PRP Records

Probable Primes Top 10000

(277034 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 ?
200132820^29059+29059^32820146485Hans Havermann12/2020
200237261^8530+8530^37261146472Hans Havermann12/2020
200366953^154+154^66953146462Hans Havermann12/2020
200496^73877-95^73877146445Robert Price10/2015
20058*10^146421+81146422Robert Price08/2019
200633153^26090+26090^33153146420Hans Havermann11/2020
2007(52^85259+1)/53146304Paul Bourdelais09/2017
2008179^64935+2146290Lelio R Paula10/2017
200932595^30758+30758^32595146285Hans Havermann11/2020
201034972^15157+15157^34972146205Hans Havermann12/2020
2011(19*10^146181-49)/3146182Robert Price05/2019
20122^485531-114621146160Enzo Doria05/2015
2013(2^485461-9)/4249146135Lelio R Paula09/2015
20142^485389+81887146117Enzo Doria08/2016
201532554^30773+30773^32554146108Hans Havermann11/2020
2016(10^146063+71)/9146063Serge Batalov07/2015
2017(2^485119+7)/2745146032Lelio R Paula09/2015
2018(22*10^146029+257)/9146030Robert Price06/2018
20197*10^145982-53145983Robert Price06/2020
20202^484743+1872923145923Enzo Doria05/2016
202137875^7112+7112^37875145895Hans Havermann01/2021
202232862^27473+27473^32862145872Hans Havermann01/2021
202332836^27587+27587^32836145815Hans Havermann01/2021
20242^484341+1879157145802Enzo Doria08/2016
20252*10^145784-91145785Robert Price04/2020
20262^484271-51145781Lelio R Paula11/2017
202770^78989-69^78989145743Robert Price01/2014
202851^85334+2145714Robert Price07/2015
20292^483886-1857101145665Enzo Doria10/2015
2030(19*10^145585+131)/3145586Robert Price06/2020
20312^483563-1863457145567Enzo Doria12/2015
20322^483516-1861409145553Enzo Doria11/2015
20332^483384-115019145514Enzo Doria06/2015
2034(259*10^145501-1)/3145503Robert Price12/2020
2035(19*10^145499-61)/3145500Robert Price05/2019
20362^483302-3221145489Lelio R Paula12/2012
203735523^12434+12434^35523145453Hans Havermann01/2021
20382^483046+1874029145412Enzo Doria06/2016
20392^482991-2789317145395Enzo Doria12/2015
20402^482978-2789711145391Enzo Doria12/2015
20412^482966-2789711145388Enzo Doria12/2015
20422^482817-1858843145343Enzo Doria10/2015
20432^482751-113635145323Enzo Doria08/2014
20442^482705-459763145309Enzo Doria05/2015
2045(4^241306+11)/3145281Robert Price03/2017
2046(238*10^145276-1)/3145278Robert Price04/2020
2047(19*2^482534+1)/7145258Lelio R Paula09/2015
204853^84239-52^84239145252Robert Price01/2013
204947952^1067+1067^47952145207Hans Havermann01/2021
2050(2^482333+5)/9287145193Lelio R Paula09/2015
20512^482087+72623145123Enzo Doria04/2016
20522^482016-286565145102Enzo Doria07/2015
2053(19*10^145093+101)/3145094Robert Price09/2019
20542^481840+15145049Robert Price09/2015
20552^481801-481801145037Henri Lifchitz03/2005
20562^481775+1869083145029Enzo Doria05/2016
205729^99167+2145022Ray Chandler08/2011
20582^481663+1875653144996Enzo Doria07/2016
205936486^9379+9379^36486144929Hans Havermann12/2020
206035111^13378+13378^35111144882Hans Havermann01/2021
20612^481149-459073144841Enzo Doria05/2015
