PRP Records

Probable Primes Top 10000

(288515 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 ?
25014*5^202913-9141831Lelio R Paula04/2015
25022*7^167812-3141818Lelio R Paula12/2014
25032^471043+35141799Robert Price11/2015
2504(11*2^470956-1)/7945141770Lelio R Paula08/2015
250543636^1773+1773^43636141761Hans Havermann05/2021
2506(11*10^141718-131)/3141719Robert Price09/2018
25072^470692+76771141693Enzo Doria05/2016
250850160^667+667^50160141659Hans Havermann05/2021
250931522^31181+31181^31522141657Hans Havermann05/2021
251033076^19135+19135^33076141626Hans Havermann04/2021
2511(21*2^470391+1)/533141601Lelio R Paula09/2015
251231932^27155+27155^31932141582Hans Havermann05/2021
251336449^7660+7660^36449141577Hans Havermann05/2021
25142^470305-459373141576Enzo Doria05/2015
251532195^24936+24936^32195141556Hans Havermann05/2021
25162^470183+72623141540Enzo Doria04/2016
25172^470173-16465141537Enzo Doria04/2013
251837297^6234+6234^37297141534Hans Havermann05/2021
251944*10^141476+9141478Robert Price10/2020
25202^469974-1841141477Enzo Doria05/2014
2521(23*2^469939+1)/25141466Lelio R Paula08/2015
25222*10^141448+63141449Robert Price05/2018
25232^469824+43141432Lelio R Paula09/2017
25242*10^141407-27141408Robert Price05/2018
2525(214*10^141385-1)/3141387Robert Price01/2021
25262^469630-59711141373Enzo Doria10/2015
252735277^10172+10172^35277141370Hans Havermann04/2021
252833397^17100+17100^33397141370Hans Havermann04/2021
2529(25*10^141366-331)/9141367Robert Price08/2018
253036986^6639+6639^36986141365Hans Havermann06/2021
253134572^12271+12271^34572141361Hans Havermann06/2021
253237179^6338+6338^37179141353Hans Havermann05/2021
2533(2^469564-3)/611141351Lelio R Paula08/2015
2534197^61601+2141342Lelio R Paula08/2017
253533420^16951+16951^33420141340Hans Havermann05/2021
253631623^29458+29458^31623141330Hans Havermann05/2021
253748112^865+865^48112141306Hans Havermann05/2021
25382^469372-112949141296Enzo Doria07/2014
25395*10^141294-63141295Robert Price04/2021
25403^296115+4141283Tyler NeSmith01/2021
2542143^(2^16)+106^(2^16)141253Valeryi Kuryshev02/2011
2541143^65536+106^65536141253Serge Batalov03/2018
2543(11*10^141243-23)/3141244Robert Price09/2021
25452^469198+782569141243Enzo Doria10/2016
254438129^5062+5062^38129141243Hans Havermann05/2021
25462^469076-2786939141206Enzo Doria11/2015
254738630^4521+4521^38630141202Hans Havermann05/2021
254831755^27836+27836^31755141139Hans Havermann05/2021
254935554^9325+9325^35554141137Hans Havermann05/2021
25502^468804+1874941141125Enzo Doria06/2016
25512^468787+81353141119Enzo Doria08/2016
25522^468595-350407141062Enzo Doria06/2015
25532^468564+87855141052Lelio R Paula01/2016
25542^468551-21987141048Enzo Doria07/2013
25552^468523-7141040Lelio R Paula08/2015
2556(25*10^141019-13)/3141020Robert Price09/2019
25572^468405+87855141004Lelio R Paula01/2016
255839338^3831+3831^39338140961Hans Havermann05/2021
255931458^30239+30239^31458140950Hans Havermann05/2021
25608*10^140932+29140933Robert Price11/2021
256133166^17691+17691^33166140881Hans Havermann06/2021
25622^467978-113051140876Enzo Doria07/2014
25632^467780-344429140816Enzo Doria07/2015
