PRP Records

Probable Primes Top 10000

(292102 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 ?
30012^467605-1855603140764Enzo Doria09/2015
30025*10^140744-7140745Robert Price09/2015
3003(5^201359-1)/4140744Paul Bourdelais12/2008
30042^467401-1850023140702Enzo Doria08/2015
3005(14*10^140693+13)/9140694Tyler Busby02/2023
3006(266*10^140681-17)/3140683Robert Price07/2020
3007(2^467270+78557)/23247140658Lelio R Paula07/2015
300832138^23781+23781^32138140644Hans Havermann05/2021
300931654^27735+27735^31654140640Hans Havermann05/2021
3010(29*2^467205+1)/2780517107140635Lelio R Paula08/2015
30112^467166-1854941140631Enzo Doria09/2015
3012(203*10^140615-11)/3140617Robert Price12/2020
3013(85*10^140609+473)/9140610Robert Price01/2020
301439231^3836+3836^39231140600Hans Havermann06/2021
30152^466866-1840571140541Enzo Doria06/2015
30162^466829-459523140530Enzo Doria05/2015
30172^466692-113213140489Enzo Doria07/2014
301823*10^140464-3140466Robert Price10/2021
3019(2*10^140461-17)/3140461Serge Batalov11/2022
302031335^30364+30364^31335140455Hans Havermann05/2021
302132795^19126+19126^32795140416Hans Havermann05/2021
3022(44*10^140410-503)/9140411Robert Price12/2018
3023153^64265-2140400Lelio R Paula11/2017
3024(112*10^140357-1)/3140359Serge Batalov12/2014
3025(29*10^140337-17)/3140338Robert Price09/2019
30262^466181-112735140335Enzo Doria07/2014
3027(16*10^140290-37)/3140291Robert Price05/2021
3028(5*10^140281-119)/3140282Robert Price03/2018
302934568^11415+11415^34568140259Hans Havermann05/2021
3030(27*2^465872+1)/691140241Lelio R Paula08/2015
303133632^14781+14781^33632140236Hans Havermann05/2021
303231803^25670+25670^31803140233Hans Havermann05/2021
30332^465803-114817140221Enzo Doria05/2015
3034floor(Pi*10^140344)%10^140165140165Serge Batalov08/2012
30352^465503-112735140131Enzo Doria07/2014
3036(16*10^140091+167)/3140092Robert Price06/2019
3037(8*10^140087-137)/3140088Robert Price03/2022
30386^179964+179964^6-1140040Robert Price04/2014
3039(89*10^140008-179)/9140009Robert Price12/2019
3040(29*2^465077-1)/9140003Lelio R Paula08/2015
30412^465072-344789140001Enzo Doria07/2015
304234742^10683+10683^34742139965Hans Havermann05/2021
30435*10^139945+81139946Robert Price03/2019
304432648^19335+19335^32648139941Hans Havermann05/2021
30452^464864-17139939Lelio R Paula09/2017
30468*10^139920+51139921Robert Price08/2019
3047(85*10^139913-1)/3139915Robert Price02/2020
304831203^30436+30436^31203139896Hans Havermann04/2021
3049(16^116139+619)/5139845Anonymous08/2022
30504*10^139839-27139840Robert Price08/2021
305133582^14573+14573^33582139821Hans Havermann05/2021
3052(17^113621+1)/18139804Paul Bourdelais09/2011
30542*10^139800-21139801Robert Price09/2020
305332628^19261+19261^32628139801Hans Havermann04/2021
3055(13*10^139782+191)/3139783Robert Price11/2018
3056(64*10^139776+791)/9139777Robert Price01/2022
3057(695*10^139772+7)/9139774Robert Price12/2021
3058(19*2^464312-1)/3139773Lelio R Paula08/2015
3059(74*10^139723+133)/9139724Robert Price06/2019
30603*10^139722+13139723Robert Price07/2018
306131577^26592+26592^31577139721Hans Havermann05/2021
306277*10^139692+3139694Robert Price06/2020
3063(31*2^463970+1)/5139670Lelio R Paula08/2015
