PRP Records

Probable Primes Top 10000

(253476 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 (> 50000) Who ? When ?
875210^61525+9^(61525-1)61526Robert Price03/2016
875114821^14166+14166^1482161526Hans Havermann01/2017
875412^57010-8561525Lelio R Paula05/2013
875310^61525-21357961525Patrick De Geest12/2016
87552^204332-9961511Lelio R Paula08/2011
87562^204323-222161508Yves Minet08/2013
87582^204317-19561506Lelio R Paula08/2011
87573^128910-8661506Lelio R Paula04/2013
87592^204318+7453961506Enzo Doria04/2016
8760(2^204334-3)/114133361505Lelio R Paula03/2012
87612^204297-103609361500Paul Bourdelais11/2012
87623^128880+5861492Lelio R Paula04/2013
87632^204216-11167761476Enzo Doria05/2014
8764(F(73524)^5-F(73523)^5)/F(73522)61462Wayne Halsdorf03/2012
876514677^14750-14750^1467761458Norbert Schneider05/2019
87662^204129+20412961449Henri Lifchitz04/2002
87673^128787+2^(128787-1)61448Robert Price05/2016
876811^58999-7861442Lelio R Paula05/2013
87692^204083-11196761436Enzo Doria05/2014
8770(45^37159+1)/4661431Robert Price11/2013
8771677^21702+21702^67761430Norbert Schneider06/2016
877214837^13810+13810^1483761429Hans Havermann02/2017
8773(7*2^204043+1)/3961423Lelio R Paula03/2012
877411^58976-174061418Enzo Doria11/2012
87752^204016-1608561415Enzo Doria04/2013
8776V(379967)61393Serge Batalov03/2015
877743777!3-3^4377761392Robert Price08/2015
87787^72642+8861390Lelio R Paula04/2013
87793^128656+3261385Lelio R Paula04/2013
87802^203916-1749361385Enzo Doria05/2013
87816^78880+2361381Lelio R Paula04/2013
8782(388*10^61374-1)/961376Robert Price11/2017
87832^203877-11179961374Enzo Doria05/2014
87842^203867-161561371Lelio R Paula10/2011
87854*10^61367+1961368Robert Price04/2016
8786(19*2^203854+1)/4231961363Lelio R Paula08/2012
8787L(293659)/7652812271961361Serge Batalov07/2017
87882^203825-1580561358Enzo Doria04/2013
87892^203816-1582561355Enzo Doria04/2013
87905*10^61348+5961349Robert Price09/2016
879121^46395-261345Lelio R Paula08/2013
8792(809*29^41946-165)/2861344Curtis Bright05/2015
87937*6^78826+561340Lelio R Paula09/2014
8794(3^128558+7)/8377316642969661324Lelio R Paula04/2012
87952^203706-11161322Lelio R Paula08/2011
879617567^3094+3094^1756761318Hans Havermann02/2017
87972^203689-3161317Thomas Masser10/2005
8798(11*2^203678-1)/5368961310Lelio R Paula01/2014
87992^203642+3961303Lelio R Paula08/2011
8800floor(Pi*10^61382)%(10^61303)61303Serge Batalov07/2012
880111^58849-604061285Enzo Doria02/2013
880243694!3-361264Robert Price10/2014
880358*(10^(3*20420)-1)/111-161260Robert Price10/2014
88042^203490+1290961257Lelio R Paula10/2011
8805(16*10^61251-31)/361252Robert Price03/2016
880620^47077-570361249Enzo Doria03/2013
88072^203434-11308161240Enzo Doria07/2014
88095^87606+461234Wojciech Florek11/2005
88082^203412-16761234Lelio R Paula08/2011
88102^203402+108961231Lelio R Paula10/2011
8811(8*10^61230+67)/361231Robert Price01/2017
8812(2^203408+lucasV(1,2,203408)+1)/(2*32993)61228Mike Oakes11/2016
