PRP Records

Probable Primes Top 10000

(291910 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) !!!


Submit your PRPs


See the Top discoverers
See the Latest PRPs
Search by form



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 ?
300134742^10683+10683^34742139965Hans Havermann05/2021
30025*10^139945+81139946Robert Price03/2019
300332648^19335+19335^32648139941Hans Havermann05/2021
30042^464864-17139939Lelio R Paula09/2017
30058*10^139920+51139921Robert Price08/2019
3006(85*10^139913-1)/3139915Robert Price02/2020
300731203^30436+30436^31203139896Hans Havermann04/2021
3008(16^116139+619)/5139845Anonymous08/2022
30094*10^139839-27139840Robert Price08/2021
301033582^14573+14573^33582139821Hans Havermann05/2021
3011(17^113621+1)/18139804Paul Bourdelais09/2011
30132*10^139800-21139801Robert Price09/2020
301232628^19261+19261^32628139801Hans Havermann04/2021
3014(13*10^139782+191)/3139783Robert Price11/2018
3015(64*10^139776+791)/9139777Robert Price01/2022
3016(695*10^139772+7)/9139774Robert Price12/2021
3017(19*2^464312-1)/3139773Lelio R Paula08/2015
3018(74*10^139723+133)/9139724Robert Price06/2019
30193*10^139722+13139723Robert Price07/2018
302031577^26592+26592^31577139721Hans Havermann05/2021
302177*10^139692+3139694Robert Price06/2020
3022(31*2^463970+1)/5139670Lelio R Paula08/2015
3023(18203^(2^15)+(18201)^(2^15))/2139597Robert Price05/2018
302439640^3321+3321^39640139584Hans Havermann05/2021
302536663^6410+6410^36663139571Hans Havermann05/2021
30262^463633-2788423139568Enzo Doria11/2015
302733659^13978+13978^33659139532Hans Havermann05/2021
302831811^24318+24318^31811139521Hans Havermann04/2021
302934149^12172+12172^34149139512Hans Havermann04/2021
3030(29*10^139476+313)/9139477Robert Price04/2021
303131721^24940+24940^31721139474Hans Havermann05/2021
303232833^17698+17698^32833139473Hans Havermann05/2021
30332^463271-109501139459Enzo Doria04/2014
3034(5*10^139457+79)/3139458Robert Price03/2018
30352^463237-99139449Lelio R Paula09/2017
3036(49*10^139442+383)/9139443Robert Price04/2019
303731155^29902+29902^31155139441Hans Havermann05/2021
3038(7*10^139417-547)/9139417Robert Price01/2018
3039(10^139398+191)/3139398Robert Price02/2018
304023*10^139386-3139388Robert Price10/2021
30412^463019+79463139383Enzo Doria06/2016
30423^292129-112756139381Enzo Doria07/2014
3043(15*2^462951+1)/527139361Lelio R Paula08/2015
304431922^23205+23205^31922139359Hans Havermann05/2021
30462^462855-1865707139334Enzo Doria02/2016
304531237^28876+28876^31237139334Hans Havermann05/2021
3047(86*10^139315+121)/9139316Robert Price08/2019
30482^462786-292043139313Enzo Doria08/2015
304938915^3798+3798^38915139299Hans Havermann05/2021
3050(26*10^139289+1)/9139290Serge Batalov05/2010
305134065^12248+12248^34065139260Hans Havermann05/2021
305236425^6654+6654^36425139256Hans Havermann05/2021
305339252^3527+3527^39252139243Hans Havermann05/2021
3054(17*10^139239+67)/3139240Robert Price01/2019
305531887^23248+23248^31887139231Hans Havermann05/2021
3056(25*10^139210-97)/9139211Robert Price01/2022
30572^462238-935139148Yves Minet02/2014
3058(29*10^139134-119)/9139135Robert Price12/2021
3059(109*10^139100-7)/3139102Robert Price03/2021
306038744^3885+3885^38744139068Hans Havermann05/2021
306131112^29499+29499^31112139065Hans Havermann05/2021
30622*10^139043-63139044Robert Price01/2022
306336390^6613+6613^36390139025Hans Havermann04/2021
30642*10^138975+33138976Robert Price11/2021
306542437^1882+1882^42437138966Hans Havermann05/2021
306632151^20990+20990^32151138958Hans Havermann05/2021
306732154^20933+20933^32154138933Hans Havermann04/2021
306831082^29499+29499^31082138931Hans Havermann04/2021
30692^461228+1870441138844Enzo Doria05/2016
30702^461204-113675138837Enzo Doria08/2014
3071(2^461139-7)/47138815Lelio R Paula08/2015
3072(17*10^138812-521)/9138813Robert Price04/2018
30733*10^138811-11138812Robert Price07/2018
3074(28*10^138768+173)/3138769Robert Price12/2019
3075(17*2^460963+1)/124051613138757Lelio R Paula08/2015
3076(379*10^138737-1)/9138739Robert Price02/2020
3077(43*10^138648+101)/9138649Robert Price11/2018
30782^460567-113541138645Enzo Doria08/2014
3079(10^138622+161)/9138622Robert Price09/2021
30807*10^138604+3138605Robert Price08/2015
3081(133*10^138600+17)/3138602Robert Price11/2021
308233912^12203+12203^33912138581Hans Havermann05/2021
30832^460330+69138574Lelio R Paula09/2017
3084(17*10^138569-77)/3138570Robert Price08/2019
308531186^27725+27725^31186138556Hans Havermann05/2021