3064(18203^(2^15)+(18201)^(2^15))/2139597Robert Price05/2018
306539640^3321+3321^39640139584Hans Havermann05/2021
306636663^6410+6410^36663139571Hans Havermann05/2021
30672^463633-2788423139568Enzo Doria11/2015
306833659^13978+13978^33659139532Hans Havermann05/2021
306931811^24318+24318^31811139521Hans Havermann04/2021
307034149^12172+12172^34149139512Hans Havermann04/2021
3071(29*10^139476+313)/9139477Robert Price04/2021
307231721^24940+24940^31721139474Hans Havermann05/2021
307332833^17698+17698^32833139473Hans Havermann05/2021
30742^463271-109501139459Enzo Doria04/2014
3075(5*10^139457+79)/3139458Robert Price03/2018
30762^463237-99139449Lelio R Paula09/2017
3077(49*10^139442+383)/9139443Robert Price04/2019
307831155^29902+29902^31155139441Hans Havermann05/2021
3079(7*10^139417-547)/9139417Robert Price01/2018
3080(10^139398+191)/3139398Robert Price02/2018
308123*10^139386-3139388Robert Price10/2021
30822^463019+79463139383Enzo Doria06/2016
30833^292129-112756139381Enzo Doria07/2014
3084(15*2^462951+1)/527139361Lelio R Paula08/2015
308531922^23205+23205^31922139359Hans Havermann05/2021
30872^462855-1865707139334Enzo Doria02/2016
308631237^28876+28876^31237139334Hans Havermann05/2021
3088(86*10^139315+121)/9139316Robert Price08/2019
30892^462786-292043139313Enzo Doria08/2015
309038915^3798+3798^38915139299Hans Havermann05/2021
3091(26*10^139289+1)/9139290Serge Batalov05/2010
309234065^12248+12248^34065139260Hans Havermann05/2021
309336425^6654+6654^36425139256Hans Havermann05/2021
309439252^3527+3527^39252139243Hans Havermann05/2021
3095(17*10^139239+67)/3139240Robert Price01/2019
309631887^23248+23248^31887139231Hans Havermann05/2021
3097(25*10^139210-97)/9139211Robert Price01/2022
30982^462238-935139148Yves Minet02/2014
3099(29*10^139134-119)/9139135Robert Price12/2021
3100(109*10^139100-7)/3139102Robert Price03/2021
310138744^3885+3885^38744139068Hans Havermann05/2021
310231112^29499+29499^31112139065Hans Havermann05/2021
31032*10^139043-63139044Robert Price01/2022
310436390^6613+6613^36390139025Hans Havermann04/2021
31052*10^138975+33138976Robert Price11/2021
310642437^1882+1882^42437138966Hans Havermann05/2021
310732151^20990+20990^32151138958Hans Havermann05/2021
310832154^20933+20933^32154138933Hans Havermann04/2021
310931082^29499+29499^31082138931Hans Havermann04/2021
31102^461228+1870441138844Enzo Doria05/2016
31112^461204-113675138837Enzo Doria08/2014
3112(2^461139-7)/47138815Lelio R Paula08/2015
3113(17*10^138812-521)/9138813Robert Price04/2018
31143*10^138811-11138812Robert Price07/2018
3115(28*10^138768+173)/3138769Robert Price12/2019
3116(17*2^460963+1)/124051613138757Lelio R Paula08/2015
3117(379*10^138737-1)/9138739Robert Price02/2020
3118(43*10^138648+101)/9138649Robert Price11/2018
31192^460567-113541138645Enzo Doria08/2014
3120(10^138622+161)/9138622Robert Price09/2021
31217*10^138604+3138605Robert Price08/2015
3122(133*10^138600+17)/3138602Robert Price11/2021
312333912^12203+12203^33912138581Hans Havermann05/2021
31242^460330+69138574Lelio R Paula09/2017
3125(17*10^138569-77)/3138570Robert Price08/2019
312631186^27725+27725^31186138556Hans Havermann05/2021
