PRP Records

Probable Primes Top 10000

(259919 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 ?
95012^215789-1882564959Lelio R Paula09/2011
9502(2^215801-509203)/4132764958Lelio R Paula05/2012
9504U(315311)64954Serge Batalov03/2015
9503(2^215773+3530)/264954Stefano Morozzi12/2019
950546072!3-5904964951Robert Price12/2015
95062^215750-595564948Lelio R Paula09/2011
9507(2^215743+2234)/264945Stefano Morozzi12/2019
950813^58281+4664922Lelio R Paula07/2013
950915633^14212+14212^1563364919Hans Havermann07/2019
95102^215623+18364909Lelio R Paula08/2011
9511(2^215611+3326)/264906Stefano Morozzi12/2019
9512(46*10^64904+521)/964905Robert Price08/2017
9513(2^215606+862)/264904Stefano Morozzi12/2019
9514(3^136043-2^136043)/(19862279*33466579)64895Mike Oakes12/2016
95155*2^215554+364889Lelio R Paula04/2014
9516(2^215553+3690)/264888Stefano Morozzi12/2019
95172^215541-11207564885Enzo Doria06/2014
95182*10^64882-364883Dmitry Domanov11/2010
952016592^8121+8121^1659264869Hans Havermann07/2019
9519(2^215490+2602)/264869Stefano Morozzi12/2019
952110^64862+34233964863Patrick De Geest05/2013
952210^64862-4764862Robert Price05/2011
952319^50718-8464856Lelio R Paula08/2013
9524(3045*2^215471-1)/(17*1151*27067*173473)64853Jens K. Andersen09/2007
952586413!6-1264846Robert Price08/2018
952710^64843+427869783964844Robert Price05/2015
952610^64843+2196764844Patrick De Geest03/2016
952810^64843-34007364843Patrick De Geest03/2016
952911^62254+7064831Lelio R Paula07/2013
95302^215351-11192564828Enzo Doria05/2014
9531(2^215331+3906)/264821Stefano Morozzi12/2019
95322^215310-11764815Lelio R Paula08/2011
9533(2^215307+1554)/264814Stefano Morozzi12/2019
9534124^30958-12364809Norbert Schneider02/2015
9535(7*10^64807+17)/364808Erik Branger03/2014
953659703!4-25664806Robert Price11/2019
9537(2^215277+2522)/264805Stefano Morozzi12/2019
9538(7*10^(2*32400+1)-27*10^32400-7)/964801Robert Price11/2015
95392^215243-1594964795Enzo Doria04/2013
954023^47581-22^4758164793Robert Price08/2012
9541(62*10^64783-17)/964784Robert Price09/2015
954210^64770+98765432164771Robert Price12/2019
954310^64770+16445164771Patrick De Geest02/2020
954410^64770-47817964770Patrick De Geest02/2020
95455*3^135747-464769Lelio R Paula04/2014
9546(59*10^64767-41)/964768Robert Price09/2015
9549(2^215140+3)/1964763Lelio R Paula04/2012
95482^215135-1716964763Enzo Doria05/2013
9547(2^215141+6)/3864763Stefano Morozzi03/2020
955016078^10665+10665^1607864762Hans Havermann07/2019
95512^215115-11127764757Enzo Doria05/2014
95529*5^92641+264755Lelio R Paula09/2014
9553(2^215069+414)/264742Stefano Morozzi12/2019
9554(2^215036+2638)/264732Stefano Morozzi12/2019
9555(lucasV(1,2,430086)-2)/(7*1033)64731Mike Oakes03/2017
9556(2^215017+762)/264727Stefano Morozzi12/2019
955714073^15602-15602^1407364724Norbert Schneider12/2019
9558(2^215008+2958)/264724Stefano Morozzi12/2019
95595791^17200+17200^579164720Norbert Schneider12/2018
9560(5*10^64715-23)/964715Robert Price11/2014
9561(2^214941+2754)/264704Stefano Morozzi12/2019