206234619^15246+15246^34619144817Hans Havermann01/2021
20632^481045-113215144809Enzo Doria07/2014
2064(64*10^144797+287)/9144798Robert Price04/2019
20652^480859-113695144753Enzo Doria09/2014
20662^480766-2787191144725Enzo Doria11/2015
2067(21*27^101106-151)/26144720Curtis Bright05/2015
20682^480678+1874239144699Enzo Doria06/2016
2069(8*10^144683+1)/9144683Serge Batalov05/2010
2070L(692147)144651Henri Lifchitz10/2008
2071(76*10^144648+77)/9144649Robert Price10/2019
207232672^26721+26721^32672144635Hans Havermann01/2021
20732^480417+35144620Robert Price11/2015
20742^480296-59879144584Enzo Doria10/2015
207533157^22878+22878^33157144546Hans Havermann12/2020
207645494^1497+1497^45494144454Hans Havermann12/2020
20772^479844+3144448Donovan Johnson06/2006
207833442^20803+20803^33442144407Hans Havermann01/2021
2079(27*2^479642+1)/733144386Lelio R Paula08/2015
208044917^1638+1638^44917144378Hans Havermann12/2020
2081(21*2^479605-1)/11144376Lelio R Paula09/2015
20822^479348-2792219144299Enzo Doria02/2016
20833^302389-6242144277Enzo Doria05/2014
208433778^18641+18641^33778144248Hans Havermann01/2021
20852*10^144220-3144221Robert Price07/2015
20862^478904-109109144165Enzo Doria04/2014
208743698^1987+1987^43698144125Hans Havermann12/2020
208836128^9723+9723^36128144072Hans Havermann01/2021
208932817^24518+24518^32817144050Hans Havermann12/2020
20902^478337-115333143994Enzo Doria07/2015
2091(7*2^478330-1)/3143993Lelio R Paula08/2015
209288^74047-87^74047143984Robert Price05/2015
209333242^21441+21441^33242143980Hans Havermann01/2021
2094(19*10^143963+467)/9143964Robert Price02/2018
2095(71^77761+1)/72143954Paul Bourdelais09/2017
209633490^19859+19859^33490143939Hans Havermann01/2021
20972^478088+27143919Robert Price11/2015
20987*10^143857-93143858Robert Price08/2020
20993*10^143844+61143845Robert Price09/2020
210041358^3005+3005^41358143837Hans Havermann01/2021
21012^477475-22071143735Enzo Doria07/2013
21022^477417-22123143717Enzo Doria07/2013
21032^477359-3577143700Yves Minet03/2017
210439435^4402+4402^39435143688Hans Havermann01/2021
2105(14*10^143662-71)/3143663Robert Price12/2018
210646371^1252+1252^46371143640Hans Havermann12/2020
210734975^12748+12748^34975143588Hans Havermann01/2021
21082^476936-396765143573Enzo Doria07/2013
21092^476888-2791229143558Enzo Doria01/2016
21102^476868-1859939143552Enzo Doria11/2015
211140807^3294+3294^40807143548Hans Havermann12/2020
2112755^49878+49878^755143547Norbert Schneider04/2019
21132^476558-113627143459Enzo Doria08/2014
21142^476478-45143435Lelio R Paula11/2017
2115(2^475854+9)/73143245Lelio R Paula08/2015
21162^475813-113239143234Enzo Doria07/2014
21172^475624-114059143178Enzo Doria11/2014
2118(11*2^475553-7)/15143156Renaud Lifchitz03/2011
21192^475480-2786129143134Enzo Doria10/2015
2120(19*10^143129-43)/3143130Robert Price05/2019
2121(14*10^143097+73)/3143098Robert Price12/2018
21222^475299-111937143080Enzo Doria05/2014
21232^475160-2797859143038Enzo Doria04/2016
2124(2^475069+3)/395143008Lelio R Paula08/2015