3127(16*10^138545+89)/3138546Robert Price03/2021
312839753^3056+3056^39753138546Hans Havermann05/2021
312931282^26847+26847^31282138545Hans Havermann05/2021
31306*10^138520-37138521Robert Price02/2021
31322^460078-69581138498Enzo Doria12/2015
313131830^22447+22447^31830138498Hans Havermann05/2021
313337384^5065+5065^37384138492Hans Havermann05/2021
313434774^9585+9585^34774138456Hans Havermann05/2021
313510^138444-5001138444Robert Price12/2021
31362^459768+1531138404Lelio R Paula06/2012
3137(266*10^138328-17)/3138330Robert Price07/2020
313832963^15696+15696^32963138306Hans Havermann05/2021
31392^459343-113611138277Enzo Doria08/2014
3140(28*10^138240+113)/3138241Robert Price03/2020
31412^459199+1874393138233Enzo Doria06/2016
314233339^14002+14002^33339138230Hans Havermann05/2021
31432^459063-345307138192Enzo Doria06/2015
31442*10^138162-43138163Robert Price04/2018
31452^458927-112747138151Enzo Doria06/2014
31462^458927-69217138151Enzo Doria11/2015
314730907^29458+29458^30907138130Hans Havermann05/2021
314832882^15837+15837^32882138094Hans Havermann05/2021
314939252^3295+3295^39252138083Hans Havermann05/2021
315033789^12190+12190^33789138062Hans Havermann06/2021
3151555555*2^458524+1513138036Darren Bedwell08/2009
315230931^29002+29002^30931138028Hans Havermann05/2021
31532^458465+2^32+1138012T. D. Noe06/2007
315432206^19275+19275^32206138003Hans Havermann05/2021
31552^458321-113053137969Enzo Doria07/2014
31566^177298+323137965Riley Fisher03/2023
31572^458298+79459137962Enzo Doria06/2016
31582^458248-21815137947Enzo Doria07/2013
31592^458194+1876549137931Enzo Doria07/2016
3160(318259#+325270)/(2^2*5*11*2957)137907Makoto Morimoto10/2017
3161(318259#+2625)/(3^2*5*7^5*22965193)137899Makoto Morimoto06/2019
3162(793*10^137887+53)/9137889Robert Price01/2022
31632^457937+57137853Lelio R Paula09/2017
3164(8*10^137845+13)/3137846Robert Price06/2018
31652^457822+105137819Donovan Johnson06/2006
31662^457754-113711137798Enzo Doria09/2014
316711^132315-360137792Enzo Doria09/2012
316832072^19689+19689^32072137725Hans Havermann06/2021
316944592^1225+1225^44592137707Hans Havermann05/2021
31702^457347-37137676Lelio R Paula09/2017
31712^457322-2786393137668Enzo Doria10/2015
3172gcd(Phi(699340,10),(10^34967+1)^3*(10^34967+1+10^17484)-(10^69934+10^34967)*(10^17484-1)+10^104901)137664Serge Batalov04/2015
317334015^11134+11134^34015137647Hans Havermann06/2021
31742^457240-59939137643Enzo Doria10/2015
3175(856*10^137633-1)/9137635Robert Price03/2020
317636232^6289+6289^36232137631Hans Havermann05/2021
31772^457120-21575137607Enzo Doria07/2013
3179(11*2^456978+1)/15137564Lelio R Paula07/2015
317830963^27722+27722^30963137564Hans Havermann04/2021
318033722^12003+12003^33722137562Hans Havermann06/2021
3181(7*25^98399+10613)/12137556Curtis Bright05/2015
318241901^1918+1918^41901137555Hans Havermann06/2021
3183(7*10^137551-1)/3137552Robert Price08/2022
318432930^15021+15021^32930137539Hans Havermann05/2021
318531178^25785+25785^31178137538Hans Havermann05/2021
3186419^52446+52446^419137525Norbert Schneider11/2020
31872^456796-113513137510Enzo Doria08/2014
318831788^21137+21137^31788137485Hans Havermann04/2021
3189(7*2^456655+1)/39137467Lelio R Paula07/2015