88131265^19732+19732^126561211Serge Batalov05/2014
88142^203330+14561209Lelio R Paula08/2011
88156^78647-13761200Lelio R Paula04/2013
881685^31718+8461198Norbert Schneider10/2015
881711^58763-27061196Enzo Doria07/2012
88182^203285-11232161195Enzo Doria06/2014
88192^203253-99514361186Paul Bourdelais11/2012
882015319^9862+9862^1531961184Hans Havermann07/2016
88217^72395-4461181Lelio R Paula04/2013
8822(49*10^61167-67)/961168Robert Price08/2017
88235*2^203176-761163Lelio R Paula04/2014
8824(26*10^61156-413)/961157Robert Price10/2017
88257^72358+5461150Lelio R Paula04/2013
88262^203133-11177561150Enzo Doria05/2014
8827(lucasV(1,2,406356)+2)/(3^2*5*11*19*31*583697*9671743)61145Mike Oakes01/2017
88282^203112-1800961143Enzo Doria05/2013
882943607!3+72961129Robert Price09/2014
88302^203065-11485361129Enzo Doria05/2015
88313^128111+19661125Lelio R Paula04/2013
8832128^29007+29007^12861124Serge Batalov05/2014
88334*10^61119+4961120Robert Price08/2017
883422355*2^203009-361117Donovan Johnson03/2004
88352^203018+3361115Lelio R Paula08/2011
88362^203017-161561115Lelio R Paula10/2011
883716697^4570+4570^1669761110Hans Havermann12/2016
88382^202998-1724161109Enzo Doria05/2013
883920^46964+9361102Lelio R Paula06/2013
8840(55*10^61097-1)/961098Ray Chandler02/2012
884120^46960-546361097Enzo Doria03/2013
8842(11*10^61095+49)/361096Robert Price05/2016
884314040^14731-14731^1404061095Norbert Schneider04/2019
88442^202934-595561090Lelio R Paula10/2011
884519^47772-6861089Lelio R Paula05/2013
88462^202877-49942361073Paul Bourdelais03/2013
88472^202763-1712561038Enzo Doria05/2013
8848(23*2^202756+1)/961037Lelio R Paula03/2012
884914788^13355+13355^1478861011Hans Havermann12/2016
885016069^6258+6258^1606961005Hans Havermann12/2016
88515^87276-1433661004Enzo Doria02/2013
885250^35899-49^3589960992Robert Price12/2012
88532^202599-304960989Yves Minet10/2014
88542^202535-11157160970Enzo Doria05/2014
8855(13*10^60966+107)/360967Robert Price11/2017
885710^60959+5760960Patrick De Geest12/2008
88566*10^60959-9160960Robert Price11/2017
885910^60959-6095960959Henri Lifchitz08/2002
885810^60959-2917760959Patrick De Geest08/2008
88605^87206+4^(87206+1)60955Robert Price07/2016
88612^202476-1590960952Enzo Doria04/2013
88622^202472-1751360951Enzo Doria05/2013
886314858^12651+12651^1485860950Hans Havermann12/2016
88642^202389-5869560926Lelio R Paula09/2011
88653^127597-3460880Lelio R Paula04/2013
886615088^10831+10831^1508860876Hans Havermann12/2016
88672^202198-11326160868Enzo Doria07/2014
88682^202182+13560863Lelio R Paula08/2011
88692^202176+8560862Lelio R Paula08/2011
88705183^16384+5182^1638460860Henri Lifchitz01/2007
8871(31*2^202163+1)/360859Lelio R Paula03/2012
887214708^13707+13707^1470860847Hans Havermann12/2016
88732^202112+202112^2-160842Robert Price04/2014
8874(13*2^202142-1)/40598427425760841Lelio R Paula01/2014
887564743*10^60832+(6^78175-11)/560837Gilbert Mozzo05/2012
8876(19*2^202098-1)/679560836Lelio R Paula01/2014
