PRP Records

Probable Primes Top 10000

(290751 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 ?
2751(203*10^140615-11)/3140617Robert Price12/2020
2752(85*10^140609+473)/9140610Robert Price01/2020
275339231^3836+3836^39231140600Hans Havermann06/2021
27542^466866-1840571140541Enzo Doria06/2015
27552^466829-459523140530Enzo Doria05/2015
27562^466692-113213140489Enzo Doria07/2014
275723*10^140464-3140466Robert Price10/2021
275831335^30364+30364^31335140455Hans Havermann05/2021
275932795^19126+19126^32795140416Hans Havermann05/2021
2760(44*10^140410-503)/9140411Robert Price12/2018
2761153^64265-2140400Lelio R Paula11/2017
2762(112*10^140357-1)/3140359Serge Batalov12/2014
2763(29*10^140337-17)/3140338Robert Price09/2019
27642^466181-112735140335Enzo Doria07/2014
2765(16*10^140290-37)/3140291Robert Price05/2021
2766(5*10^140281-119)/3140282Robert Price03/2018
276734568^11415+11415^34568140259Hans Havermann05/2021
2768(27*2^465872+1)/691140241Lelio R Paula08/2015
276933632^14781+14781^33632140236Hans Havermann05/2021
277031803^25670+25670^31803140233Hans Havermann05/2021
27712^465803-114817140221Enzo Doria05/2015
2772floor(Pi*10^140344)%10^140165140165Serge Batalov08/2012
27732^465503-112735140131Enzo Doria07/2014
2774(16*10^140091+167)/3140092Robert Price06/2019
2775(8*10^140087-137)/3140088Robert Price03/2022
27766^179964+179964^6-1140040Robert Price04/2014
2777(89*10^140008-179)/9140009Robert Price12/2019
2778(29*2^465077-1)/9140003Lelio R Paula08/2015
27792^465072-344789140001Enzo Doria07/2015
278034742^10683+10683^34742139965Hans Havermann05/2021
27815*10^139945+81139946Robert Price03/2019
278232648^19335+19335^32648139941Hans Havermann05/2021
27832^464864-17139939Lelio R Paula09/2017
27848*10^139920+51139921Robert Price08/2019
2785(85*10^139913-1)/3139915Robert Price02/2020
278631203^30436+30436^31203139896Hans Havermann04/2021
27874*10^139839-27139840Robert Price08/2021
278833582^14573+14573^33582139821Hans Havermann05/2021
2789(17^113621+1)/18139804Paul Bourdelais09/2011
27912*10^139800-21139801Robert Price09/2020
279032628^19261+19261^32628139801Hans Havermann04/2021
2792(13*10^139782+191)/3139783Robert Price11/2018
2793(64*10^139776+791)/9139777Robert Price01/2022
2794(695*10^139772+7)/9139774Robert Price12/2021
2795(19*2^464312-1)/3139773Lelio R Paula08/2015
2796(74*10^139723+133)/9139724Robert Price06/2019
27973*10^139722+13139723Robert Price07/2018
279831577^26592+26592^31577139721Hans Havermann05/2021
279977*10^139692+3139694Robert Price06/2020
2800(31*2^463970+1)/5139670Lelio R Paula08/2015
2801(18203^(2^15)+(18201)^(2^15))/2139597Robert Price05/2018
280239640^3321+3321^39640139584Hans Havermann05/2021
280336663^6410+6410^36663139571Hans Havermann05/2021
28042^463633-2788423139568Enzo Doria11/2015
280533659^13978+13978^33659139532Hans Havermann05/2021
280631811^24318+24318^31811139521Hans Havermann04/2021
280734149^12172+12172^34149139512Hans Havermann04/2021
2808(29*10^139476+313)/9139477Robert Price04/2021
280931721^24940+24940^31721139474Hans Havermann05/2021
281032833^17698+17698^32833139473Hans Havermann05/2021
28112^463271-109501139459Enzo Doria04/2014
2812(5*10^139457+79)/3139458Robert Price03/2018