31902^456503-114361137422Enzo Doria01/2015
3191(11*2^456387+1)/19137386Lelio R Paula07/2015
319236248^6147+6147^36248137332Hans Havermann05/2021
319331986^19651+19651^31986137329Hans Havermann05/2021
319431817^20656+20656^31817137292Hans Havermann05/2021
3195(71*10^137250+1)/9137251Serge Batalov05/2010
31962^455922+76249137247Enzo Doria05/2016
319731310^24171+24171^31310137241Hans Havermann05/2021
319814^119741-119741^14137239Serge Batalov04/2016
319935014^8297+8297^35014137218Hans Havermann05/2021
3200(19*2^455760+1)/3455137196Lelio R Paula07/2015
3202124^(2^16)+57^(2^16)137195Valeryi Kuryshev02/2011
3201124^65536+57^65536137195Serge Batalov03/2018
32032^455689+72677137177Enzo Doria04/2016
3204(17948!)^2+Prime(17948)137118Robert Price08/2014
320531287^24128+24128^31287137116Hans Havermann05/2021
3206(37^87421-1)/36137093Robert Price03/2012
320736233^6070+6070^36233137077Hans Havermann05/2021
3208(8*10^137073-17)/9137073Serge Batalov11/2022
320938418^3697+3697^38418137070Hans Havermann04/2021
32102^455323-57137066Lelio R Paula09/2017
3211(56*10^137019+583)/9137020Robert Price08/2021
3212(73*17^111333-9)/16136991Curtis Bright05/2015
32132^455025-112723136977Enzo Doria06/2014
321433876^11039+11039^33876136959Hans Havermann05/2021
321535142^7873+7873^35142136919Hans Havermann05/2021
321666*10^136894+7136896Robert Price07/2020
32172^454675-1777136871Yves Minet10/2011
321831676^20931+20931^31676136866Hans Havermann05/2021
32193*10^136829+29136830Robert Price05/2018
32204*10^136813-57136814Robert Price10/2018
3221(6092*28^94536-143)/9136812Curtis Bright05/2015
322237359^4588+4588^37359136795Hans Havermann05/2021
32232^454348-53136773Lelio R Paula09/2017
322431^91680-2136729Lelio R Paula05/2017
32252^454199-113697136728Enzo Doria09/2014
322630785^27622+27622^30785136725Hans Havermann05/2021
322732973^14014+14014^32973136725Hans Havermann05/2021
32297*10^136716+69136717Robert Price07/2019
322836002^6273+6273^36002136717Hans Havermann05/2021
32306*10^136692+53136693Robert Price05/2020
3231(13*10^136687+47)/3136688Robert Price10/2018
32322^453935-2791357136649Enzo Doria01/2016
32332^453906-69131136640Enzo Doria11/2015
323433232^12915+12915^33232136620Hans Havermann05/2021
32352^453791+1873913136605Enzo Doria06/2016
323634166^9951+9951^34166136592Hans Havermann05/2021
3237(21*2^453740-1)/2735136588Lelio R Paula07/2015
323831102^24635+24635^31102136587Hans Havermann05/2021
3239580^49413+49413^580136550Norbert Schneider02/2019
32402^453503-2788297136519Enzo Doria11/2015
324134989^7958+7958^34989136486Hans Havermann12/2020
3242(2*10^136484+187)/9136484Robert Price06/2022
324331007^25158+25158^31007136452Hans Havermann11/2020
32442^453267-113827136447Enzo Doria09/2014
324532234^17085+17085^32234136435Hans Havermann12/2020
32462^453102+1877629136398Enzo Doria08/2016
324731016^24981+24981^31016136397Hans Havermann12/2020
3248(62*10^136384-791)/9136385Robert Price06/2019
324934171^9798+9798^34171136382Hans Havermann12/2020
3250(17*10^136354-113)/3136355Robert Price06/2021


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: March, 20 2023 09:01 (Time in France)

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