8877(6^78175-11)/560832Paul Bourdelais11/2011
88782^202063+160560828Lelio R Paula09/2011
88792^202058+85960826Lelio R Paula09/2011
88801576^19021+19021^157660821Serge Batalov05/2014
8881(2^202009+3)/600560807Lelio R Paula03/2012
888210^60776+360777Robert Price01/2011
888310^60776-1481960776Patrick De Geest12/2012
888455*10^60772+760774Robert Price10/2017
8885(6883*2^201869-1)/3560771Lelio R Paula04/2015
888614801^12750+12750^1480160766Hans Havermann05/2019
8887(27*2^201841-1)/4360760Lelio R Paula01/2014
88882^201822-17760755Lelio R Paula08/2011
8889(13*10^60744+17)/360745Robert Price06/2015
8890(31*2^201754-1)/9960734Lelio R Paula01/2014
8891(26*10^60717-71)/960718Robert Price03/2015
889237^38712-260709Lelio R Paula08/2013
88932^201657-11200360705Enzo Doria05/2014
8894(10^60703+3^60703)/1360702Robert Price01/2013
88952^201622-11281760695Enzo Doria06/2014
88962^201620-1717760694Enzo Doria05/2013
8897(2^201615-3)*6-760693Gilbert Mozzo05/2016
88982^201609-4978960691Henri Lifchitz03/2005
88992^201582-1906160683Enzo Doria05/2013
890043316!3+2760679Robert Price09/2014
8901(509203*2^201564-1)/506760679Lelio R Paula04/2015
89022^201560+10560676Lelio R Paula08/2011
8903(27*2^201584-1)/64675548645760673Lelio R Paula01/2014
89042^201545-1802160672Enzo Doria05/2013
89052^201543+1171560671Lelio R Paula09/2011
89062^201512-11175560662Enzo Doria05/2014
8908p(13013)#/2+6460662Robert Price03/2017
890715962^6315+6315^1596260662Hans Havermann05/2019
890911^58248+1660660Lelio R Paula05/2013
89102^201496-2760657Lelio R Paula08/2011
89115*10^60655+5760656Robert Price11/2017
891216239^5432+5432^1623960653Hans Havermann05/2019
8913(7*10^60643+197)/360644Robert Price07/2017
89142^201426-1609760636Enzo Doria04/2013
8915(17*10^60631-11)/360632Robert Price07/2015
89166^77916-7760631Lelio R Paula04/2013
8917(27*2^201410-1)/49160630Lelio R Paula01/2014
89185^86727+9860620Lelio R Paula04/2013
891917^49266-2660620Lelio R Paula05/2013
892020^46589-3360614Lelio R Paula05/2013
89216^77889+6560610Lelio R Paula04/2013
892214921^11536+11536^1492160610Hans Havermann05/2019
8923139901#+14838760595Nicolas PALAU09/2016
89242^201285-11172360593Enzo Doria05/2014
892546199*2^201268+12964760593Paul Vanderveen11/2016
89263^126991-10060591Lelio R Paula04/2013
89272^201278-11162360591Enzo Doria05/2014
89285^86682-1600460589Enzo Doria05/2014
8929(865*10^60583-1)/960585Robert Price11/2017
8930(58*10^60579+221)/960580Robert Price02/2017
89319*2^201231-560578Lelio R Paula04/2014
89324*10^60572-8960573Robert Price08/2017
8933(78557*2^201207+1)/1306760571Lelio R Paula06/2014
89342^201186-6694560564Lelio R Paula09/2011
89352^201186-9439560564Lelio R Paula09/2011
893665^33403+3260557Lelio R Paula01/2016
8937103^30079+10260545Norbert Schneider10/2016
8938(1000159^10091+1)/100016060541Faysal YAtim08/2008
89392^201098-1771760537Enzo Doria05/2013
8940(3^126881+8)/482960534Lelio R Paula03/2012
89412^201074+7504960530Enzo Doria04/2016
894211^58111-129060517Enzo Doria11/2012
