PRP Records

Probable Primes Top 10000

(255244 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) !!!


Submit your PRPs


See the Top discoverers
See the Latest PRPs
Search by form



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 ?
825110^65537+2765538Robert Price01/2011
825210^65537-7685965537Patrick De Geest05/2013
8253(28*10^65532+359)/965533Robert Price11/2017
8254(10223*2^217676+1)/365531Lelio R Paula06/2014
8255PadovanNumber[536485]65518Eric W. Weisstein05/2009
82565*10^65509+2365510Robert Price11/2017
8257(8*10^65507-83)/365508Robert Price10/2017
82587*10^65492-4765493Robert Price02/2017
82592^217547-186840765489Enzo Doria04/2016
82602^217531-11176965484Enzo Doria05/2014
82617^77484-1865482Lelio R Paula06/2013
82625754^17413+17413^575465473Norbert Schneider05/2019
82632^217488-11328565471Enzo Doria07/2014
8264151153#/30-3065468Henri Lifchitz12/2011
82652^217466+425765464Lelio R Paula10/2011
826646396!3-8165455Robert Price09/2014
82672^217421-11318565451Enzo Doria07/2014
8268(6883*2^217440-1)/106119329589365448Lelio R Paula04/2015
82692^217408-214565447Lelio R Paula10/2011
82702^217398-1694765444Enzo Doria05/2013
827116097^11628+11628^1609765443Hans Havermann07/2019
82728*5^93613+365434Lelio R Paula09/2014
827315929^12810+12810^1592965430Hans Havermann07/2019
827411^62828-531065429Enzo Doria01/2013
827510^65426+1365427Robert Price01/2011
82762^217341-655565427Lelio R Paula10/2011
827710^65426-5484965426Patrick De Geest05/2013
8278(21*2^217363-1)/5600362666765424Lelio R Paula01/2014
827930011^14608-10865405Enzo Doria07/2012
8280119^31504-265389Lelio R Paula10/2017
8281(43^40031-1)/4265388Robert Price04/2014
82822^217190+9439565381Henri Lifchitz02/2005
828315^55587+4665376Lelio R Paula08/2013
828418443^3502+3502^1844365368Hans Havermann07/2019
82852^217088-11183365350Enzo Doria05/2014
8286(13*2^217069-1)/168294565340Lelio R Paula01/2014
8287(10^65340+47)/365340Robert Price11/2017
8288(62*10^65331+1)/965332Serge Batalov11/2010
82892^216947-11135165308Enzo Doria05/2014
8290-E(18022)/77520184568268532294394923506835965307Thomas Ritschel02/2017
8291(13*10^65297+83)/365298Robert Price09/2016
829216413^9502+9502^1641365288Hans Havermann07/2019
82935^93400-865284Lelio R Paula06/2013
82942^216802-16565264Lelio R Paula08/2011
82952^216799-2863565264Lelio R Paula10/2011
82965*10^65255+5165256Robert Price01/2017
82972^216762-16765252Lelio R Paula08/2011
829811^62657-579065251Enzo Doria01/2013
82993^136756-11288065250Enzo Doria06/2014
83002^216752+2165249Lelio R Paula08/2011
83013*10^65247+1165248Robert Price11/2017
830211^62651-270065245Enzo Doria12/2012
830315130^15609-15609^1513065244Norbert Schneider07/2018
8305Pell-LucasQ(170413)/265230Eric W. Weisstein12/2006
8304gcd(V(790525),5*F(158105)*(F(158105)+1)+1)65230Serge Batalov04/2015
8306(2^216676-1017)/63765224Lelio R Paula04/2012
83072^216652-232765219Yves Minet10/2013
8308(9179*2^216648-1)/466765218Lelio R Paula04/2015
8309(5*10^65203-119)/365204Robert Price04/2016
831015977^12034+12034^1597765193Hans Havermann07/2019
