PRP Records

Probable Primes Top 10000

(255312 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 ?
500110^90610-2657390610Patrick De Geest07/2019
500210^90609-22817390609Patrick De Geest07/2019
50032^300980-2790605Lelio R Paula11/2012
50042*10^90597-790598Dmitry Domanov11/2010
5005197^39485+290597Lelio R Paula06/2013
50067^107198+4890593Lelio R Paula04/2016
5007(86*10^90588+121)/990589Robert Price03/2017
50082^300923+5390587Lelio R Paula11/2012
50092^300874+790573Lelio R Paula10/2012
501010^90567+948990568Patrick De Geest11/2018
501110^90567-23135390567Patrick De Geest07/2019
50125^129568-5690565Lelio R Paula04/2016
50132^300847-11283190564Enzo Doria06/2014
501410^90562+79019790563Patrick De Geest07/2019
501510^90562-298190562Patrick De Geest11/2018
501610^90549+381190550Patrick De Geest11/2018
501710^90549-63030390549Patrick De Geest07/2019
50182^300790-454190547Yves Minet03/2019
501910^90532+816990533Patrick De Geest11/2018
502010^90531+983190532Patrick De Geest11/2018
502110^90532-15488990532Patrick De Geest07/2019
502210^90531-106058990531Patrick De Geest07/2019
50232^300718+25525590526Lelio R Paula02/2016
502410^90516+21591790517Patrick De Geest07/2019
502510^90516-678390516Patrick De Geest11/2018
502610^90511+3017790512Patrick De Geest07/2019
502710^90511-697790511Patrick De Geest11/2018
50282^300637+9590501Lelio R Paula11/2012
50307^107087-2490500Lelio R Paula04/2016
502910^90499+19154790500Patrick De Geest07/2019
503110^90499-582390499Patrick De Geest11/2018
5033(10^90499+3^90499)/1390498Robert Price01/2013
503213^81241+9090498Lelio R Paula06/2016
503410^90480+513190481Patrick De Geest11/2018
503510^90480-8572190480Patrick De Geest07/2019
50366^116273-8590478Lelio R Paula05/2016
503710^90473+313990474Patrick De Geest11/2018
503810^90473-15059990473Patrick De Geest07/2019
503910^90470+231990471Patrick De Geest11/2018
504010^90470-7163790470Patrick De Geest07/2019
50416^116256-1757390465Enzo Doria02/2013
50422^300502+5461590461Lelio R Paula02/2016
5043(13*2^300487+1)/4590456Lelio R Paula09/2013
504410^90453+14184390454Patrick De Geest07/2019
504510^90453-396990453Patrick De Geest11/2018
504610^90440+135990441Patrick De Geest11/2018
504710^90440-1882190440Patrick De Geest07/2019
5048(3^189545-8)/590436Lelio R Paula01/2013
5049(7*2^300406-1)/390432Lelio R Paula02/2014
505010^90430+333990431Patrick De Geest11/2018
505110^90430-6347790430Patrick De Geest07/2019
505210^90414+22959390415Patrick De Geest07/2019
505310^90414-154790414Patrick De Geest11/2018
505410^90404+4704190405Patrick De Geest07/2019
505510^90404-642990404Patrick De Geest11/2018
505610^90401+207790402Patrick De Geest11/2018
505710^90401-36863790401Patrick De Geest07/2019
50584*5^129332+390400Lelio R Paula10/2014
505910^90397+1978390398Patrick De Geest07/2019
506010^90397-32390397Patrick De Geest11/2018
50612^300249-1624590384Enzo Doria04/2013
5062(7*10^90371-313)/990371Robert Price11/2016
506310^90363+5867790364Patrick De Geest07/2019
506410^90363-355790363Patrick De Geest11/2018
506510^90358+10464190359Patrick De Geest07/2019
50672*6^116118+790358Lelio R Paula10/2014
506810^90358-497990358Patrick De Geest11/2018
506610^90357+11283790358Patrick De Geest07/2019
506910^90357-18959390357Patrick De Geest07/2019
507010^90356+5311390357Patrick De Geest07/2019
507110^90356-719790356Patrick De Geest11/2018
507210^90353+60321190354Patrick De Geest07/2019
507310^90353-108990353Patrick De Geest11/2018
5074(24737*2^300101+1)/2590343Lelio R Paula06/2014
50754*10^90334-2190335Robert Price04/2016
507610^90322+13769190323Patrick De Geest07/2019
507710^90322-955190322Patrick De Geest11/2018
507810^90316+999190317Patrick De Geest11/2018
507910^90316-4562790316Patrick De Geest07/2019
508010^90315+3288990316Patrick De Geest07/2019
50812^300019-11033590315Enzo Doria05/2014
508210^90315-856190315Patrick De Geest11/2018
5083FAB2(300001,5032)90310Robert Price05/2019