28132^463237-99139449Lelio R Paula09/2017
2814(49*10^139442+383)/9139443Robert Price04/2019
281531155^29902+29902^31155139441Hans Havermann05/2021
2816(7*10^139417-547)/9139417Robert Price01/2018
2817(10^139398+191)/3139398Robert Price02/2018
281823*10^139386-3139388Robert Price10/2021
28192^463019+79463139383Enzo Doria06/2016
28203^292129-112756139381Enzo Doria07/2014
2821(15*2^462951+1)/527139361Lelio R Paula08/2015
282231922^23205+23205^31922139359Hans Havermann05/2021
28242^462855-1865707139334Enzo Doria02/2016
282331237^28876+28876^31237139334Hans Havermann05/2021
2825(86*10^139315+121)/9139316Robert Price08/2019
28262^462786-292043139313Enzo Doria08/2015
282738915^3798+3798^38915139299Hans Havermann05/2021
2828(26*10^139289+1)/9139290Serge Batalov05/2010
282934065^12248+12248^34065139260Hans Havermann05/2021
283036425^6654+6654^36425139256Hans Havermann05/2021
283139252^3527+3527^39252139243Hans Havermann05/2021
2832(17*10^139239+67)/3139240Robert Price01/2019
283331887^23248+23248^31887139231Hans Havermann05/2021
2834(25*10^139210-97)/9139211Robert Price01/2022
28352^462238-935139148Yves Minet02/2014
2836(29*10^139134-119)/9139135Robert Price12/2021
2837(109*10^139100-7)/3139102Robert Price03/2021
283838744^3885+3885^38744139068Hans Havermann05/2021
283931112^29499+29499^31112139065Hans Havermann05/2021
28402*10^139043-63139044Robert Price01/2022
284136390^6613+6613^36390139025Hans Havermann04/2021
28422*10^138975+33138976Robert Price11/2021
284342437^1882+1882^42437138966Hans Havermann05/2021
284432151^20990+20990^32151138958Hans Havermann05/2021
284532154^20933+20933^32154138933Hans Havermann04/2021
284631082^29499+29499^31082138931Hans Havermann04/2021
28472^461228+1870441138844Enzo Doria05/2016
28482^461204-113675138837Enzo Doria08/2014
2849(2^461139-7)/47138815Lelio R Paula08/2015
2850(17*10^138812-521)/9138813Robert Price04/2018
28513*10^138811-11138812Robert Price07/2018
2852(28*10^138768+173)/3138769Robert Price12/2019
2853(17*2^460963+1)/124051613138757Lelio R Paula08/2015
2854(379*10^138737-1)/9138739Robert Price02/2020
2855(43*10^138648+101)/9138649Robert Price11/2018
28562^460567-113541138645Enzo Doria08/2014
2857(10^138622+161)/9138622Robert Price09/2021
28587*10^138604+3138605Robert Price08/2015
2859(133*10^138600+17)/3138602Robert Price11/2021
286033912^12203+12203^33912138581Hans Havermann05/2021
28612^460330+69138574Lelio R Paula09/2017
2862(17*10^138569-77)/3138570Robert Price08/2019
286331186^27725+27725^31186138556Hans Havermann05/2021
2864(16*10^138545+89)/3138546Robert Price03/2021
286539753^3056+3056^39753138546Hans Havermann05/2021
286631282^26847+26847^31282138545Hans Havermann05/2021
28676*10^138520-37138521Robert Price02/2021
28692^460078-69581138498Enzo Doria12/2015
286831830^22447+22447^31830138498Hans Havermann05/2021
287037384^5065+5065^37384138492Hans Havermann05/2021
287134774^9585+9585^34774138456Hans Havermann05/2021
287210^138444-5001138444Robert Price12/2021
28732^459768+1531138404Lelio R Paula06/2012
2874(266*10^138328-17)/3138330Robert Price07/2020
287532963^15696+15696^32963138306Hans Havermann05/2021
28762^459343-113611138277Enzo Doria08/2014