83112^216555-11326965190Enzo Doria07/2014
8313(9513^16384+1)/265181Henri Lifchitz02/2007
831215753^13730+13730^1575365181Hans Havermann07/2019
83142^216474+1291565166Lelio R Paula02/2013
831519^50958-3265163Lelio R Paula08/2013
83162^216442-11213365156Enzo Doria06/2014
83172^216437-11221365155Enzo Doria06/2014
83182^216435-11276765154Enzo Doria06/2014
83192^216420+1270565149Lelio R Paula02/2013
83208*3^136507-765132Lelio R Paula04/2014
8321(-lucasV(1,2,432719)-2)/(5*461)65128Mike Oakes03/2017
832216803^7496+7496^1680365109Hans Havermann07/2019
832315132^15575-15575^1513265102Norbert Schneider07/2018
83245*10^65086-5165087Robert Price10/2017
83252^216197-11176965082Enzo Doria05/2014
83276^83631-7965078Lelio R Paula07/2013
8326572^23601+23601^57265078Norbert Schneider08/2016
8328(3^136399-7)/54422065074Lelio R Paula04/2012
832915592^14911+14911^1559265074Hans Havermann07/2019
83302^216154-142165069Yves Minet01/2013
83312^216145-11266365067Enzo Doria06/2014
8332(7*10^65064+53)/365065Robert Price10/2017
8333132013*10^65050+2^216091-165056Gilbert Mozzo01/2014
8334132019*10^65050+2^216091-165056Gilbert Mozzo01/2014
8335148918*10^65050+2^216091-165056Gilbert Mozzo02/2014
8336194014*10^65050+2^216091-165056Gilbert Mozzo02/2014
8337223864*10^65050+2^216091-165056Gilbert Mozzo04/2014
833982090*10^65050+2^216091-165055Gilbert Mozzo07/2012
834095133*10^65050+2^216091-165055Gilbert Mozzo12/2013
833898142*10^65050+2^216091-165055Gilbert Mozzo12/2013
8341((2^216091-1)*34009-48)/2565054Serge Batalov01/2012
83425977*10^65050+2^216091-165054Gilbert Mozzo03/2012
83437*2^216091+2^298-1365051Peter Lesala03/2007
83442^216091+2*29208-165050Makoto Morimoto10/2013
834515845^12736+12736^1584565045Hans Havermann07/2019
8346(10^(2*32521+1)-6*10^32521-1)/365043Robert Price02/2016
8347p(13861)#/2+25665039Robert Price05/2017
8348(2^216091-2096)/(2^4*3*2918437*5220283)65036Makoto Morimoto10/2017
834911^62439-438065024Enzo Doria01/2013
835016489^8776+8776^1648965022Hans Havermann07/2019
83513^136244+265005Mike Oakes11/2009
835213^58343-5064991Lelio R Paula07/2013
8353331^25791-1000264989Enzo Doria07/2012
83542^215877+13164986Lelio R Paula08/2011
83554*5^92959+964977Lelio R Paula09/2014
83562^215789-1882564959Lelio R Paula09/2011
8357(2^215801-509203)/4132764958Lelio R Paula05/2012
8358U(315311)64954Serge Batalov03/2015
835946072!3-5904964951Robert Price12/2015
83602^215750-595564948Lelio R Paula09/2011
836113^58281+4664922Lelio R Paula07/2013
836215633^14212+14212^1563364919Hans Havermann07/2019
83632^215623+18364909Lelio R Paula08/2011
8364(46*10^64904+521)/964905Robert Price08/2017
8365(3^136043-2^136043)/(19862279*33466579)64895Mike Oakes12/2016
83665*2^215554+364889Lelio R Paula04/2014
83672^215541-11207564885Enzo Doria06/2014
83682*10^64882-364883Dmitry Domanov11/2010
836916592^8121+8121^1659264869Hans Havermann07/2019
837010^64862+34233964863Patrick De Geest05/2013
837110^64862-4764862Robert Price05/2011
837219^50718-8464856Lelio R Paula08/2013
8373(3045*2^215471-1)/(17*1151*27067*173473)64853Jens K. Andersen09/2007