21252^475027-461437142998Enzo Doria07/2015
2126(2^474958+78557)/3142977Lelio R Paula07/2015
2127(8*10^142932+43)/3142933Robert Price06/2018
2128(54^82471-1)/53142871Paul Bourdelais09/2017
2129(11*2^474432-1)/95142818Lelio R Paula09/2015
21302^474417-59923142814Enzo Doria10/2015
21314*10^142810-21142811Robert Price09/2018
2132(3*2^474166+1)/7142738Lelio R Paula08/2015
21332^474053+2897142705Lelio R Paula08/2012
2134(10^142699+359)/9142699Serge Batalov12/2014
2135898^48311-897^48311142676Jean-Louis Charton12/2012
21362^473740-1856639142610Enzo Doria09/2015
2137(25*10^142573-403)/9142574Robert Price12/2020
21382^473617-114223142573Enzo Doria12/2014
21392^473257+1873217142465Enzo Doria06/2016
2140(19*2^473242+1)/11142461Lelio R Paula09/2015
2141(61*10^142446-1)/3142448Robert Price01/2020
2142(14*10^142440+61)/3142441Robert Price12/2018
2143(10^142425+359)/9142425Serge Batalov12/2014
21442^473101+773027142418Enzo Doria05/2016
2145(13*2^472838-1)/3142340Lelio R Paula09/2015
2146(17*2^472789-1)/187347142320Lelio R Paula09/2015
21472^472634-109511142278Enzo Doria04/2014
2148(48^84589+1)/49142213Robert Price01/2014
21497*10^142189+87142190Robert Price07/2019
21502^472258+7142164Lelio R Paula08/2015
2151(23*10^142105+91)/3142106Robert Price08/2019
2152tau(317^10330)142098Nik Lygeros / Olivier Rozier / LR team10/2013
2153(11*2^471913-1)/21142060Lelio R Paula09/2015
2154(16*10^142058+197)/3142059Robert Price04/2019
21559*10^142037+91142038Robert Price10/2020
21562^471792+1880881142024Enzo Doria11/2016
2157(31*2^471580-1)/135141960Lelio R Paula08/2015
2158(4*10^141926-79)/3141927Robert Price02/2018
2159(904*19^110984-1)/3141924Curtis Bright05/2015
2160(14*10^141853+37)/3141854Robert Price12/2018
2161(41*10^141836-59)/9141837Robert Price10/2018
21624*5^202913-9141831Lelio R Paula04/2015
21632*7^167812-3141818Lelio R Paula12/2014
21642^471043+35141799Robert Price11/2015
2165(11*2^470956-1)/7945141770Lelio R Paula08/2015
2166(11*10^141718-131)/3141719Robert Price09/2018
21672^470692+76771141693Enzo Doria05/2016
2168(21*2^470391+1)/533141601Lelio R Paula09/2015
21692^470305-459373141576Enzo Doria05/2015
21702^470183+72623141540Enzo Doria04/2016
21712^470173-16465141537Enzo Doria04/2013
217244*10^141476+9141478Robert Price10/2020
21732^469974-1841141477Enzo Doria05/2014
2174(23*2^469939+1)/25141466Lelio R Paula08/2015
21752*10^141448+63141449Robert Price05/2018
21762^469824+43141432Lelio R Paula09/2017
21772*10^141407-27141408Robert Price05/2018
2178(214*10^141385-1)/3141387Robert Price01/2021
21792^469630-59711141373Enzo Doria10/2015
2180(25*10^141366-331)/9141367Robert Price08/2018
2181(2^469564-3)/611141351Lelio R Paula08/2015
2182197^61601+2141342Lelio R Paula08/2017
21832^469372-112949141296Enzo Doria07/2014
2185143^(2^16)+106^(2^16)141253Valeryi Kuryshev02/2011
2184143^65536+106^65536141253Serge Batalov03/2018
21862^469198+782569141243Enzo Doria10/2016
21872^469076-2786939141206Enzo Doria11/2015
21882^468804+1874941141125Enzo Doria06/2016
21892^468787+81353141119Enzo Doria08/2016
