PRP Records

Probable Primes Top 10000

(252675 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 ?
45012^303191-11125991270Enzo Doria05/2014
450310^91230+9^(91230+1)91231Robert Price08/2016
450210^91230+792191231Patrick De Geest11/2016
450410^91230-91114191230Patrick De Geest11/2016
450510^91229-247191229Patrick De Geest01/2019
450610^91225+527191226Patrick De Geest01/2019
45076^117232-1742391225Enzo Doria02/2013
45087*10^91215+391216Erik Branger11/2009
450910^91215-453991215Patrick De Geest01/2019
451010^91210+242191211Patrick De Geest01/2019
451110^91210-173791210Patrick De Geest01/2019
451297*10^91205-391207Robert Price01/2017
45132^302979-16118191206Enzo Doria04/2013
45142^302949+8191197Henri Lifchitz02/2007
45154*6^117192-591194Lelio R Paula10/2014
451610^91194-866391194Patrick De Geest01/2019
45172^302918+9991188Lelio R Paula11/2012
451810^91186-776391186Patrick De Geest01/2019
451910^91181-136791181Patrick De Geest01/2019
452010^91178-471991178Patrick De Geest01/2019
452110^91165+304391166Patrick De Geest01/2019
452210^91156+386191157Patrick De Geest01/2019
45232^302797+186958791151Enzo Doria05/2016
4524265^37614+37614^26591148Norbert Schneider01/2015
45257^107852+8291146Lelio R Paula04/2016
4526(38*10^91144-11)/991145Robert Price05/2015
4527(55*10^91142+377)/991143Robert Price10/2017
452810^91128+996191129Patrick De Geest01/2019
4529249^38030+38030^24991128Norbert Schneider01/2015
45306^117094-21104991117Mike Oakes05/2011
45312^302602-186718191093Enzo Doria03/2016
453210^91092-910791092Patrick De Geest01/2019
4533(1017*2^302592-1)/5391091Lelio R Paula04/2015
453415^77445-1691083Lelio R Paula07/2016
45352^302505+8191064Henri Lifchitz02/2007
45362^302496-11234991061Enzo Doria06/2014
453717^73999-7291052Lelio R Paula07/2016
453810^91047+933191048Patrick De Geest01/2019
453910^91044+207791045Patrick De Geest01/2019
454010^91041+934991042Patrick De Geest01/2019
454110^91041-782391041Patrick De Geest01/2019
454210^91040+407791041Patrick De Geest01/2019
454310^91037+276991038Patrick De Geest01/2019
4544(16*10^91032+41)/391033Robert Price10/2017
454510^91023-647191023Patrick De Geest01/2019
454610^91018+787391019Patrick De Geest01/2019
454710^91016-797391016Patrick De Geest01/2019
45482^302332+57729457591012Lelio R Paula08/2016
454910^91004+907391005Patrick De Geest01/2019
455010^91003-390391003Patrick De Geest01/2019
45512^302274+7420990994Enzo Doria04/2016
455210^90991-627990991Patrick De Geest01/2019
455310^90983+139390984Patrick De Geest01/2019
4554(311^36497-1)/31090976Eric Chen09/2017
4555(3^190668+2)/8990970Lelio R Paula04/2013
45562^302188+9019590968Lelio R Paula02/2016
4557(53*10^90965-71)/990966Robert Price09/2015
455810^90965-683390965Patrick De Geest01/2019
455910^90963-365990963Patrick De Geest01/2019
456010^90962+765790963Patrick De Geest01/2019
456110^90959+879190960Patrick De Geest01/2019
456210^90948+986790949Patrick De Geest01/2019
45632^302113+7410590946Enzo Doria04/2016
45642^302102-655590942Lelio R Paula02/2016
456510^90930-362390930Patrick De Geest01/2019
4566156*(10^(4*22731)-1)/101-190925Robert Price05/2014
45673^190568+3890925Lelio R Paula04/2016
456810^90917-669390917Patrick De Geest01/2019
45692^302009-1644990914Enzo Doria04/2013
457010^90908+318190909Patrick De Geest01/2019
457110^90904-516990904Patrick De Geest01/2019
457210^90902+261390903Patrick De Geest01/2019
4573(17*2^301951-1)/16590896Lelio R Paula02/2014
45743^190497+7490891Lelio R Paula04/2016
4575(24737*2^301896+1)/39990882Lelio R Paula06/2014
457610^90880+570790881Patrick De Geest01/2019
457718^72397+8990878Lelio R Paula06/2016
4578134^42719-13390868Norbert Schneider03/2019
45796^116769-4790864Lelio R Paula05/2016
458010^90858-830190858Patrick De Geest01/2019
458110^90849-472190849Patrick De Geest01/2019
45822^301712-46590825Lelio R Paula02/2016