95622^214938-178164703Yves Minet03/2013
9563(2^214914+2202)/264696Stefano Morozzi12/2019
956421003^1202+1202^2100364688Hans Havermann07/2019
956511^62111-42064682Enzo Doria08/2012
956618870^2677+2677^1887064680Hans Havermann07/2019
95675^92525+4264673Lelio R Paula06/2013
95682^214824+7189364669Enzo Doria04/2016
957019157^2374+2374^1915764665Hans Havermann08/2019
9569(2^214812+3162)/264665Stefano Morozzi12/2019
95712^214799-222164661Yves Minet08/2013
957218393^3274+3274^1839364653Hans Havermann07/2019
9573(2^214766+2562)/264651Stefano Morozzi12/2019
9574(2^214746+1242)/264645Stefano Morozzi12/2019
9575(2^214740+1846)/264643Stefano Morozzi12/2019
95765939^17128+17128^593964637Norbert Schneider10/2018
9577(2^214703+2594)/264632Stefano Morozzi12/2019
9578(21*2^214688+1)/29364627Lelio R Paula08/2012
957992^32907+32907^9264623Serge Batalov05/2014
958017650^4579+4579^1765064613Hans Havermann07/2019
9581(89*10^64608-539)/964609Robert Price11/2017
95826^83013+10164597Lelio R Paula07/2013
9583p(13775)#/2+864594Robert Price01/2017
9584(2^214528+3378)/264580Stefano Morozzi12/2019
9585(7*10^64568-43)/964568Robert Price10/2014
9586Pell-LucasQ(168677)/264566Eric W. Weisstein11/2006
9587(24737*2^214476+1)/287764565Lelio R Paula06/2014
9588(47*2^214463+1)/764561Lelio R Paula04/2015
95892^214458+5461564559Lelio R Paula10/2011
9590(3^135322+7)/12291140864557Lelio R Paula04/2012
9591(2^214445+3282)/264555Stefano Morozzi12/2019
9592(2^214443+2558)/264554Stefano Morozzi12/2019
9593(2^214442+3738)/264554Stefano Morozzi12/2019
9594(2^214406+3550)/264543Stefano Morozzi12/2019
95952^214389-68311364538Paul Bourdelais03/2013
9596(76*10^64534+113)/964535Robert Price11/2017
95972^214369-11124164532Enzo Doria05/2014
9598(19^50461+3^50461)/2264526Robert Price07/2013
959911^61954-366064519Enzo Doria12/2012
9600(23*2^214319-1)/2164517Lelio R Paula01/2014
9601(58695*2^214310-1)/57164516Lelio R Paula04/2015
96022^214300-454764511Yves Minet03/2019
960335^41779-3464510Norbert Schneider04/2014
9604(159^29303+1)/16064506Eric Chen12/2017
9605(89*10^64504-179)/964505Robert Price11/2017
960611^61939-522064503Enzo Doria01/2013
9607(2^214271+78557)/3564501Lelio R Paula05/2012
9608L(308604)+P(308604)64495Robert Price12/2017
9609126^30706-12564494Norbert Schneider02/2015
9610gcd(V(1157265),5*F(231453)*(F(231453)-1)+1)64492Serge Batalov04/2015
961113661^15594-15594^1366164489Norbert Schneider12/2019
9612(2^214219+1014)/264487Stefano Morozzi12/2019
96132^214215+1290964486Lelio R Paula10/2011
9614(2^214206+1458)/264483Stefano Morozzi12/2019
961516581^7738+7738^1658164478Hans Havermann07/2019
96165^92225+6664463Lelio R Paula06/2013
96172^214126-24055164459Paul Bourdelais03/2013
96188*6^82827+564453Lelio R Paula09/2014
9619(31*2^214120-1)/217048564452Lelio R Paula01/2014
9620(2^214092+3966)/264448Stefano Morozzi12/2019
9621(31*2^214088-1)/595564445Lelio R Paula01/2014
962214^56227+8964444Lelio R Paula08/2013
96252^214055-15964437Lelio R Paula08/2011
962310^64436+266764437Patrick De Geest05/2013