2877(28*10^138240+113)/3138241Robert Price03/2020
28782^459199+1874393138233Enzo Doria06/2016
287933339^14002+14002^33339138230Hans Havermann05/2021
28802^459063-345307138192Enzo Doria06/2015
28812*10^138162-43138163Robert Price04/2018
28822^458927-112747138151Enzo Doria06/2014
28832^458927-69217138151Enzo Doria11/2015
288430907^29458+29458^30907138130Hans Havermann05/2021
288532882^15837+15837^32882138094Hans Havermann05/2021
288639252^3295+3295^39252138083Hans Havermann05/2021
288733789^12190+12190^33789138062Hans Havermann06/2021
2888555555*2^458524+1513138036Darren Bedwell08/2009
288930931^29002+29002^30931138028Hans Havermann05/2021
28902^458465+2^32+1138012T. D. Noe06/2007
289132206^19275+19275^32206138003Hans Havermann05/2021
28922^458321-113053137969Enzo Doria07/2014
28932^458298+79459137962Enzo Doria06/2016
28942^458248-21815137947Enzo Doria07/2013
28952^458194+1876549137931Enzo Doria07/2016
2896(318259#+325270)/(2^2*5*11*2957)137907Makoto Morimoto10/2017
2897(318259#+2625)/(3^2*5*7^5*22965193)137899Makoto Morimoto06/2019
2898(793*10^137887+53)/9137889Robert Price01/2022
28992^457937+57137853Lelio R Paula09/2017
2900(8*10^137845+13)/3137846Robert Price06/2018
29012^457822+105137819Donovan Johnson06/2006
29022^457754-113711137798Enzo Doria09/2014
290311^132315-360137792Enzo Doria09/2012
290432072^19689+19689^32072137725Hans Havermann06/2021
290544592^1225+1225^44592137707Hans Havermann05/2021
29062^457347-37137676Lelio R Paula09/2017
29072^457322-2786393137668Enzo Doria10/2015
2908gcd(Phi(699340,10),(10^34967+1)^3*(10^34967+1+10^17484)-(10^69934+10^34967)*(10^17484-1)+10^104901)137664Serge Batalov04/2015
290934015^11134+11134^34015137647Hans Havermann06/2021
29102^457240-59939137643Enzo Doria10/2015
2911(856*10^137633-1)/9137635Robert Price03/2020
291236232^6289+6289^36232137631Hans Havermann05/2021
29132^457120-21575137607Enzo Doria07/2013
2914(11*2^456978+1)/15137564Lelio R Paula07/2015
291530963^27722+27722^30963137564Hans Havermann04/2021
291633722^12003+12003^33722137562Hans Havermann06/2021
2917(7*25^98399+10613)/12137556Curtis Bright05/2015
291841901^1918+1918^41901137555Hans Havermann06/2021
291932930^15021+15021^32930137539Hans Havermann05/2021
292031178^25785+25785^31178137538Hans Havermann05/2021
2921419^52446+52446^419137525Norbert Schneider11/2020
29222^456796-113513137510Enzo Doria08/2014
292331788^21137+21137^31788137485Hans Havermann04/2021
2924(7*2^456655+1)/39137467Lelio R Paula07/2015
29252^456503-114361137422Enzo Doria01/2015
2926(11*2^456387+1)/19137386Lelio R Paula07/2015
292736248^6147+6147^36248137332Hans Havermann05/2021
292831986^19651+19651^31986137329Hans Havermann05/2021
292931817^20656+20656^31817137292Hans Havermann05/2021
2930(71*10^137250+1)/9137251Serge Batalov05/2010
29312^455922+76249137247Enzo Doria05/2016
293231310^24171+24171^31310137241Hans Havermann05/2021
293314^119741-119741^14137239Serge Batalov04/2016
293435014^8297+8297^35014137218Hans Havermann05/2021
2935(19*2^455760+1)/3455137196Lelio R Paula07/2015
2937124^(2^16)+57^(2^16)137195Valeryi Kuryshev02/2011
2936124^65536+57^65536137195Serge Batalov03/2018
29382^455689+72677137177Enzo Doria04/2016
