PRP Records

Probable Primes Top 10000

(252538 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 ?
450110^90807+727990808Patrick De Geest01/2019
450210^90800-645390800Patrick De Geest11/2018
450311^87187-171090796Enzo Doria12/2012
45045*10^90793+2190794Robert Price01/2017
4505(22*10^90792-13)/990793Robert Price03/2015
45062^301591-161590788Lelio R Paula02/2016
4507(52^52901+1)/5390777Paul Bourdelais08/2017
45082^301546-10903790775Enzo Doria04/2014
450910^90772+402990773Patrick De Geest11/2018
451010^90770-43190770Patrick De Geest11/2018
451114^79195-390768Lelio R Paula06/2016
451210^90766+87790767Patrick De Geest11/2018
45132^301517-186169390766Enzo Doria11/2015
451410^90765-479790765Patrick De Geest11/2018
451510^90757+757390758Patrick De Geest11/2018
451610^90756-872790756Patrick De Geest11/2018
451710^90749+82390750Patrick De Geest11/2018
45192^301460-17390749Lelio R Paula11/2012
451810^90748+421390749Patrick De Geest11/2018
452010^90747-927990747Patrick De Geest11/2018
4521(85*10^90745-103)/990746Robert Price10/2017
452210^90726+407790727Patrick De Geest11/2018
452310^90721+18190722Patrick De Geest11/2018
45242^301312-8990704Lelio R Paula11/2012
452510^90696+634990697Patrick De Geest11/2018
45262^301285-12990696Lelio R Paula11/2012
45272^301282-10999190695Enzo Doria04/2014
452810^90690+887790691Patrick De Geest11/2018
452910^90683-257790683Patrick De Geest11/2018
45302^301228-185426990679Enzo Doria09/2015
4531(151*10^90669-1)/390671Robert Price04/2017
4532(32*10^90669+13)/990670Robert Price04/2015
453310^90669+979390670Patrick De Geest11/2018
453410^90665-308790665Patrick De Geest11/2018
453510^90662-951990662Patrick De Geest11/2018
453610^90661+237390662Patrick De Geest11/2018
45373*5^129698+890656Lelio R Paula10/2014
4538F(433781)90655Henri Lifchitz09/2003
453919^70891+8290653Lelio R Paula06/2016
4540(29*2^301124-1)/1390648Lelio R Paula02/2014
454110^90636-310190636Patrick De Geest11/2018
45427*3^189953-890632Lelio R Paula08/2014
454310^90626-113190626Patrick De Geest11/2018
454411^87022-180090625Enzo Doria12/2012
454510^90623+86190624Patrick De Geest11/2018
4546(2^301042+47)/1203696990616Lelio R Paula06/2013
45472^301004-278693990612Enzo Doria03/2016
454810^90611-973790611Patrick De Geest11/2018
454910^90609+682390610Patrick De Geest11/2018
45502^300980-2790605Lelio R Paula11/2012
45512*10^90597-790598Dmitry Domanov11/2010
4552197^39485+290597Lelio R Paula06/2013
45537^107198+4890593Lelio R Paula04/2016
4554(86*10^90588+121)/990589Robert Price03/2017
45552^300923+5390587Lelio R Paula11/2012
45562^300874+790573Lelio R Paula10/2012
455710^90567+948990568Patrick De Geest11/2018
45585^129568-5690565Lelio R Paula04/2016
45592^300847-11283190564Enzo Doria06/2014
456010^90562-298190562Patrick De Geest11/2018
456110^90549+381190550Patrick De Geest11/2018
456210^90532+816990533Patrick De Geest11/2018
456310^90531+983190532Patrick De Geest11/2018
45642^300718+25525590526Lelio R Paula02/2016
456510^90516-678390516Patrick De Geest11/2018
456610^90511-697790511Patrick De Geest11/2018
45672^300637+9590501Lelio R Paula11/2012
45687^107087-2490500Lelio R Paula04/2016
456910^90499-582390499Patrick De Geest11/2018
4571(10^90499+3^90499)/1390498Robert Price01/2013
457013^81241+9090498Lelio R Paula06/2016
457210^90480+513190481Patrick De Geest11/2018
45736^116273-8590478Lelio R Paula05/2016
457410^90473+313990474Patrick De Geest11/2018
457510^90470+231990471Patrick De Geest11/2018
45766^116256-1757390465Enzo Doria02/2013
45772^300502+5461590461Lelio R Paula02/2016
4578(13*2^300487+1)/4590456Lelio R Paula09/2013
457910^90453-396990453Patrick De Geest11/2018
458010^90440+135990441Patrick De Geest11/2018
4581(3^189545-8)/590436Lelio R Paula01/2013
4582(7*2^300406-1)/390432Lelio R Paula02/2014
458310^90430+333990431Patrick De Geest11/2018
458410^90414-154790414Patrick De Geest11/2018