962465^35543-64^3554364437Robert Price08/2013
962610^64436-5364436Robert Price05/2011
9627(3^135043-lucasV(1,3,135043)+1)/364432Paul Vanderveen11/2017
9628(2^214030+1722)/264430Stefano Morozzi12/2019
9629Phi(128878,10)/3950329792764428Maksym Voznyy11/2015
96303^135027+10064425Lelio R Paula05/2013
9631(3^134972-7)/264398Lelio R Paula04/2012
96326*10^64387+764388Dmitry Domanov11/2010
96332^213864-1837764380Enzo Doria05/2013
963417929^3892+3892^1792964369Hans Havermann06/2019
9635(2^213821+9)/20964365Lelio R Paula04/2012
9636(2^213799+3650)/264360Stefano Morozzi12/2019
96372^213788+13564357Lelio R Paula08/2011
963817703^4316+4316^1770364352Hans Havermann06/2019
9639(3^134883+2)/4831364351Lelio R Paula04/2012
9640(49^38069-46^38069)/364344Serge Batalov12/2016
9641(11^61781+2^61781)/1364338Robert Price02/2013
96426^82670+3764330Lelio R Paula07/2013
9643(3^134839+4)/3231295964328Lelio R Paula04/2012
9644(22*10^64326+161)/364327Robert Price02/2017
964511^61767-405064324Enzo Doria12/2012
96462^213645-11485364314Enzo Doria05/2015
9647(2^213641+1794)/264313Stefano Morozzi12/2019
964813^57733+1864312Lelio R Paula07/2013
96492^213621+7270764307Enzo Doria04/2016
965010^64305+13679164306Patrick De Geest05/2011
965110^64305-964305Alexander Gramolin01/2011
9652V(307652)64295Serge Batalov03/2015
96534*10^64286-8964287Robert Price08/2017
9654(2^213552+3082)/264286Stefano Morozzi12/2019
9655(2^213546-5)/222164281Lelio R Paula04/2012
9656(2^213473+702)/264262Stefano Morozzi12/2019
96582^213438-5869564252Lelio R Paula10/2011
9657(2^213439+1170)/264252Stefano Morozzi12/2019
9659(2^213398+2094)/264239Stefano Morozzi12/2019
96602^213367-10564230Lelio R Paula08/2011
9661595^23148+23148^59564225Norbert Schneider07/2016
96633^134601+868064221Lelio R Paula05/2013
9662(26*10^64220+61)/364221Robert Price06/2017
9664500^23793+23793^50064217Norbert Schneider08/2016
9665179^28504-264216Lelio R Paula10/2017
96672^213314-45564214Yves Minet02/2012
966639^40359-3864214Norbert Schneider05/2014
96682^213292-1608564208Enzo Doria04/2013
9669(2^213282+3922)/264204Stefano Morozzi12/2019
9670(72524!5+1)/2564203Joe McLean10/2018
96712^213274-7764202Lelio R Paula08/2011
967219^50203+7864198Lelio R Paula08/2013
9673(44*10^64192-233)/964193Robert Price10/2017
96742^213240-11286564192Enzo Doria06/2014
9675(2^213196+3186)/264179Stefano Morozzi12/2019
96762^213190-11239164177Enzo Doria06/2014
9677(2^213209+11)/1823077764176Stefano Morozzi03/2020
9678(9913*2^213184-1)/965764175Lelio R Paula04/2015
967914^55991+2764173Lelio R Paula07/2013
96802^213158-11258164167Enzo Doria06/2014
96812^213148+9164164Lelio R Paula08/2011
9682(96^32369+1)/9764163Paul Bourdelais08/2017
96846^82439+12564151Lelio R Paula07/2013
96837*2^213102+964151Lelio R Paula04/2014
9685(2^213063+3186)/264139Stefano Morozzi12/2019
9686L(306854)+F(306855)64129Henri Lifchitz01/2007
968715621^12736+12736^1562164125Hans Havermann07/2019
968815633^12622+12622^1563364113Hans Havermann07/2019
9689610^23017+23017^61064110Norbert Schneider07/2016
