PRP Records

Probable Primes Top 10000

(255169 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 ?
475110^91230+9^(91230+1)91231Robert Price08/2016
475210^91230-91114191230Patrick De Geest11/2016
475310^91229+34879391230Patrick De Geest07/2019
475410^91229-247191229Patrick De Geest01/2019
475510^91225+527191226Patrick De Geest01/2019
47576^117232-1742391225Enzo Doria02/2013
475610^91225-14721991225Patrick De Geest07/2019
47587*10^91215+391216Erik Branger11/2009
475910^91215+23061191216Patrick De Geest07/2019
476010^91215-453991215Patrick De Geest01/2019
476110^91210+242191211Patrick De Geest01/2019
476210^91210-173791210Patrick De Geest01/2019
476397*10^91205-391207Robert Price01/2017
47642^302979-16118191206Enzo Doria04/2013
47652^302949+8191197Henri Lifchitz02/2007
476610^91194+20036191195Patrick De Geest07/2019
47684*6^117192-591194Lelio R Paula10/2014
476710^91194-866391194Patrick De Geest01/2019
47692^302918+9991188Lelio R Paula11/2012
477010^91186+26811191187Patrick De Geest07/2019
477110^91186-776391186Patrick De Geest01/2019
477210^91181+55047191182Patrick De Geest07/2019
477310^91181-136791181Patrick De Geest01/2019
477410^91178+7188391179Patrick De Geest07/2019
477510^91178-471991178Patrick De Geest01/2019
477610^91165+304391166Patrick De Geest01/2019
477710^91165-39941391165Patrick De Geest07/2019
477810^91156+386191157Patrick De Geest01/2019
477910^91156-23149791156Patrick De Geest07/2019
47802^302797+186958791151Enzo Doria05/2016
4781265^37614+37614^26591148Norbert Schneider01/2015
47827^107852+8291146Lelio R Paula04/2016
4783(38*10^91144-11)/991145Robert Price05/2015
4784(55*10^91142+377)/991143Robert Price10/2017
478510^91128+996191129Patrick De Geest01/2019
4787249^38030+38030^24991128Norbert Schneider01/2015
478610^91128-18915391128Patrick De Geest07/2019
47886^117094-21104991117Mike Oakes05/2011
47902^302602-186718191093Enzo Doria03/2016
478910^91092+5612791093Patrick De Geest07/2019
479110^91092-910791092Patrick De Geest01/2019
4792(1017*2^302592-1)/5391091Lelio R Paula04/2015
479315^77445-1691083Lelio R Paula07/2016
47942^302505+8191064Henri Lifchitz02/2007
47952^302496-11234991061Enzo Doria06/2014
479617^73999-7291052Lelio R Paula07/2016
479710^91047+933191048Patrick De Geest01/2019
479810^91047-67116991047Patrick De Geest07/2019
479910^91044+207791045Patrick De Geest01/2019
480010^91044-13635991044Patrick De Geest07/2019
480110^91041+934991042Patrick De Geest01/2019
480210^91041-782391041Patrick De Geest01/2019
480310^91040+407791041Patrick De Geest01/2019
480410^91040-11942191040Patrick De Geest07/2019
480510^91037+276991038Patrick De Geest01/2019
480610^91037-2264991037Patrick De Geest07/2019
4807(16*10^91032+41)/391033Robert Price10/2017
480810^91023+5803991024Patrick De Geest07/2019
480910^91023-647191023Patrick De Geest01/2019
481010^91018+787391019Patrick De Geest01/2019
481110^91018-33317791018Patrick De Geest07/2019
481210^91017+6876791018Patrick De Geest07/2019
481310^91017-42832791017Patrick De Geest07/2019
481410^91016+7311191017Patrick De Geest07/2019
481510^91016-797391016Patrick De Geest01/2019
48162^302332+57729457591012Lelio R Paula08/2016
481710^91004+907391005Patrick De Geest01/2019
481810^91004-49151991004Patrick De Geest07/2019
481910^91003+7426991004Patrick De Geest07/2019
482010^91003-390391003Patrick De Geest01/2019
48212^302274+7420990994Enzo Doria04/2016
482210^90991+8114790992Patrick De Geest07/2019
482310^90991-627990991Patrick De Geest01/2019
482410^90983+139390984Patrick De Geest01/2019
482510^90983-56238390983Patrick De Geest07/2019
4826(311^36497-1)/31090976Eric Chen09/2017
4827(3^190668+2)/8990970Lelio R Paula04/2013
48282^302188+9019590968Lelio R Paula02/2016
4829(53*10^90965-71)/990966Robert Price09/2015
483010^90965+57398790966Patrick De Geest07/2019
483110^90965-683390965Patrick De Geest01/2019
483210^90964+4878990965Patrick De Geest07/2019
483310^90964-5210390964Patrick De Geest07/2019