458510^90404-642990404Patrick De Geest11/2018
458610^90401+207790402Patrick De Geest11/2018
45874*5^129332+390400Lelio R Paula10/2014
458810^90397-32390397Patrick De Geest11/2018
45892^300249-1624590384Enzo Doria04/2013
4590(7*10^90371-313)/990371Robert Price11/2016
459110^90363-355790363Patrick De Geest11/2018
45932*6^116118+790358Lelio R Paula10/2014
459210^90358-497990358Patrick De Geest11/2018
459410^90356-719790356Patrick De Geest11/2018
459510^90353-108990353Patrick De Geest11/2018
4596(24737*2^300101+1)/2590343Lelio R Paula06/2014
45974*10^90334-2190335Robert Price04/2016
459810^90322-955190322Patrick De Geest11/2018
459910^90316+999190317Patrick De Geest11/2018
46012^300019-11033590315Enzo Doria05/2014
460010^90315-856190315Patrick De Geest11/2018
46022^299949-100590294Lelio R Paula11/2013
460310^90279-155190279Patrick De Geest09/2018
46042^299868-10961390270Enzo Doria04/2014
460510^90259-944390259Patrick De Geest09/2018
460610^90252-810390252Patrick De Geest09/2018
46075*2^299799-390250Lelio R Paula08/2014
460813^81008-290239Lelio R Paula09/2013
460964^49957-63^4995790232Robert Price07/2013
461010^90227+5628190228Patrick De Geest06/2016
46132^299725+31590227Lelio R Paula11/2013
461110^90227-100000000190227Robert Price05/2016
461210^90227-6876390227Patrick De Geest06/2016
46145^129082+4890225Lelio R Paula03/2016
46152^299699+19590219Lelio R Paula10/2012
4616(55*10^90211-1)/990212Ray Chandler02/2012
461710^90209+897190210Patrick De Geest09/2018
461810^90208-224790208Patrick De Geest09/2018
4619116^43693-11590203Norbert Schneider08/2018
462010^90202+355390203Patrick De Geest09/2018
46213^189053+28090202Lelio R Paula04/2016
46222^299639-18790201Lelio R Paula10/2012
462310^90199-289190199Patrick De Geest09/2018
46242^299631+18390198Lelio R Paula10/2012
462510^90196-968390196Patrick De Geest09/2018
462610^90193-980990193Patrick De Geest09/2018
4627(21*2^299611-1)/2990192Lelio R Paula02/2014
46282^299567+11390179Lelio R Paula10/2012
46292^299550+18990174Lelio R Paula10/2012
463010^90170-674990170Patrick De Geest09/2018
4631(2^299535+3)/2990168Lelio R Paula01/2013
463210^90160-561390160Patrick De Geest09/2018
4633(97*10^90155-1)/390157Serge Batalov12/2014
46343^188938+868090147Lelio R Paula04/2016
463510^90146-202790146Patrick De Geest09/2018
46376^115840-5590142Lelio R Paula05/2016
4636(5*10^90142-473)/990142Robert Price12/2017
46388*7^106659+590139Lelio R Paula10/2014
46392^299406-1665390131Enzo Doria05/2013
4641208049#+(216091#)/(208049#)90128Makoto Morimoto04/2016
464010^90128-838790128Patrick De Geest09/2018
4642(F(5)^128941-F(4)^128941)/F(3)90126Wayne Halsdorf03/2012
46436^115819-5390125Lelio R Paula05/2016
464410^90123+631390124Patrick De Geest09/2018
46456^115816-1685390123Enzo Doria02/2013
46466^115813-2390121Lelio R Paula05/2016
4647(22*10^90110+161)/390111Robert Price02/2017
4648(2^299330-509203)/6990106Lelio R Paula01/2013
464910^90105-76790105Patrick De Geest09/2018
465010^90104-770390104Patrick De Geest09/2018
465110^90103+915990104Patrick De Geest09/2018
465210^90101-320790101Patrick De Geest09/2018
4653(29*10^90096-17)/390097Erik Branger09/2014
465410^90089-357390089Patrick De Geest09/2018
46552^299247+187052990083Enzo Doria05/2016
465610^90079+160990080Patrick De Geest09/2018
46572^299229-279778390077Enzo Doria04/2016
46582^299220-1631790075Enzo Doria04/2013
465911^86491-135090072Enzo Doria12/2012
466010^90071-123390071Patrick De Geest09/2018
466110^90069-784190069Patrick De Geest09/2018
4662(31*10^90064-1)/390066Robert Price03/2017
466310^90060-83990060Patrick De Geest09/2018
466410^90052+236190053Patrick De Geest09/2018
466510^90047+61990048Patrick De Geest09/2018
4666L(430949)/861899/144038756153990045Serge Batalov07/2017
46672^299112+7395190042Enzo Doria04/2016
46688^99702+7^(99702-1)90040Robert Price02/2016
466910^90038-968790038Patrick De Geest09/2018