96902^212950-6487564105Lelio R Paula10/2011
9691(266*10^64102-17)/364104Robert Price06/2016
9692p(13679)#/2+6464097Robert Price03/2017
969319^50119+9464090Lelio R Paula08/2013
96942^212880-14764084Lelio R Paula08/2011
9695(2^212876+2826)/264082Stefano Morozzi12/2019
969611^61523-459064070Enzo Doria01/2013
96975^91663+3864070Lelio R Paula05/2013
96985^91650+5264061Lelio R Paula05/2013
9699(2^212801+2822)/264060Stefano Morozzi12/2019
9700(2^212798+2442)/264059Stefano Morozzi12/2019
9701(2^212795+1734)/264058Stefano Morozzi12/2019
97022^212770+6964051Lelio R Paula08/2011
9703(3^134227+1)/464042Paul Bourdelais11/2007
9704(2*10^64041-17)/364041Robert Price08/2014
9705(15^54449+1)/1664036Paul Bourdelais03/2010
9706(29*10^64027+91)/364028Robert Price03/2016
9707(lucasV(1,2,425405)+2)/(17*89)64027Mike Oakes03/2017
970816878!+16878#-164022D. Gazzoni Filho & Lucas Teixeira05/2005
970915862^10863+10863^1586264019Hans Havermann06/2019
97102^212663+5364018Lelio R Paula08/2011
9711(4*10^64014+197)/364015Robert Price03/2017
971285402!6-364014Robert Price08/2018
9713(140^29819+1)/14163994Richard Fischer05/2018
971415313^15094+15094^1531363991Hans Havermann06/2019
971510^63986+6363987Robert Price01/2011
971610^63986-3155763986Patrick De Geest05/2013
971715699^11900+11900^1569963983Hans Havermann07/2019
971831487!2-2^3148763982Robert Price09/2015
9719(2^212539+3950)/263981Stefano Morozzi12/2019
9720(21*2^212522-1)/141632363971Lelio R Paula01/2014
97215^91517+9863968Lelio R Paula04/2013
9722(2^212486+2874)/263965Stefano Morozzi12/2019
9723(19*10^63960-43)/363961Robert Price10/2017
9724(62*10^63954-17)/963955Robert Price09/2015
97265^91493-4^9149363951Predrag Minovic04/2004
9725V(364793)63951Serge Batalov03/2015
972719^50004+5863943Lelio R Paula05/2013
97285*6^82172-763943Lelio R Paula09/2014
9729(56*10^63942+223)/963943Robert Price07/2016
973019^50000-2463938Lelio R Paula05/2013
9731(23*2^212374-1)/2701963928Lelio R Paula01/2014
9732(9*2^212355-1)/76163924Lelio R Paula01/2014
97342^212344-18363922Lelio R Paula08/2011
9733(58695*2^212336-1)/37963922Lelio R Paula04/2015
973510^63916+7963917Robert Price01/2011
973610^63916-7682363916Patrick De Geest05/2013
9737(2^212318+462)/263914Stefano Morozzi12/2019
97382^212295-2563908Lelio R Paula08/2011
97392^212285-238363905Yves Minet10/2013
9740267^26336+26336^26763905Norbert Schneider09/2014
9741(-lucasV(1,2,424552)-2)/160163899Mike Oakes03/2017
974319^49962+6063890Lelio R Paula05/2013
97423^133906-11305663890Enzo Doria07/2014
97447933^16384+7932^1638463889Richard Fischer09/2019
9745(lucasV(1,2,424451)+2)/363886Mike Oakes03/2017
97463*6^82092+563881Lelio R Paula09/2014
974715441^13706+13706^1544163879Hans Havermann02/2017
97482^212154-77635163865Paul Bourdelais03/2013
974935^41359+263862Lelio R Paula05/2013
9750(61*10^63857-43)/963858Robert Price09/2015


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: March, 29 2020 17:41 (Time in France)

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