25649*10^140802-89140803Robert Price04/2020
25652^467605-1855603140764Enzo Doria09/2015
25665*10^140744-7140745Robert Price09/2015
2567(5^201359-1)/4140744Paul Bourdelais12/2008
25682^467401-1850023140702Enzo Doria08/2015
2569(266*10^140681-17)/3140683Robert Price07/2020
2570(2^467270+78557)/23247140658Lelio R Paula07/2015
257132138^23781+23781^32138140644Hans Havermann05/2021
257231654^27735+27735^31654140640Hans Havermann05/2021
2573(29*2^467205+1)/2780517107140635Lelio R Paula08/2015
25742^467166-1854941140631Enzo Doria09/2015
2575(203*10^140615-11)/3140617Robert Price12/2020
2576(85*10^140609+473)/9140610Robert Price01/2020
257739231^3836+3836^39231140600Hans Havermann06/2021
25782^466866-1840571140541Enzo Doria06/2015
25792^466829-459523140530Enzo Doria05/2015
25802^466692-113213140489Enzo Doria07/2014
258123*10^140464-3140466Robert Price10/2021
258231335^30364+30364^31335140455Hans Havermann05/2021
258332795^19126+19126^32795140416Hans Havermann05/2021
2584(44*10^140410-503)/9140411Robert Price12/2018
2585153^64265-2140400Lelio R Paula11/2017
2586(112*10^140357-1)/3140359Serge Batalov12/2014
2587(29*10^140337-17)/3140338Robert Price09/2019
25882^466181-112735140335Enzo Doria07/2014
2589(16*10^140290-37)/3140291Robert Price05/2021
2590(5*10^140281-119)/3140282Robert Price03/2018
259134568^11415+11415^34568140259Hans Havermann05/2021
2592(27*2^465872+1)/691140241Lelio R Paula08/2015
259333632^14781+14781^33632140236Hans Havermann05/2021
259431803^25670+25670^31803140233Hans Havermann05/2021
25952^465803-114817140221Enzo Doria05/2015
2596floor(Pi*10^140344)%10^140165140165Serge Batalov08/2012
25972^465503-112735140131Enzo Doria07/2014
2598(16*10^140091+167)/3140092Robert Price06/2019
25996^179964+179964^6-1140040Robert Price04/2014
2600(89*10^140008-179)/9140009Robert Price12/2019
2601(29*2^465077-1)/9140003Lelio R Paula08/2015
26022^465072-344789140001Enzo Doria07/2015
260334742^10683+10683^34742139965Hans Havermann05/2021
26045*10^139945+81139946Robert Price03/2019
260532648^19335+19335^32648139941Hans Havermann05/2021
26062^464864-17139939Lelio R Paula09/2017
26078*10^139920+51139921Robert Price08/2019
2608(85*10^139913-1)/3139915Robert Price02/2020
260931203^30436+30436^31203139896Hans Havermann04/2021
26104*10^139839-27139840Robert Price08/2021
261133582^14573+14573^33582139821Hans Havermann05/2021
2612(17^113621+1)/18139804Paul Bourdelais09/2011
26142*10^139800-21139801Robert Price09/2020
261332628^19261+19261^32628139801Hans Havermann04/2021
2615(13*10^139782+191)/3139783Robert Price11/2018
2616(19*2^464312-1)/3139773Lelio R Paula08/2015
2617(74*10^139723+133)/9139724Robert Price06/2019
26183*10^139722+13139723Robert Price07/2018
261931577^26592+26592^31577139721Hans Havermann05/2021
262077*10^139692+3139694Robert Price06/2020
2621(31*2^463970+1)/5139670Lelio R Paula08/2015
2622(18203^(2^15)+(18201)^(2^15))/2139597Robert Price05/2018
262339640^3321+3321^39640139584Hans Havermann05/2021
262436663^6410+6410^36663139571Hans Havermann05/2021
26252^463633-2788423139568Enzo Doria11/2015
262633659^13978+13978^33659139532Hans Havermann05/2021
262731811^24318+24318^31811139521Hans Havermann04/2021
