2015
75002^198903-1790159876Enzo Doria05/2013


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: August, 20 2017 08:36 (Time in France)

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