45832^301693-6990819Lelio R Paula11/2012
45842^301683-301683^290816Henri Lifchitz05/2005
458510^90807+727990808Patrick De Geest01/2019
458610^90800-645390800Patrick De Geest11/2018
458711^87187-171090796Enzo Doria12/2012
45885*10^90793+2190794Robert Price01/2017
4589(22*10^90792-13)/990793Robert Price03/2015
45902^301591-161590788Lelio R Paula02/2016
4591(52^52901+1)/5390777Paul Bourdelais08/2017
45922^301546-10903790775Enzo Doria04/2014
459310^90772+402990773Patrick De Geest11/2018
459410^90770-43190770Patrick De Geest11/2018
459514^79195-390768Lelio R Paula06/2016
459610^90766+87790767Patrick De Geest11/2018
45972^301517-186169390766Enzo Doria11/2015
459810^90765-479790765Patrick De Geest11/2018
459910^90757+757390758Patrick De Geest11/2018
460010^90756-872790756Patrick De Geest11/2018
460110^90749+82390750Patrick De Geest11/2018
46032^301460-17390749Lelio R Paula11/2012
460210^90748+421390749Patrick De Geest11/2018
460410^90747-927990747Patrick De Geest11/2018
4605(85*10^90745-103)/990746Robert Price10/2017
460610^90726+407790727Patrick De Geest11/2018
460710^90721+18190722Patrick De Geest11/2018
46082^301312-8990704Lelio R Paula11/2012
460910^90696+634990697Patrick De Geest11/2018
46102^301285-12990696Lelio R Paula11/2012
46112^301282-10999190695Enzo Doria04/2014
461210^90690+887790691Patrick De Geest11/2018
461310^90683-257790683Patrick De Geest11/2018
46142^301228-185426990679Enzo Doria09/2015
4615(151*10^90669-1)/390671Robert Price04/2017
4616(32*10^90669+13)/990670Robert Price04/2015
461710^90669+979390670Patrick De Geest11/2018
461810^90665-308790665Patrick De Geest11/2018
461910^90662-951990662Patrick De Geest11/2018
462010^90661+237390662Patrick De Geest11/2018
46213*5^129698+890656Lelio R Paula10/2014
4622F(433781)90655Henri Lifchitz09/2003
462319^70891+8290653Lelio R Paula06/2016
4624(29*2^301124-1)/1390648Lelio R Paula02/2014
462510^90636-310190636Patrick De Geest11/2018
46267*3^189953-890632Lelio R Paula08/2014
462710^90626-113190626Patrick De Geest11/2018
462811^87022-180090625Enzo Doria12/2012
462910^90623+86190624Patrick De Geest11/2018
4630(2^301042+47)/1203696990616Lelio R Paula06/2013
46312^301004-278693990612Enzo Doria03/2016
463210^90611-973790611Patrick De Geest11/2018
463310^90609+682390610Patrick De Geest11/2018
46342^300980-2790605Lelio R Paula11/2012
46352*10^90597-790598Dmitry Domanov11/2010
4636197^39485+290597Lelio R Paula06/2013
46377^107198+4890593Lelio R Paula04/2016
4638(86*10^90588+121)/990589Robert Price03/2017
46392^300923+5390587Lelio R Paula11/2012
46402^300874+790573Lelio R Paula10/2012
464110^90567+948990568Patrick De Geest11/2018
46425^129568-5690565Lelio R Paula04/2016
46432^300847-11283190564Enzo Doria06/2014
464410^90562-298190562Patrick De Geest11/2018
464510^90549+381190550Patrick De Geest11/2018
46462^300790-454190547Yves Minet03/2019
464710^90532+816990533Patrick De Geest11/2018
464810^90531+983190532Patrick De Geest11/2018
46492^300718+25525590526Lelio R Paula02/2016
465010^90516-678390516Patrick De Geest11/2018
465110^90511-697790511Patrick De Geest11/2018
46522^300637+9590501Lelio R Paula11/2012
46537^107087-2490500Lelio R Paula04/2016
465410^90499-582390499Patrick De Geest11/2018
4656(10^90499+3^90499)/1390498Robert Price01/2013
465513^81241+9090498Lelio R Paula06/2016
465710^90480+513190481Patrick De Geest11/2018
46586^116273-8590478Lelio R Paula05/2016
465910^90473+313990474Patrick De Geest11/2018
466010^90470+231990471Patrick De Geest11/2018
46616^116256-1757390465Enzo Doria02/2013
46622^300502+5461590461Lelio R Paula02/2016
4663(13*2^300487+1)/4590456Lelio R Paula09/2013
466410^90453-396990453Patrick De Geest11/2018
466510^90440+135990441Patrick De Geest11/2018
4666(3^189545-8)/590436Lelio R Paula01/2013
4667(7*2^300406-1)/390432Lelio R Paula02/2014
466810^90430+333990431Patrick De Geest11/2018