8943(509203*2^201012-1)/960516Lelio R Paula04/2015
894414447^14544-14544^1444760500Norbert Schneider12/2018
89452^200911+571160481Lelio R Paula10/2011
8946(2^200912-3)/2360480Lelio R Paula03/2012
894718^48179-17^4817960478Jean-Louis Charton12/2010
894938^38281-37^3828160476Robert Price09/2012
89484*7^71560-360476Lelio R Paula09/2014
895012869^14714-14714^1286960468Norbert Schneider04/2019
8951(10^(2*30232+1)+15*10^30232-1)/360465Robert Price04/2016
8952lucasV(1,2,401712)+260464Mike Oakes01/2017
89532^200833-1849360457Enzo Doria05/2013
895420^46465-504360453Enzo Doria03/2013
89552^200810-1825760450Enzo Doria05/2013
895612127^14802-14802^1212760448Norbert Schneider06/2019
8957((2)^(2*100400-1)+(2)^(100400-1)+1)+2667260447Faysal YAtim04/2018
89585^86466-1433660438Enzo Doria02/2013
8959Phi(145558,10)/103928413/161714939/14779231531/36075385837/24241141985360432Maksym Voznyy10/2011
896015397^8398+8398^1539760421Hans Havermann06/2019
8961(29*2^200703-1)/23160417Lelio R Paula01/2014
89622^200682-101683160412Paul Bourdelais11/2012
89632^200617-1788160392Enzo Doria05/2013
8964(25^43201+1)/2660391Robert Price06/2013
89662^200609-13360390Lelio R Paula08/2011
89652^200608-1283760390Enzo Doria10/2012
89672^200607-1712160389Enzo Doria05/2013
896811^57975-162060375Enzo Doria11/2012
8969(9913*2^200538-1)/380160369Lelio R Paula04/2015
89705^86342+6460351Lelio R Paula04/2013
897113088^14659-14659^1308860350Norbert Schneider03/2019
8972(14*10^60346-23)/960347Robert Price04/2015
897314633^13302+13302^1463360346Hans Havermann05/2019
897415008^10491+10491^1500860345Hans Havermann05/2019
89752^200457-829560344Lelio R Paula09/2011
89766^77546+11360343Lelio R Paula04/2013
897716026^5815+5815^1602660331Hans Havermann06/2019
897937^38461-36^3846160315Robert Price06/2012
89782^200361-1759360315Enzo Doria05/2013
898010103^15059-10660304Enzo Doria07/2012
89812^200301-1740160297Enzo Doria05/2013
8982(37*10^60290+71)/960291Robert Price04/2015
89832^200266-9439560287Lelio R Paula09/2011
89842^200261-11161360285Enzo Doria05/2014
898513717^14570-14570^1371760280Norbert Schneider01/2019
89862^200191-459760264Yves Minet03/2019
898716282^5021+5021^1628260257Hans Havermann05/2019
898846^36238-4560256Norbert Schneider07/2014
898913^54091+9460255Lelio R Paula05/2013
8990311^24171-15460253Enzo Doria07/2012
89912^200120-8108960243Paul Bourdelais01/2012
89923^126262+868060243Lelio R Paula04/2013
899343031!3-5904960239Robert Price12/2015
89942^200100-11126960237Enzo Doria05/2014
8995(29*2^200069-1)/537360225Lelio R Paula01/2014
899620^46283-192360216Enzo Doria03/2013
89972^200011-11207560210Enzo Doria05/2014
89982^200002+7453960207Enzo Doria04/2016
8999(38602791*2^200026-1)/(577849*2645749*3427009)60203Jens K. Andersen09/2007
9000(2^199962+28410)/260195Stefano Morozzi08/2019


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: August, 25 2019 15:53 (Time in France)

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