21902^468595-350407141062Enzo Doria06/2015
21912^468564+87855141052Lelio R Paula01/2016
21922^468551-21987141048Enzo Doria07/2013
21932^468523-7141040Lelio R Paula08/2015
2194(25*10^141019-13)/3141020Robert Price09/2019
21952^468405+87855141004Lelio R Paula01/2016
21962^467978-113051140876Enzo Doria07/2014
21972^467780-344429140816Enzo Doria07/2015
21989*10^140802-89140803Robert Price04/2020
21992^467605-1855603140764Enzo Doria09/2015
22005*10^140744-7140745Robert Price09/2015
2201(5^201359-1)/4140744Paul Bourdelais12/2008
22022^467401-1850023140702Enzo Doria08/2015
2203(266*10^140681-17)/3140683Robert Price07/2020
2204(2^467270+78557)/23247140658Lelio R Paula07/2015
2205(29*2^467205+1)/2780517107140635Lelio R Paula08/2015
22062^467166-1854941140631Enzo Doria09/2015
2207(203*10^140615-11)/3140617Robert Price12/2020
2208(85*10^140609+473)/9140610Robert Price01/2020
22092^466866-1840571140541Enzo Doria06/2015
22102^466829-459523140530Enzo Doria05/2015
22112^466692-113213140489Enzo Doria07/2014
2212(44*10^140410-503)/9140411Robert Price12/2018
2213153^64265-2140400Lelio R Paula11/2017
2214(112*10^140357-1)/3140359Serge Batalov12/2014
2215(29*10^140337-17)/3140338Robert Price09/2019
22162^466181-112735140335Enzo Doria07/2014
2217(5*10^140281-119)/3140282Robert Price03/2018
2218(27*2^465872+1)/691140241Lelio R Paula08/2015
22192^465803-114817140221Enzo Doria05/2015
2220floor(Pi*10^140344)%10^140165140165Serge Batalov08/2012
22212^465503-112735140131Enzo Doria07/2014
2222(16*10^140091+167)/3140092Robert Price06/2019
22236^179964+179964^6-1140040Robert Price04/2014
2224(89*10^140008-179)/9140009Robert Price12/2019
2225(29*2^465077-1)/9140003Lelio R Paula08/2015
22262^465072-344789140001Enzo Doria07/2015
22275*10^139945+81139946Robert Price03/2019
22282^464864-17139939Lelio R Paula09/2017
22298*10^139920+51139921Robert Price08/2019
2230(85*10^139913-1)/3139915Robert Price02/2020
2231(17^113621+1)/18139804Paul Bourdelais09/2011
22322*10^139800-21139801Robert Price09/2020
2233(13*10^139782+191)/3139783Robert Price11/2018
2234(19*2^464312-1)/3139773Lelio R Paula08/2015
2235(74*10^139723+133)/9139724Robert Price06/2019
22363*10^139722+13139723Robert Price07/2018
223777*10^139692+3139694Robert Price06/2020
2238(31*2^463970+1)/5139670Lelio R Paula08/2015
2239(18203^(2^15)+(18201)^(2^15))/2139597Robert Price05/2018
22402^463633-2788423139568Enzo Doria11/2015
22412^463271-109501139459Enzo Doria04/2014
2242(5*10^139457+79)/3139458Robert Price03/2018
22432^463237-99139449Lelio R Paula09/2017
2244(49*10^139442+383)/9139443Robert Price04/2019
2245(7*10^139417-547)/9139417Robert Price01/2018
2246(10^139398+191)/3139398Robert Price02/2018
22472^463019+79463139383Enzo Doria06/2016
22483^292129-112756139381Enzo Doria07/2014
2249(15*2^462951+1)/527139361Lelio R Paula08/2015
22502^462855-1865707139334Enzo Doria02/2016


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: January, 18 2021 19:57 (Time in France)

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