483410^90963+19188990964Patrick De Geest07/2019
483510^90963-365990963Patrick De Geest01/2019
483610^90962+765790963Patrick De Geest01/2019
483710^90962-21563390962Patrick De Geest07/2019
483810^90961+6747190962Patrick De Geest07/2019
483910^90961-21104390961Patrick De Geest07/2019
484010^90960+107211790961Patrick De Geest07/2019
484110^90959+879190960Patrick De Geest01/2019
484210^90960-61065990960Patrick De Geest07/2019
484310^90959-27521390959Patrick De Geest07/2019
484410^90948+986790949Patrick De Geest01/2019
484510^90948-10923990948Patrick De Geest07/2019
48462^302113+7410590946Enzo Doria04/2016
48472^302102-655590942Lelio R Paula02/2016
484810^90930+9522390931Patrick De Geest07/2019
484910^90930-362390930Patrick De Geest01/2019
4851156*(10^(4*22731)-1)/101-190925Robert Price05/2014
48503^190568+3890925Lelio R Paula04/2016
485210^90917+17986390918Patrick De Geest07/2019
485310^90917-669390917Patrick De Geest01/2019
48542^302009-1644990914Enzo Doria04/2013
485510^90908+318190909Patrick De Geest01/2019
485610^90908-13951190908Patrick De Geest07/2019
485710^90904+10694790905Patrick De Geest07/2019
485810^90904-516990904Patrick De Geest01/2019
485910^90903+12096390904Patrick De Geest07/2019
486010^90902+261390903Patrick De Geest01/2019
486110^90903-19073790903Patrick De Geest07/2019
486210^90902-95232990902Patrick De Geest07/2019
4863(17*2^301951-1)/16590896Lelio R Paula02/2014
48643^190497+7490891Lelio R Paula04/2016
4865(24737*2^301896+1)/39990882Lelio R Paula06/2014
486610^90880+570790881Patrick De Geest01/2019
486710^90880-15299390880Patrick De Geest07/2019
486818^72397+8990878Lelio R Paula06/2016
4869134^42719-13390868Norbert Schneider03/2019
48706^116769-4790864Lelio R Paula05/2016
487110^90858+23343390859Patrick De Geest07/2019
487210^90858-830190858Patrick De Geest01/2019
487310^90849+4014190850Patrick De Geest07/2019
487410^90849-472190849Patrick De Geest01/2019
48752^301712-46590825Lelio R Paula02/2016
48762^301693-6990819Lelio R Paula11/2012
48772^301683-301683^290816Henri Lifchitz05/2005
487810^90807+727990808Patrick De Geest01/2019
487910^90807-16226390807Patrick De Geest07/2019
488010^90800-645390800Patrick De Geest11/2018
488111^87187-171090796Enzo Doria12/2012
48825*10^90793+2190794Robert Price01/2017
4883(22*10^90792-13)/990793Robert Price03/2015
48842^301591-161590788Lelio R Paula02/2016
4885(52^52901+1)/5390777Paul Bourdelais08/2017
48862^301546-10903790775Enzo Doria04/2014
488710^90772+402990773Patrick De Geest11/2018
488810^90772-3662790772Patrick De Geest07/2019
488910^90771+6773790772Patrick De Geest07/2019
489010^90771-44100390771Patrick De Geest07/2019
489110^90770+2894190771Patrick De Geest07/2019
489210^90770-43190770Patrick De Geest11/2018
489314^79195-390768Lelio R Paula06/2016
489410^90766+87790767Patrick De Geest11/2018
48952^301517-186169390766Enzo Doria11/2015
489610^90766-10924190766Patrick De Geest07/2019
489710^90765+48536190766Patrick De Geest07/2019
489810^90765-479790765Patrick De Geest11/2018
489910^90757+757390758Patrick De Geest11/2018
490010^90757-55497990757Patrick De Geest07/2019
490110^90756+43810990757Patrick De Geest07/2019
490210^90756-872790756Patrick De Geest11/2018
490310^90749+82390750Patrick De Geest11/2018
49062^301460-17390749Lelio R Paula11/2012
490410^90748+421390749Patrick De Geest11/2018
490510^90749-13041390749Patrick De Geest07/2019
490710^90748-7541190748Patrick De Geest07/2019
490810^90747+43847190748Patrick De Geest07/2019
490910^90747-927990747Patrick De Geest11/2018
4910(85*10^90745-103)/990746Robert Price10/2017
491110^90726+407790727Patrick De Geest11/2018
491210^90726-50495190726Patrick De Geest07/2019
491310^90721+18190722Patrick De Geest11/2018
491410^90721-17714990721Patrick De Geest07/2019
49152^301312-8990704Lelio R Paula11/2012
491610^90696+634990697Patrick De Geest11/2018
49182^301285-12990696Lelio R Paula11/2012