5084FAB2(300001,29405)90310Robert Price05/2019
50852^299949-100590294Lelio R Paula11/2013
508610^90279+6245790280Patrick De Geest07/2019
508710^90279-155190279Patrick De Geest09/2018
50882^299868-10961390270Enzo Doria04/2014
508910^90259+35929990260Patrick De Geest07/2019
509010^90259-944390259Patrick De Geest09/2018
509110^90252+10287390253Patrick De Geest07/2019
509210^90252-810390252Patrick De Geest09/2018
50935*2^299799-390250Lelio R Paula08/2014
509413^81008-290239Lelio R Paula09/2013
509580697!4-25690234Robert Price11/2019
509664^49957-63^4995790232Robert Price07/2013
509710^90227+5628190228Patrick De Geest06/2016
51002^299725+31590227Lelio R Paula11/2013
509810^90227-100000000190227Robert Price05/2016
509910^90227-6876390227Patrick De Geest06/2016
51015^129082+4890225Lelio R Paula03/2016
51022^299699+19590219Lelio R Paula10/2012
5103(55*10^90211-1)/990212Ray Chandler02/2012
510410^90209+897190210Patrick De Geest09/2018
510510^90209-72479790209Patrick De Geest07/2019
510610^90208+18953190209Patrick De Geest07/2019
510710^90208-224790208Patrick De Geest09/2018
5108116^43693-11590203Norbert Schneider08/2018
510910^90202+355390203Patrick De Geest09/2018
51103^189053+28090202Lelio R Paula04/2016
511110^90202-6779390202Patrick De Geest07/2019
51122^299639-18790201Lelio R Paula10/2012
511310^90199+25403190200Patrick De Geest07/2019
511410^90199-289190199Patrick De Geest09/2018
51152^299631+18390198Lelio R Paula10/2012
511610^90196+18753990197Patrick De Geest07/2019
511710^90196-968390196Patrick De Geest09/2018
511810^90193+10497390194Patrick De Geest07/2019
511910^90193-980990193Patrick De Geest09/2018
5120(21*2^299611-1)/2990192Lelio R Paula02/2014
51212^299567+11390179Lelio R Paula10/2012
51222^299550+18990174Lelio R Paula10/2012
512310^90170+37606390171Patrick De Geest07/2019
512410^90170-674990170Patrick De Geest09/2018
5125(2^299535+3)/2990168Lelio R Paula01/2013
512610^90160+27194790161Patrick De Geest07/2019
512710^90160-561390160Patrick De Geest09/2018
5128(97*10^90155-1)/390157Serge Batalov12/2014
51303^188938+868090147Lelio R Paula04/2016
512910^90146+16020990147Patrick De Geest07/2019
513110^90146-202790146Patrick De Geest09/2018
51326^115840-5590142Lelio R Paula05/2016
5133(5*10^90142-473)/990142Robert Price12/2017
51348*7^106659+590139Lelio R Paula10/2014
51362^299406-1665390131Enzo Doria05/2013
5135(317057^16384+1)/290131Richard Fischer10/2019
513710^90128+28867390129Patrick De Geest07/2019
5138208049#+(216091#)/(208049#)90128Makoto Morimoto04/2016
513910^90128-838790128Patrick De Geest09/2018
5140(F(5)^128941-F(4)^128941)/F(3)90126Wayne Halsdorf03/2012
51416^115819-5390125Lelio R Paula05/2016
514210^90123+631390124Patrick De Geest09/2018
51446^115816-1685390123Enzo Doria02/2013
514310^90123-2261790123Patrick De Geest07/2019
51456^115813-2390121Lelio R Paula05/2016
5146(22*10^90110+161)/390111Robert Price02/2017
5148(2^299330-509203)/6990106Lelio R Paula01/2013
514710^90105+91575990106Patrick De Geest07/2019
515010^90105-76790105Patrick De Geest09/2018
514910^90104+4818990105Patrick De Geest07/2019
515110^90104-770390104Patrick De Geest09/2018
515210^90103+915990104Patrick De Geest09/2018
515310^90103-20845790103Patrick De Geest07/2019
515410^90102+7301190103Patrick De Geest07/2019
515510^90102-60243390102Patrick De Geest07/2019
515610^90101+122553790102Patrick De Geest07/2019
515710^90101-320790101Patrick De Geest09/2018
5158(29*10^90096-17)/390097Erik Branger09/2014
515910^90089+14318190090Patrick De Geest07/2019
516010^90089-357390089Patrick De Geest09/2018
51612^299247+187052990083Enzo Doria05/2016
516210^90079+160990080Patrick De Geest09/2018
516310^90079-23004390079Patrick De Geest07/2019
51642^299229-279778390077Enzo Doria04/2016
51652^299220-1631790075Enzo Doria04/2013
516611^86491-135090072Enzo Doria12/2012
516710^90071+5233390072Patrick De Geest07/2019
516810^90071-123390071Patrick De Geest09/2018