262834149^12172+12172^34149139512Hans Havermann04/2021
2629(29*10^139476+313)/9139477Robert Price04/2021
263031721^24940+24940^31721139474Hans Havermann05/2021
263132833^17698+17698^32833139473Hans Havermann05/2021
26322^463271-109501139459Enzo Doria04/2014
2633(5*10^139457+79)/3139458Robert Price03/2018
26342^463237-99139449Lelio R Paula09/2017
2635(49*10^139442+383)/9139443Robert Price04/2019
263631155^29902+29902^31155139441Hans Havermann05/2021
2637(7*10^139417-547)/9139417Robert Price01/2018
2638(10^139398+191)/3139398Robert Price02/2018
263923*10^139386-3139388Robert Price10/2021
26402^463019+79463139383Enzo Doria06/2016
26413^292129-112756139381Enzo Doria07/2014
2642(15*2^462951+1)/527139361Lelio R Paula08/2015
264331922^23205+23205^31922139359Hans Havermann05/2021
26452^462855-1865707139334Enzo Doria02/2016
264431237^28876+28876^31237139334Hans Havermann05/2021
2646(86*10^139315+121)/9139316Robert Price08/2019
26472^462786-292043139313Enzo Doria08/2015
264838915^3798+3798^38915139299Hans Havermann05/2021
2649(26*10^139289+1)/9139290Serge Batalov05/2010
265034065^12248+12248^34065139260Hans Havermann05/2021
265136425^6654+6654^36425139256Hans Havermann05/2021
265239252^3527+3527^39252139243Hans Havermann05/2021
2653(17*10^139239+67)/3139240Robert Price01/2019
265431887^23248+23248^31887139231Hans Havermann05/2021
26552^462238-935139148Yves Minet02/2014
2656(109*10^139100-7)/3139102Robert Price03/2021
265738744^3885+3885^38744139068Hans Havermann05/2021
265831112^29499+29499^31112139065Hans Havermann05/2021
265936390^6613+6613^36390139025Hans Havermann04/2021
26602*10^138975+33138976Robert Price11/2021
266142437^1882+1882^42437138966Hans Havermann05/2021
266232151^20990+20990^32151138958Hans Havermann05/2021
266332154^20933+20933^32154138933Hans Havermann04/2021
266431082^29499+29499^31082138931Hans Havermann04/2021
26652^461228+1870441138844Enzo Doria05/2016
26662^461204-113675138837Enzo Doria08/2014
2667(2^461139-7)/47138815Lelio R Paula08/2015
2668(17*10^138812-521)/9138813Robert Price04/2018
26693*10^138811-11138812Robert Price07/2018
2670(28*10^138768+173)/3138769Robert Price12/2019
2671(17*2^460963+1)/124051613138757Lelio R Paula08/2015
2672(379*10^138737-1)/9138739Robert Price02/2020
2673(43*10^138648+101)/9138649Robert Price11/2018
26742^460567-113541138645Enzo Doria08/2014
2675(10^138622+161)/9138622Robert Price09/2021
26767*10^138604+3138605Robert Price08/2015
2677(133*10^138600+17)/3138602Robert Price11/2021
267833912^12203+12203^33912138581Hans Havermann05/2021
26792^460330+69138574Lelio R Paula09/2017
2680(17*10^138569-77)/3138570Robert Price08/2019
268131186^27725+27725^31186138556Hans Havermann05/2021
2682(16*10^138545+89)/3138546Robert Price03/2021
268339753^3056+3056^39753138546Hans Havermann05/2021
268431282^26847+26847^31282138545Hans Havermann05/2021
26856*10^138520-37138521Robert Price02/2021
26872^460078-69581138498Enzo Doria12/2015
268631830^22447+22447^31830138498Hans Havermann05/2021
268837384^5065+5065^37384138492Hans Havermann05/2021
268934774^9585+9585^34774138456Hans Havermann05/2021
26902^459768+1531138404Lelio R Paula06/2012
2691(266*10^138328-17)/3138330Robert Price07/2020