491710^90696-63504990696Patrick De Geest07/2019
49192^301282-10999190695Enzo Doria04/2014
492010^90690+887790691Patrick De Geest11/2018
492110^90690-22743390690Patrick De Geest07/2019
492210^90683+6141190684Patrick De Geest07/2019
492310^90683-257790683Patrick De Geest11/2018
49242^301228-185426990679Enzo Doria09/2015
4925(151*10^90669-1)/390671Robert Price04/2017
4926(32*10^90669+13)/990670Robert Price04/2015
492710^90669+979390670Patrick De Geest11/2018
492810^90669-22393190669Patrick De Geest07/2019
492910^90665+1098990666Patrick De Geest07/2019
493010^90665-308790665Patrick De Geest11/2018
493110^90662+8963790663Patrick De Geest07/2019
493210^90662-951990662Patrick De Geest11/2018
493310^90661+237390662Patrick De Geest11/2018
493410^90661-19478190661Patrick De Geest07/2019
49353*5^129698+890656Lelio R Paula10/2014
4936F(433781)90655Henri Lifchitz09/2003
493719^70891+8290653Lelio R Paula06/2016
4938(29*2^301124-1)/1390648Lelio R Paula02/2014
493910^90636+6415990637Patrick De Geest07/2019
494010^90636-310190636Patrick De Geest11/2018
49417*3^189953-890632Lelio R Paula08/2014
494210^90626+33928990627Patrick De Geest07/2019
494310^90626-113190626Patrick De Geest11/2018
494411^87022-180090625Enzo Doria12/2012
494510^90623+86190624Patrick De Geest11/2018
494610^90623-30584190623Patrick De Geest07/2019
4947(2^301042+47)/1203696990616Lelio R Paula06/2013
49492^301004-278693990612Enzo Doria03/2016
494810^90611+16997790612Patrick De Geest07/2019
495110^90611-973790611Patrick De Geest11/2018
495010^90610+3674790611Patrick De Geest07/2019
495210^90609+682390610Patrick De Geest11/2018
495310^90610-2657390610Patrick De Geest07/2019
495410^90609-22817390609Patrick De Geest07/2019
49552^300980-2790605Lelio R Paula11/2012
49562*10^90597-790598Dmitry Domanov11/2010
4957197^39485+290597Lelio R Paula06/2013
49587^107198+4890593Lelio R Paula04/2016
4959(86*10^90588+121)/990589Robert Price03/2017
49602^300923+5390587Lelio R Paula11/2012
49612^300874+790573Lelio R Paula10/2012
496210^90567+948990568Patrick De Geest11/2018
496310^90567-23135390567Patrick De Geest07/2019
49645^129568-5690565Lelio R Paula04/2016
49652^300847-11283190564Enzo Doria06/2014
496610^90562+79019790563Patrick De Geest07/2019
496710^90562-298190562Patrick De Geest11/2018
496810^90549+381190550Patrick De Geest11/2018
496910^90549-63030390549Patrick De Geest07/2019
49702^300790-454190547Yves Minet03/2019
497110^90532+816990533Patrick De Geest11/2018
497210^90531+983190532Patrick De Geest11/2018
497310^90532-15488990532Patrick De Geest07/2019
497410^90531-106058990531Patrick De Geest07/2019
49752^300718+25525590526Lelio R Paula02/2016
497610^90516+21591790517Patrick De Geest07/2019
497710^90516-678390516Patrick De Geest11/2018
497810^90511+3017790512Patrick De Geest07/2019
497910^90511-697790511Patrick De Geest11/2018
49802^300637+9590501Lelio R Paula11/2012
49827^107087-2490500Lelio R Paula04/2016
498110^90499+19154790500Patrick De Geest07/2019
498310^90499-582390499Patrick De Geest11/2018
4985(10^90499+3^90499)/1390498Robert Price01/2013
498413^81241+9090498Lelio R Paula06/2016
498610^90480+513190481Patrick De Geest11/2018
498710^90480-8572190480Patrick De Geest07/2019
49886^116273-8590478Lelio R Paula05/2016
498910^90473+313990474Patrick De Geest11/2018
499010^90473-15059990473Patrick De Geest07/2019
499110^90470+231990471Patrick De Geest11/2018
499210^90470-7163790470Patrick De Geest07/2019
49936^116256-1757390465Enzo Doria02/2013
49942^300502+5461590461Lelio R Paula02/2016
4995(13*2^300487+1)/4590456Lelio R Paula09/2013
499610^90453+14184390454Patrick De Geest07/2019
499710^90453-396990453Patrick De Geest11/2018
499810^90440+135990441Patrick De Geest11/2018
499910^90440-1882190440Patrick De Geest07/2019
5000(3^189545-8)/590436Lelio R Paula01/2013


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: October, 13 2019 10:51 (Time in France)

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