PRP Records

Probable Primes Top 10000

(191107 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 ?
750112^57026-7361542Lelio R Paula05/2013
750217^50013+9061539Lelio R Paula05/2013
750356^35201-55^3520161538Robert Price10/2013
75048*7^72810+561533Lelio R Paula09/2014
7506204^26641-203^2664161531Jean-Louis Charton08/2009
750543867!3-656161531Robert Price11/2015
750910^61525+9^(61525-1)61526Robert Price03/2016
750710^61525+6225761526Patrick De Geest12/2016
750814821^14166+14166^1482161526Hans Havermann01/2017
751112^57010-8561525Lelio R Paula05/2013
751010^61525-21357961525Patrick De Geest12/2016
75122^204332-9961511Lelio R Paula08/2011
75132^204323-222161508Yves Minet08/2013
75152^204317-19561506Lelio R Paula08/2011
75143^128910-8661506Lelio R Paula04/2013
75162^204318+7453961506Enzo Doria04/2016
7517(2^204334-3)/114133361505Lelio R Paula03/2012
75182^204297-103609361500Paul Bourdelais11/2012
75193^128880+5861492Lelio R Paula04/2013
75202^204216-11167761476Enzo Doria05/2014
7521(F(73524)^5-F(73523)^5)/F(73522)61462Wayne Halsdorf03/2012
75222^204129+20412961449Henri Lifchitz04/2002
75233^128787+2^(128787-1)61448Robert Price05/2016
752411^58999-7861442Lelio R Paula05/2013
75252^204083-11196761436Enzo Doria05/2014
7526(45^37159+1)/4661431Robert Price11/2013
7527677^21702+21702^67761430Norbert Schneider06/2016
752814837^13810+13810^1483761429Hans Havermann02/2017
7529(7*2^204043+1)/3961423Lelio R Paula03/2012
753011^58976-174061418Enzo Doria11/2012
75312^204016-1608561415Enzo Doria04/2013
7532V(379967)61393Serge Batalov03/2015
753343777!3-3^4377761392Robert Price08/2015
75347^72642+8861390Lelio R Paula04/2013
75353^128656+3261385Lelio R Paula04/2013
75362^203916-1749361385Enzo Doria05/2013
75376^78880+2361381Lelio R Paula04/2013
75382^203877-11179961374Enzo Doria05/2014
75392^203867-161561371Lelio R Paula10/2011
75404*10^61367+1961368Robert Price04/2016
7541(19*2^203854+1)/4231961363Lelio R Paula08/2012
7542L(293659)/7652812271961361Serge Batalov07/2017
75432^203825-1580561358Enzo Doria04/2013
75442^203816-1582561355Enzo Doria04/2013
75455*10^61348+5961349Robert Price09/2016
754621^46395-261345Lelio R Paula08/2013
7547(809*29^41946-165)/2861344Curtis Bright05/2015
75487*6^78826+561340Lelio R Paula09/2014
7549(3^128558+7)/8377316642969661324Lelio R Paula04/2012
75502^203706-11161322Lelio R Paula08/2011
755117567^3094+3094^1756761318Hans Havermann02/2017
75522^203689-3161317Thomas Masser10/2005
7553(11*2^203678-1)/5368961310Lelio R Paula01/2014
75542^203642+3961303Lelio R Paula08/2011
7555floor(Pi*10^61382)%(10^61303)61303Serge Batalov07/2012
755611^58849-604061285Enzo Doria02/2013
755743694!3-361264Robert Price10/2014
755858*(10^(3*20420)-1)/111-161260Robert Price10/2014
75592^203490+1290961257Lelio R Paula10/2011
7560(16*10^61251-31)/361252Robert Price03/2016
756120^47077-570361249Enzo Doria03/2013
75622^203434-11308161240Enzo Doria07/2014
75635^87606+461234Wojciech Florek11/2005
75642^203412-16761234Lelio R Paula08/2011
75652^203402+108961231Lelio R Paula10/2011
7566(8*10^61230+67)/361231Robert Price01/2017
7567(2^203408+lucasV(1,2,203408)+1)/(2*32993)61228Mike Oakes11/2016
75681265^19732+19732^126561211Serge Batalov05/2014
75692^203330+14561209Lelio R Paula08/2011
75706^78647-13761200Lelio R Paula04/2013
757185^31718+8461198Norbert Schneider10/2015
757211^58763-27061196Enzo Doria07/2012
75732^203285-11232161195Enzo Doria06/2014
75742^203253-99514361186Paul Bourdelais11/2012
757515319^9862+9862^1531961184Hans Havermann07/2016
75767^72395-4461181Lelio R Paula04/2013
7577(49*10^61167-67)/961168Robert Price08/2017
75785*2^203176-761163Lelio R Paula04/2014
7579(26*10^61156-413)/961157Robert Price10/2017
75807^72358+5461150Lelio R Paula04/2013
75812^203133-11177561150Enzo Doria05/2014
7582(lucasV(1,2,406356)+2)/(3^2*5*11*19*31*583697*9671743)61145Mike Oakes01/2017
75832^203112-1800961143Enzo Doria05/2013