837486413!6-1264846Robert Price08/2018
837510^64843+427869783964844Robert Price05/2015
837610^64843+2196764844Patrick De Geest03/2016
837710^64843-34007364843Patrick De Geest03/2016
837811^62254+7064831Lelio R Paula07/2013
83792^215351-11192564828Enzo Doria05/2014
83802^215310-11764815Lelio R Paula08/2011
8381124^30958-12364809Norbert Schneider02/2015
8382(7*10^64807+17)/364808Erik Branger03/2014
838359703!4-25664806Robert Price11/2019
8384(7*10^(2*32400+1)-27*10^32400-7)/964801Robert Price11/2015
83852^215243-1594964795Enzo Doria04/2013
838623^47581-22^4758164793Robert Price08/2012
8387(62*10^64783-17)/964784Robert Price09/2015
83885*3^135747-464769Lelio R Paula04/2014
8389(59*10^64767-41)/964768Robert Price09/2015
8391(2^215140+3)/1964763Lelio R Paula04/2012
83902^215135-1716964763Enzo Doria05/2013
839216078^10665+10665^1607864762Hans Havermann07/2019
83932^215115-11127764757Enzo Doria05/2014
83949*5^92641+264755Lelio R Paula09/2014
8395(lucasV(1,2,430086)-2)/(7*1033)64731Mike Oakes03/2017
83965791^17200+17200^579164720Norbert Schneider12/2018
8397(5*10^64715-23)/964715Robert Price11/2014
83982^214938-178164703Yves Minet03/2013
839921003^1202+1202^2100364688Hans Havermann07/2019
840011^62111-42064682Enzo Doria08/2012
840118870^2677+2677^1887064680Hans Havermann07/2019
84025^92525+4264673Lelio R Paula06/2013
84032^214824+7189364669Enzo Doria04/2016
840419157^2374+2374^1915764665Hans Havermann08/2019
84052^214799-222164661Yves Minet08/2013
840618393^3274+3274^1839364653Hans Havermann07/2019
84075939^17128+17128^593964637Norbert Schneider10/2018
8408(21*2^214688+1)/29364627Lelio R Paula08/2012
840992^32907+32907^9264623Serge Batalov05/2014
841017650^4579+4579^1765064613Hans Havermann07/2019
8411(89*10^64608-539)/964609Robert Price11/2017
84126^83013+10164597Lelio R Paula07/2013
8413p(13775)#/2+864594Robert Price01/2017
8414(7*10^64568-43)/964568Robert Price10/2014
8415Pell-LucasQ(168677)/264566Eric W. Weisstein11/2006
8416(24737*2^214476+1)/287764565Lelio R Paula06/2014
8417(47*2^214463+1)/764561Lelio R Paula04/2015
84182^214458+5461564559Lelio R Paula10/2011
8419(3^135322+7)/12291140864557Lelio R Paula04/2012
84202^214389-68311364538Paul Bourdelais03/2013
8421(76*10^64534+113)/964535Robert Price11/2017
84222^214369-11124164532Enzo Doria05/2014
8423(19^50461+3^50461)/2264526Robert Price07/2013
842411^61954-366064519Enzo Doria12/2012
8425(23*2^214319-1)/2164517Lelio R Paula01/2014
8426(58695*2^214310-1)/57164516Lelio R Paula04/2015
84272^214300-454764511Yves Minet03/2019
842835^41779-3464510Norbert Schneider04/2014
8429(159^29303+1)/16064506Eric Chen12/2017
8430(89*10^64504-179)/964505Robert Price11/2017
843111^61939-522064503Enzo Doria01/2013
8432(2^214271+78557)/3564501Lelio R Paula05/2012
8433L(308604)+P(308604)64495Robert Price12/2017
8434126^30706-12564494Norbert Schneider02/2015
8435gcd(V(1157265),5*F(231453)*(F(231453)-1)+1)64492Serge Batalov04/2015
84362^214215+1290964486Lelio R Paula10/2011
843716581^7738+7738^1658164478Hans Havermann07/2019