466910^90414-154790414Patrick De Geest11/2018
467010^90404-642990404Patrick De Geest11/2018
467110^90401+207790402Patrick De Geest11/2018
46724*5^129332+390400Lelio R Paula10/2014
467310^90397-32390397Patrick De Geest11/2018
46742^300249-1624590384Enzo Doria04/2013
4675(7*10^90371-313)/990371Robert Price11/2016
467610^90363-355790363Patrick De Geest11/2018
46782*6^116118+790358Lelio R Paula10/2014
467710^90358-497990358Patrick De Geest11/2018
467910^90356-719790356Patrick De Geest11/2018
468010^90353-108990353Patrick De Geest11/2018
4681(24737*2^300101+1)/2590343Lelio R Paula06/2014
46824*10^90334-2190335Robert Price04/2016
468310^90322-955190322Patrick De Geest11/2018
468410^90316+999190317Patrick De Geest11/2018
46862^300019-11033590315Enzo Doria05/2014
468510^90315-856190315Patrick De Geest11/2018
46872^299949-100590294Lelio R Paula11/2013
468810^90279-155190279Patrick De Geest09/2018
46892^299868-10961390270Enzo Doria04/2014
469010^90259-944390259Patrick De Geest09/2018
469110^90252-810390252Patrick De Geest09/2018
46925*2^299799-390250Lelio R Paula08/2014
469313^81008-290239Lelio R Paula09/2013
469464^49957-63^4995790232Robert Price07/2013
469510^90227+5628190228Patrick De Geest06/2016
46982^299725+31590227Lelio R Paula11/2013
469610^90227-100000000190227Robert Price05/2016
469710^90227-6876390227Patrick De Geest06/2016
46995^129082+4890225Lelio R Paula03/2016
47002^299699+19590219Lelio R Paula10/2012
4701(55*10^90211-1)/990212Ray Chandler02/2012
470210^90209+897190210Patrick De Geest09/2018
470310^90208-224790208Patrick De Geest09/2018
4704116^43693-11590203Norbert Schneider08/2018
470510^90202+355390203Patrick De Geest09/2018
47063^189053+28090202Lelio R Paula04/2016
47072^299639-18790201Lelio R Paula10/2012
470810^90199-289190199Patrick De Geest09/2018
47092^299631+18390198Lelio R Paula10/2012
471010^90196-968390196Patrick De Geest09/2018
471110^90193-980990193Patrick De Geest09/2018
4712(21*2^299611-1)/2990192Lelio R Paula02/2014
47132^299567+11390179Lelio R Paula10/2012
47142^299550+18990174Lelio R Paula10/2012
471510^90170-674990170Patrick De Geest09/2018
4716(2^299535+3)/2990168Lelio R Paula01/2013
471710^90160-561390160Patrick De Geest09/2018
4718(97*10^90155-1)/390157Serge Batalov12/2014
47193^188938+868090147Lelio R Paula04/2016
472010^90146-202790146Patrick De Geest09/2018
47226^115840-5590142Lelio R Paula05/2016
4721(5*10^90142-473)/990142Robert Price12/2017
47238*7^106659+590139Lelio R Paula10/2014
47242^299406-1665390131Enzo Doria05/2013
4726208049#+(216091#)/(208049#)90128Makoto Morimoto04/2016
472510^90128-838790128Patrick De Geest09/2018
4727(F(5)^128941-F(4)^128941)/F(3)90126Wayne Halsdorf03/2012
47286^115819-5390125Lelio R Paula05/2016
472910^90123+631390124Patrick De Geest09/2018
47306^115816-1685390123Enzo Doria02/2013
47316^115813-2390121Lelio R Paula05/2016
4732(22*10^90110+161)/390111Robert Price02/2017
4733(2^299330-509203)/6990106Lelio R Paula01/2013
473410^90105-76790105Patrick De Geest09/2018
473510^90104-770390104Patrick De Geest09/2018
473610^90103+915990104Patrick De Geest09/2018
473710^90101-320790101Patrick De Geest09/2018
4738(29*10^90096-17)/390097Erik Branger09/2014
473910^90089-357390089Patrick De Geest09/2018
47402^299247+187052990083Enzo Doria05/2016
474110^90079+160990080Patrick De Geest09/2018
47422^299229-279778390077Enzo Doria04/2016
47432^299220-1631790075Enzo Doria04/2013
474411^86491-135090072Enzo Doria12/2012
474510^90071-123390071Patrick De Geest09/2018
474610^90069-784190069Patrick De Geest09/2018
4747(31*10^90064-1)/390066Robert Price03/2017
474810^90060-83990060Patrick De Geest09/2018
474910^90052+236190053Patrick De Geest09/2018
475010^90047+61990048Patrick De Geest09/2018


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: April, 20 2019 09:21 (Time in France)

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