2939(17948!)^2+Prime(17948)137118Robert Price08/2014
294031287^24128+24128^31287137116Hans Havermann05/2021
2941(37^87421-1)/36137093Robert Price03/2012
294236233^6070+6070^36233137077Hans Havermann05/2021
294338418^3697+3697^38418137070Hans Havermann04/2021
29442^455323-57137066Lelio R Paula09/2017
2945(56*10^137019+583)/9137020Robert Price08/2021
2946(73*17^111333-9)/16136991Curtis Bright05/2015
29472^455025-112723136977Enzo Doria06/2014
294833876^11039+11039^33876136959Hans Havermann05/2021
294935142^7873+7873^35142136919Hans Havermann05/2021
295066*10^136894+7136896Robert Price07/2020
29512^454675-1777136871Yves Minet10/2011
295231676^20931+20931^31676136866Hans Havermann05/2021
29533*10^136829+29136830Robert Price05/2018
29544*10^136813-57136814Robert Price10/2018
2955(6092*28^94536-143)/9136812Curtis Bright05/2015
295637359^4588+4588^37359136795Hans Havermann05/2021
29572^454348-53136773Lelio R Paula09/2017
295831^91680-2136729Lelio R Paula05/2017
29592^454199-113697136728Enzo Doria09/2014
296030785^27622+27622^30785136725Hans Havermann05/2021
296132973^14014+14014^32973136725Hans Havermann05/2021
29637*10^136716+69136717Robert Price07/2019
296236002^6273+6273^36002136717Hans Havermann05/2021
29646*10^136692+53136693Robert Price05/2020
2965(13*10^136687+47)/3136688Robert Price10/2018
29662^453935-2791357136649Enzo Doria01/2016
29672^453906-69131136640Enzo Doria11/2015
296833232^12915+12915^33232136620Hans Havermann05/2021
29692^453791+1873913136605Enzo Doria06/2016
297034166^9951+9951^34166136592Hans Havermann05/2021
2971(21*2^453740-1)/2735136588Lelio R Paula07/2015
297231102^24635+24635^31102136587Hans Havermann05/2021
2973580^49413+49413^580136550Norbert Schneider02/2019
29742^453503-2788297136519Enzo Doria11/2015
297534989^7958+7958^34989136486Hans Havermann12/2020
2976(2*10^136484+187)/9136484Robert Price06/2022
297731007^25158+25158^31007136452Hans Havermann11/2020
29782^453267-113827136447Enzo Doria09/2014
297932234^17085+17085^32234136435Hans Havermann12/2020
29802^453102+1877629136398Enzo Doria08/2016
298131016^24981+24981^31016136397Hans Havermann12/2020
2982(62*10^136384-791)/9136385Robert Price06/2019
298334171^9798+9798^34171136382Hans Havermann12/2020
2984(17*10^136354-113)/3136355Robert Price06/2021
298532756^14541+14541^32756136350Hans Havermann11/2020
298632205^17086+17086^32205136313Hans Havermann12/2020
2987(25*10^136303+161)/3136304Robert Price09/2019
298835337^7196+7196^35337136299Hans Havermann12/2020
2989(182*10^136291+1)/3136293Robert Price02/2020
2990(88*10^136234+83)/9136235Robert Price03/2022
299123*10^136225-7136227Robert Price02/2020
2992L(651821)136223Henri Lifchitz09/2008
29932^452460+77701136205Enzo Doria05/2016
29942^452440-114755136199Enzo Doria04/2015
299532286^16489+16489^32286136157Hans Havermann11/2020
2996(47*10^136141+493)/9136142Robert Price03/2019
299740392^2339+2339^40392136082Hans Havermann12/2020
29982*10^136057-43136058Robert Price04/2018
2999(2^451956-5)/181136051Lelio R Paula07/2015
30002^451947-22165136050Enzo Doria07/2013


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: June, 23 2022 21:24 (Time in France)

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