84385^92225+6664463Lelio R Paula06/2013
84392^214126-24055164459Paul Bourdelais03/2013
84408*6^82827+564453Lelio R Paula09/2014
8441(31*2^214120-1)/217048564452Lelio R Paula01/2014
8442(31*2^214088-1)/595564445Lelio R Paula01/2014
844314^56227+8964444Lelio R Paula08/2013
84462^214055-15964437Lelio R Paula08/2011
844410^64436+266764437Patrick De Geest05/2013
844565^35543-64^3554364437Robert Price08/2013
844710^64436-5364436Robert Price05/2011
8448(3^135043-lucasV(1,3,135043)+1)/364432Paul Vanderveen11/2017
8449Phi(128878,10)/3950329792764428Maksym Voznyy11/2015
84503^135027+10064425Lelio R Paula05/2013
8451(3^134972-7)/264398Lelio R Paula04/2012
84526*10^64387+764388Dmitry Domanov11/2010
84532^213864-1837764380Enzo Doria05/2013
845417929^3892+3892^1792964369Hans Havermann06/2019
8455(2^213821+9)/20964365Lelio R Paula04/2012
84562^213788+13564357Lelio R Paula08/2011
845717703^4316+4316^1770364352Hans Havermann06/2019
8458(3^134883+2)/4831364351Lelio R Paula04/2012
8459(49^38069-46^38069)/364344Serge Batalov12/2016
8460(11^61781+2^61781)/1364338Robert Price02/2013
84616^82670+3764330Lelio R Paula07/2013
8462(3^134839+4)/3231295964328Lelio R Paula04/2012
8463(22*10^64326+161)/364327Robert Price02/2017
846411^61767-405064324Enzo Doria12/2012
84652^213645-11485364314Enzo Doria05/2015
846613^57733+1864312Lelio R Paula07/2013
84672^213621+7270764307Enzo Doria04/2016
846810^64305+13679164306Patrick De Geest05/2011
846910^64305-964305Alexander Gramolin01/2011
8470V(307652)64295Serge Batalov03/2015
84714*10^64286-8964287Robert Price08/2017
8472(2^213546-5)/222164281Lelio R Paula04/2012
84732^213438-5869564252Lelio R Paula10/2011
84742^213367-10564230Lelio R Paula08/2011
8475595^23148+23148^59564225Norbert Schneider07/2016
84773^134601+868064221Lelio R Paula05/2013
8476(26*10^64220+61)/364221Robert Price06/2017
8478500^23793+23793^50064217Norbert Schneider08/2016
8479179^28504-264216Lelio R Paula10/2017
84812^213314-45564214Yves Minet02/2012
848039^40359-3864214Norbert Schneider05/2014
84822^213292-1608564208Enzo Doria04/2013
8483(72524!5+1)/2564203Joe McLean10/2018
84842^213274-7764202Lelio R Paula08/2011
848519^50203+7864198Lelio R Paula08/2013
8486(44*10^64192-233)/964193Robert Price10/2017
84872^213240-11286564192Enzo Doria06/2014
84882^213190-11239164177Enzo Doria06/2014
8489(9913*2^213184-1)/965764175Lelio R Paula04/2015
849014^55991+2764173Lelio R Paula07/2013
84912^213158-11258164167Enzo Doria06/2014
84922^213148+9164164Lelio R Paula08/2011
8493(96^32369+1)/9764163Paul Bourdelais08/2017
84956^82439+12564151Lelio R Paula07/2013
84947*2^213102+964151Lelio R Paula04/2014
8496L(306854)+F(306855)64129Henri Lifchitz01/2007
849715621^12736+12736^1562164125Hans Havermann07/2019
849815633^12622+12622^1563364113Hans Havermann07/2019
8499610^23017+23017^61064110Norbert Schneider07/2016
85002^212950-6487564105Lelio R Paula10/2011


Find by discoverer :


Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: November, 10 2019 12:07 (Time in France)

Go back
Valid XHTML 1.0!    Valid CSS!