758443607!3+72961129Robert Price09/2014
75852^203065-11485361129Enzo Doria05/2015
75863^128111+19661125Lelio R Paula04/2013
7587128^29007+29007^12861124Serge Batalov05/2014
75884*10^61119+4961120Robert Price08/2017
758922355*2^203009-361117Donovan Johnson03/2004
75902^203018+3361115Lelio R Paula08/2011
75912^203017-161561115Lelio R Paula10/2011
759216697^4570+4570^1669761110Hans Havermann12/2016
75932^202998-1724161109Enzo Doria05/2013
759420^46964+9361102Lelio R Paula06/2013
7595(55*10^61097-1)/961098Ray Chandler02/2012
759620^46960-546361097Enzo Doria03/2013
7597(11*10^61095+49)/361096Robert Price05/2016
75982^202934-595561090Lelio R Paula10/2011
759919^47772-6861089Lelio R Paula05/2013
76002^202877-49942361073Paul Bourdelais03/2013
76012^202763-1712561038Enzo Doria05/2013
7602(23*2^202756+1)/961037Lelio R Paula03/2012
760314788^13355+13355^1478861011Hans Havermann12/2016
760416069^6258+6258^1606961005Hans Havermann12/2016
76055^87276-1433661004Enzo Doria02/2013
760650^35899-49^3589960992Robert Price12/2012
76072^202599-304960989Yves Minet10/2014
76082^202535-11157160970Enzo Doria05/2014
7609(13*10^60966+107)/360967Robert Price11/2017
761110^60959+5760960Patrick De Geest12/2008
76106*10^60959-9160960Robert Price11/2017
761310^60959-6095960959Henri Lifchitz08/2002
761210^60959-2917760959Patrick De Geest08/2008
76145^87206+4^(87206+1)60955Robert Price07/2016
76152^202476-1590960952Enzo Doria04/2013
76162^202472-1751360951Enzo Doria05/2013
761714858^12651+12651^1485860950Hans Havermann12/2016
76182^202389-5869560926Lelio R Paula09/2011
76193^127597-3460880Lelio R Paula04/2013
762015088^10831+10831^1508860876Hans Havermann12/2016
76212^202198-11326160868Enzo Doria07/2014
76222^202182+13560863Lelio R Paula08/2011
76232^202176+8560862Lelio R Paula08/2011
76245183^16384+5182^1638460860Henri Lifchitz01/2007
7625(31*2^202163+1)/360859Lelio R Paula03/2012
762614708^13707+13707^1470860847Hans Havermann12/2016
76272^202112+202112^2-160842Robert Price04/2014
7628(13*2^202142-1)/40598427425760841Lelio R Paula01/2014
762964743*10^60832+(6^78175-11)/560837Gilbert Mozzo05/2012
7630(19*2^202098-1)/679560836Lelio R Paula01/2014
7631(6^78175-11)/560832Paul Bourdelais11/2011
76322^202063+160560828Lelio R Paula09/2011
76332^202058+85960826Lelio R Paula09/2011
76341576^19021+19021^157660821Serge Batalov05/2014
7635(2^202009+3)/600560807Lelio R Paula03/2012
763610^60776+360777Robert Price01/2011
763710^60776-1481960776Patrick De Geest12/2012
763855*10^60772+760774Robert Price10/2017
7639(6883*2^201869-1)/3560771Lelio R Paula04/2015
7640(27*2^201841-1)/4360760Lelio R Paula01/2014
76412^201822-17760755Lelio R Paula08/2011
7642(13*10^60744+17)/360745Robert Price06/2015
7643(31*2^201754-1)/9960734Lelio R Paula01/2014
7644(26*10^60717-71)/960718Robert Price03/2015
764537^38712-260709Lelio R Paula08/2013
76462^201657-11200360705Enzo Doria05/2014
7647(10^60703+3^60703)/1360702Robert Price01/2013
76482^201622-11281760695Enzo Doria06/2014
76492^201620-1717760694Enzo Doria05/2013
7650(2^201615-3)*6-760693Gilbert Mozzo05/2016
76512^201609-4978960691Henri Lifchitz03/2005
76522^201582-1906160683Enzo Doria05/2013
765343316!3+2760679Robert Price09/2014
7654(509203*2^201564-1)/506760679Lelio R Paula04/2015
76552^201560+10560676Lelio R Paula08/2011
7656(27*2^201584-1)/64675548645760673Lelio R Paula01/2014
76572^201545-1802160672Enzo Doria05/2013
76582^201543+1171560671Lelio R Paula09/2011
76602^201512-11175560662Enzo Doria05/2014
7659p(13013)#/2+6460662Robert Price03/2017
766111^58248+1660660Lelio R Paula05/2013
76622^201496-2760657Lelio R Paula08/2011
7663(7*10^60643+197)/360644Robert Price07/2017
76642^201426-1609760636Enzo Doria04/2013
7665(17*10^60631-11)/360632Robert Price07/2015
76666^77916-7760631Lelio R Paula04/2013
7667(27*2^201410-1)/49160630Lelio R Paula01/2014
76685^86727+9860620Lelio R Paula04/2013