46705*10^90033+390034Dmitry Domanov11/2010
467110^90030-146190030Patrick De Geest09/2018
4672243^37738+37738^24390029Norbert Schneider01/2015
467310^90025-870390025Patrick De Geest09/2018
46742^299048-11329790023Enzo Doria07/2014
467510^90015+84990016Patrick De Geest09/2018
467610^90010+681190011Patrick De Geest09/2018
467710^90010-18359790010Patrick De Geest11/2018
467810^90009+5832190010Patrick De Geest11/2018
467910^90008+84790009Patrick De Geest09/2018
468010^90009-35601390009Patrick De Geest11/2018
46823^188648+9290008Lelio R Paula12/2015
468110^90008-70604990008Patrick De Geest11/2018
46835*2^298991+790006Lelio R Paula08/2014
4684(25*2^298997+1)/326790005Lelio R Paula01/2013
468510^90000+886990001Patrick De Geest12/2009
468710^89999+8293990000Dirk Augustin04/2007
468610^90000-14034390000Patrick De Geest12/2009
468810^89999-19489189999Patrick De Geest11/2009
468919^70365-7889980Lelio R Paula12/2015
4690NaturalLogarithmOf2(89973)89973Eric W. Weisstein10/2015
46912^298852-6487589964Lelio R Paula11/2013
469218^71659+3789952Lelio R Paula12/2015
4693(2908*29^61501-3)/789942Curtis Bright05/2015
469417^73067+2089906Lelio R Paula11/2015
46952^298637-9989899Lelio R Paula10/2012
46969^94188+3*8^94188-2*4^94188-3*2^9418889879Mike Oakes01/2011
46979*10^89858+1989859Robert Price05/2016
46982^298501+187006789858Enzo Doria05/2016
469911^86280-9889852Lelio R Paula11/2015
47002^298473-11005989850Enzo Doria04/2014
470119^70263-3289850Lelio R Paula12/2015
4702(299*10^89836-17)/389838Robert Price01/2017
47033^188286+1489836Robert Price09/2013
4704gcd(V(1091095),5*F(218219)*(F(218219)+1)+1)89822Serge Batalov04/2015
47052^298367+5890589818Lelio R Paula11/2013
47062^298319-10965789803Enzo Doria04/2014
47078*10^89800+8189801Robert Price05/2017
470818^71505-9189759Lelio R Paula12/2015
4709(7^106187+1)/889738Paul Bourdelais04/2008
47102^298079-10953189731Enzo Doria04/2014
4711117^43380+11689718Norbert Schneider08/2018
4712(22699*2^298016+1)/38589714Lelio R Paula06/2014
4713156*(10^(4*22427)-1)/101-189709Robert Price05/2014
47142^298003-6694589708Lelio R Paula11/2013
4715(23*10^89705-83)/389706Robert Price09/2017
471617^72900-5489700Lelio R Paula11/2015
47173*2^297956+589695Lelio R Paula08/2014
471820^68938-1189691Lelio R Paula01/2016
471989*10^89687-789689Robert Price03/2017
47202^297923+7778389684Enzo Doria05/2016
472111^86107-2457600089672Enzo Doria02/2013
47222^297878-11191189671Enzo Doria05/2014
47237^106084+4089652Lelio R Paula10/2015
4724(86*10^89640-311)/989641Robert Price10/2017
47253*10^89608-5989609Robert Price10/2017
47263^187780-1103889594Enzo Doria05/2014
4727(13*2^297560-1)/4915178789568Lelio R Paula02/2014
47285^128141-3689567Lelio R Paula10/2015
47294*7^105951+989540Lelio R Paula10/2014
4730(7*10^89539-439)/989539Robert Price09/2017
47312^297397+17725789526Enzo Doria05/2016
47322^297346-1624189511Enzo Doria04/2013
4733(5*10^89510+79)/389511Robert Price11/2017
47354^148663-3^14866389505Jean-Louis Charton11/2005
47342^297328-86968810589505Lelio R Paula07/2016
47362^297325-45904389504Enzo Doria05/2015
47372^297310-11239189500Enzo Doria06/2014
47382^297296-11215789496Enzo Doria06/2014
473957^50966-289490Lelio R Paula08/2013
4740(266*10^89482+1)/389484Robert Price02/2016
4741(14*10^89480-101)/389481Robert Price04/2017
47422^297122+9989443Lelio R Paula10/2012
4743(3^187435-5)/128689427Lelio R Paula01/2013
4744(25*10^89413+161)/389414Robert Price01/2017
47452^296990+187069989403Enzo Doria05/2016
47462^296972-101789398Lelio R Paula11/2013
4747(7*10^89383+167)/389384Robert Kinser10/2017
4748(85*10^89375-31)/989376Robert Price11/2015
47499*2^296870+789368Lelio R Paula08/2014
4750100^44683-99^4468389366Robert Price07/2013


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: February, 14 2019 10:37 (Time in France)

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