269232963^15696+15696^32963138306Hans Havermann05/2021
26932^459343-113611138277Enzo Doria08/2014
2694(28*10^138240+113)/3138241Robert Price03/2020
26952^459199+1874393138233Enzo Doria06/2016
269633339^14002+14002^33339138230Hans Havermann05/2021
26972^459063-345307138192Enzo Doria06/2015
26982*10^138162-43138163Robert Price04/2018
26992^458927-112747138151Enzo Doria06/2014
27002^458927-69217138151Enzo Doria11/2015
270130907^29458+29458^30907138130Hans Havermann05/2021
270232882^15837+15837^32882138094Hans Havermann05/2021
270339252^3295+3295^39252138083Hans Havermann05/2021
270433789^12190+12190^33789138062Hans Havermann06/2021
2705555555*2^458524+1513138036Darren Bedwell08/2009
270630931^29002+29002^30931138028Hans Havermann05/2021
27072^458465+2^32+1138012T. D. Noe06/2007
270832206^19275+19275^32206138003Hans Havermann05/2021
27092^458321-113053137969Enzo Doria07/2014
27102^458298+79459137962Enzo Doria06/2016
27112^458248-21815137947Enzo Doria07/2013
27122^458194+1876549137931Enzo Doria07/2016
2713(318259#+325270)/(2^2*5*11*2957)137907Makoto Morimoto10/2017
2714(318259#+2625)/(3^2*5*7^5*22965193)137899Makoto Morimoto06/2019
27152^457937+57137853Lelio R Paula09/2017
2716(8*10^137845+13)/3137846Robert Price06/2018
27172^457822+105137819Donovan Johnson06/2006
27182^457754-113711137798Enzo Doria09/2014
271911^132315-360137792Enzo Doria09/2012
272032072^19689+19689^32072137725Hans Havermann06/2021
272144592^1225+1225^44592137707Hans Havermann05/2021
27222^457347-37137676Lelio R Paula09/2017
27232^457322-2786393137668Enzo Doria10/2015
2724gcd(Phi(699340,10),(10^34967+1)^3*(10^34967+1+10^17484)-(10^69934+10^34967)*(10^17484-1)+10^104901)137664Serge Batalov04/2015
272534015^11134+11134^34015137647Hans Havermann06/2021
27262^457240-59939137643Enzo Doria10/2015
2727(856*10^137633-1)/9137635Robert Price03/2020
272836232^6289+6289^36232137631Hans Havermann05/2021
27292^457120-21575137607Enzo Doria07/2013
2730(11*2^456978+1)/15137564Lelio R Paula07/2015
273130963^27722+27722^30963137564Hans Havermann04/2021
273233722^12003+12003^33722137562Hans Havermann06/2021
2733(7*25^98399+10613)/12137556Curtis Bright05/2015
273441901^1918+1918^41901137555Hans Havermann06/2021
273532930^15021+15021^32930137539Hans Havermann05/2021
273631178^25785+25785^31178137538Hans Havermann05/2021
2737419^52446+52446^419137525Norbert Schneider11/2020
27382^456796-113513137510Enzo Doria08/2014
273931788^21137+21137^31788137485Hans Havermann04/2021
2740(7*2^456655+1)/39137467Lelio R Paula07/2015
27412^456503-114361137422Enzo Doria01/2015
2742(11*2^456387+1)/19137386Lelio R Paula07/2015
274336248^6147+6147^36248137332Hans Havermann05/2021
274431986^19651+19651^31986137329Hans Havermann05/2021
274531817^20656+20656^31817137292Hans Havermann05/2021
2746(71*10^137250+1)/9137251Serge Batalov05/2010
27472^455922+76249137247Enzo Doria05/2016
274831310^24171+24171^31310137241Hans Havermann05/2021
274914^119741-119741^14137239Serge Batalov04/2016
275035014^8297+8297^35014137218Hans Havermann05/2021


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: December, 01 2021 22:29 (Time in France)

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