766917^49266-2660620Lelio R Paula05/2013
767020^46589-3360614Lelio R Paula05/2013
76716^77889+6560610Lelio R Paula04/2013
7672139901#+14838760595Nicolas PALAU09/2016
76742^201285-11172360593Enzo Doria05/2014
767346199*2^201268+12964760593Paul Vanderveen11/2016
76763^126991-10060591Lelio R Paula04/2013
76752^201278-11162360591Enzo Doria05/2014
76775^86682-1600460589Enzo Doria05/2014
7678(865*10^60583-1)/960585Robert Price11/2017
7679(58*10^60579+221)/960580Robert Price02/2017
76809*2^201231-560578Lelio R Paula04/2014
76814*10^60572-8960573Robert Price08/2017
7682(78557*2^201207+1)/1306760571Lelio R Paula06/2014
76832^201186-6694560564Lelio R Paula09/2011
76842^201186-9439560564Lelio R Paula09/2011
768565^33403+3260557Lelio R Paula01/2016
7686103^30079+10260545Norbert Schneider10/2016
7687(1000159^10091+1)/100016060541Faysal YAtim08/2008
76882^201098-1771760537Enzo Doria05/2013
7689(3^126881+8)/482960534Lelio R Paula03/2012
76902^201074+7504960530Enzo Doria04/2016
769111^58111-129060517Enzo Doria11/2012
7692(509203*2^201012-1)/960516Lelio R Paula04/2015
76932^200911+571160481Lelio R Paula10/2011
7694(2^200912-3)/2360480Lelio R Paula03/2012
769518^48179-17^4817960478Jean-Louis Charton12/2010
769738^38281-37^3828160476Robert Price09/2012
76964*7^71560-360476Lelio R Paula09/2014
7698(10^(2*30232+1)+15*10^30232-1)/360465Robert Price04/2016
7699lucasV(1,2,401712)+260464Mike Oakes01/2017
77002^200833-1849360457Enzo Doria05/2013
770120^46465-504360453Enzo Doria03/2013
77022^200810-1825760450Enzo Doria05/2013
77035^86466-1433660438Enzo Doria02/2013
7704Phi(145558,10)/103928413/161714939/14779231531/36075385837/24241141985360432Maksym Voznyy10/2011
7705(29*2^200703-1)/23160417Lelio R Paula01/2014
77062^200682-101683160412Paul Bourdelais11/2012
77072^200617-1788160392Enzo Doria05/2013
7708(25^43201+1)/2660391Robert Price06/2013
77102^200609-13360390Lelio R Paula08/2011
77092^200608-1283760390Enzo Doria10/2012
77112^200607-1712160389Enzo Doria05/2013
771211^57975-162060375Enzo Doria11/2012
7713(9913*2^200538-1)/380160369Lelio R Paula04/2015
77145^86342+6460351Lelio R Paula04/2013
7715(14*10^60346-23)/960347Robert Price04/2015
77162^200457-829560344Lelio R Paula09/2011
77176^77546+11360343Lelio R Paula04/2013
771937^38461-36^3846160315Robert Price06/2012
77182^200361-1759360315Enzo Doria05/2013
772010103^15059-10660304Enzo Doria07/2012
77212^200301-1740160297Enzo Doria05/2013
7722(37*10^60290+71)/960291Robert Price04/2015
77232^200266-9439560287Lelio R Paula09/2011
77242^200261-11161360285Enzo Doria05/2014
772546^36238-4560256Norbert Schneider07/2014
772613^54091+9460255Lelio R Paula05/2013
7727311^24171-15460253Enzo Doria07/2012
77282^200120-8108960243Paul Bourdelais01/2012
77293^126262+868060243Lelio R Paula04/2013
773043031!3-5904960239Robert Price12/2015
77312^200100-11126960237Enzo Doria05/2014
7732(29*2^200069-1)/537360225Lelio R Paula01/2014
773320^46283-192360216Enzo Doria03/2013
77342^200011-11207560210Enzo Doria05/2014
77352^200002+7453960207Enzo Doria04/2016
7736(38602791*2^200026-1)/(577849*2645749*3427009)60203Jens K. Andersen09/2007
7737(28*10^60180+149)/360181Robert Price10/2017
77382^199872+9360168Donovan Johnson06/2008
77396^77321+7760168Lelio R Paula04/2013
7740(86*10^60165-77)/960166Robert Price05/2016
7741(2^199868+78557)/2337360162Lelio R Paula05/2012
77427^71180+8260155Lelio R Paula04/2013
77432^199814-11229560151Enzo Doria06/2014
7744(51^35227-1)/5060151Paul Bourdelais08/2017
774542964!3-8160135Robert Price09/2014
77462^199709-5160119Lelio R Paula05/2011
77472^199700-11162360116Enzo Doria05/2014
7748(15185*2^199681-1)/15960112Lelio R Paula04/2015
77492^199672+253360108Henri Lifchitz09/2004
775020^46198-1160105Lelio R Paula04/2013


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: November, 22 2017 23:29 (Time in France)

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