5169(314401^16384+1)/290071Richard Fischer10/2019
517010^90069+15852790070Patrick De Geest07/2019
517110^90069-784190069Patrick De Geest09/2018
5172(31*10^90064-1)/390066Robert Price03/2017
517310^90060+14943190061Patrick De Geest07/2019
517410^90060-83990060Patrick De Geest09/2018
517510^90052+236190053Patrick De Geest09/2018
517610^90052-9092990052Patrick De Geest07/2019
517710^90047+61990048Patrick De Geest09/2018
517810^90047-15107190047Patrick De Geest07/2019
5179L(430949)/861899/144038756153990045Serge Batalov07/2017
51802^299112+7395190042Enzo Doria04/2016
51818^99702+7^(99702-1)90040Robert Price02/2016
518210^90038+15780390039Patrick De Geest07/2019
518310^90038-968790038Patrick De Geest09/2018
51845*10^90033+390034Dmitry Domanov11/2010
518510^90030+22581390031Patrick De Geest07/2019
518610^90030-146190030Patrick De Geest09/2018
5187243^37738+37738^24390029Norbert Schneider01/2015
518810^90025+7056990026Patrick De Geest07/2019
518910^90025-870390025Patrick De Geest09/2018
51902^299048-11329790023Enzo Doria07/2014
519110^90015+84990016Patrick De Geest09/2018
519210^90015-22838790015Patrick De Geest07/2019
519310^90010+681190011Patrick De Geest09/2018
519410^90010-18359790010Patrick De Geest11/2018
519510^90009+5832190010Patrick De Geest11/2018
519610^90008+84790009Patrick De Geest09/2018
519710^90009-35601390009Patrick De Geest11/2018
51993^188648+9290008Lelio R Paula12/2015
519810^90008-70604990008Patrick De Geest11/2018
52005*2^298991+790006Lelio R Paula08/2014
5201(25*2^298997+1)/326790005Lelio R Paula01/2013
520210^90000+886990001Patrick De Geest12/2009
520410^89999+8293990000Dirk Augustin04/2007
520310^90000-14034390000Patrick De Geest12/2009
520510^89999-19489189999Patrick De Geest11/2009
520619^70365-7889980Lelio R Paula12/2015
5207NaturalLogarithmOf2(89973)89973Eric W. Weisstein10/2015
52082^298852-6487589964Lelio R Paula11/2013
520918^71659+3789952Lelio R Paula12/2015
5210(2908*29^61501-3)/789942Curtis Bright05/2015
521117^73067+2089906Lelio R Paula11/2015
52122^298637-9989899Lelio R Paula10/2012
52139^94188+3*8^94188-2*4^94188-3*2^9418889879Mike Oakes01/2011
52149*10^89858+1989859Robert Price05/2016
52152^298501+187006789858Enzo Doria05/2016
521611^86280-9889852Lelio R Paula11/2015
52172^298473-11005989850Enzo Doria04/2014
521819^70263-3289850Lelio R Paula12/2015
5219(299*10^89836-17)/389838Robert Price01/2017
52203^188286+1489836Robert Price09/2013
5221gcd(V(1091095),5*F(218219)*(F(218219)+1)+1)89822Serge Batalov04/2015
52222^298367+5890589818Lelio R Paula11/2013
52232^298319-10965789803Enzo Doria04/2014
52248*10^89800+8189801Robert Price05/2017
522518^71505-9189759Lelio R Paula12/2015
5226(7^106187+1)/889738Paul Bourdelais04/2008
52272^298079-10953189731Enzo Doria04/2014
5228117^43380+11689718Norbert Schneider08/2018
5229(22699*2^298016+1)/38589714Lelio R Paula06/2014
5230156*(10^(4*22427)-1)/101-189709Robert Price05/2014
52312^298003-6694589708Lelio R Paula11/2013
5232(23*10^89705-83)/389706Robert Price09/2017
523317^72900-5489700Lelio R Paula11/2015
52343*2^297956+589695Lelio R Paula08/2014
523520^68938-1189691Lelio R Paula01/2016
523689*10^89687-789689Robert Price03/2017
5237(297847^16384+1)/289686Richard Fischer08/2019
52382^297923+7778389684Enzo Doria05/2016
523911^86107-2457600089672Enzo Doria02/2013
52402^297878-11191189671Enzo Doria05/2014
52417^106084+4089652Lelio R Paula10/2015
5242(86*10^89640-311)/989641Robert Price10/2017
52433*10^89608-5989609Robert Price10/2017
52443^187780-1103889594Enzo Doria05/2014
5245(13*2^297560-1)/4915178789568Lelio R Paula02/2014
52465^128141-3689567Lelio R Paula10/2015
52474*7^105951+989540Lelio R Paula10/2014
5248(7*10^89539-439)/989539Robert Price09/2017
52492^297397+17725789526Enzo Doria05/2016
5250(5*10^89510+79)/389511Robert Price11/2017


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: December, 14 2019 11:13 (Time in France)

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