3086(16*10^138545+89)/3138546Robert Price03/2021
308739753^3056+3056^39753138546Hans Havermann05/2021
308831282^26847+26847^31282138545Hans Havermann05/2021
30896*10^138520-37138521Robert Price02/2021
30912^460078-69581138498Enzo Doria12/2015
309031830^22447+22447^31830138498Hans Havermann05/2021
309237384^5065+5065^37384138492Hans Havermann05/2021
309334774^9585+9585^34774138456Hans Havermann05/2021
309410^138444-5001138444Robert Price12/2021
30952^459768+1531138404Lelio R Paula06/2012
3096(266*10^138328-17)/3138330Robert Price07/2020
309732963^15696+15696^32963138306Hans Havermann05/2021
30982^459343-113611138277Enzo Doria08/2014
3099(28*10^138240+113)/3138241Robert Price03/2020
31002^459199+1874393138233Enzo Doria06/2016
310133339^14002+14002^33339138230Hans Havermann05/2021
31022^459063-345307138192Enzo Doria06/2015
31032*10^138162-43138163Robert Price04/2018
31042^458927-112747138151Enzo Doria06/2014
31052^458927-69217138151Enzo Doria11/2015
310630907^29458+29458^30907138130Hans Havermann05/2021
310732882^15837+15837^32882138094Hans Havermann05/2021
310839252^3295+3295^39252138083Hans Havermann05/2021
310933789^12190+12190^33789138062Hans Havermann06/2021
3110555555*2^458524+1513138036Darren Bedwell08/2009
311130931^29002+29002^30931138028Hans Havermann05/2021
31122^458465+2^32+1138012T. D. Noe06/2007
311332206^19275+19275^32206138003Hans Havermann05/2021
31142^458321-113053137969Enzo Doria07/2014
31152^458298+79459137962Enzo Doria06/2016
31162^458248-21815137947Enzo Doria07/2013
31172^458194+1876549137931Enzo Doria07/2016
3118(318259#+325270)/(2^2*5*11*2957)137907Makoto Morimoto10/2017
3119(318259#+2625)/(3^2*5*7^5*22965193)137899Makoto Morimoto06/2019
3120(793*10^137887+53)/9137889Robert Price01/2022
31212^457937+57137853Lelio R Paula09/2017
3122(8*10^137845+13)/3137846Robert Price06/2018
31232^457822+105137819Donovan Johnson06/2006
31242^457754-113711137798Enzo Doria09/2014
312511^132315-360137792Enzo Doria09/2012
312632072^19689+19689^32072137725Hans Havermann06/2021
312744592^1225+1225^44592137707Hans Havermann05/2021
31282^457347-37137676Lelio R Paula09/2017
31292^457322-2786393137668Enzo Doria10/2015
3130gcd(Phi(699340,10),(10^34967+1)^3*(10^34967+1+10^17484)-(10^69934+10^34967)*(10^17484-1)+10^104901)137664Serge Batalov04/2015
313134015^11134+11134^34015137647Hans Havermann06/2021
31322^457240-59939137643Enzo Doria10/2015
3133(856*10^137633-1)/9137635Robert Price03/2020
313436232^6289+6289^36232137631Hans Havermann05/2021
31352^457120-21575137607Enzo Doria07/2013
3137(11*2^456978+1)/15137564Lelio R Paula07/2015
313630963^27722+27722^30963137564Hans Havermann04/2021
313833722^12003+12003^33722137562Hans Havermann06/2021
3139(7*25^98399+10613)/12137556Curtis Bright05/2015
314041901^1918+1918^41901137555Hans Havermann06/2021
3141(7*10^137551-1)/3137552Robert Price08/2022
314232930^15021+15021^32930137539Hans Havermann05/2021
314331178^25785+25785^31178137538Hans Havermann05/2021
3144419^52446+52446^419137525Norbert Schneider11/2020
31452^456796-113513137510Enzo Doria08/2014
314631788^21137+21137^31788137485Hans Havermann04/2021
3147(7*2^456655+1)/39137467Lelio R Paula07/2015
31482^456503-114361137422Enzo Doria01/2015
3149(11*2^456387+1)/19137386Lelio R Paula07/2015
315036248^6147+6147^36248137332Hans Havermann05/2021
315131986^19651+19651^31986137329Hans Havermann05/2021
315231817^20656+20656^31817137292Hans Havermann05/2021
3153(71*10^137250+1)/9137251Serge Batalov05/2010
31542^455922+76249137247Enzo Doria05/2016
315531310^24171+24171^31310137241Hans Havermann05/2021
315614^119741-119741^14137239Serge Batalov04/2016
315735014^8297+8297^35014137218Hans Havermann05/2021
3158(19*2^455760+1)/3455137196Lelio R Paula07/2015
3160124^(2^16)+57^(2^16)137195Valeryi Kuryshev02/2011
3159124^65536+57^65536137195Serge Batalov03/2018
31612^455689+72677137177Enzo Doria04/2016
3162(17948!)^2+Prime(17948)137118Robert Price08/2014
316331287^24128+24128^31287137116Hans Havermann05/2021
3164(37^87421-1)/36137093Robert Price03/2012
316536233^6070+6070^36233137077Hans Havermann05/2021
3166(8*10^137073-17)/9137073Serge Batalov11/2022
316738418^3697+3697^38418137070Hans Havermann04/2021
31682^455323-57137066Lelio R Paula09/2017
3169(56*10^137019+583)/9137020Robert Price08/2021
3170(73*17^111333-9)/16136991Curtis Bright05/2015
31712^455025-112723136977Enzo Doria06/2014
317233876^11039+11039^33876136959Hans Havermann05/2021
317335142^7873+7873^35142136919Hans Havermann05/2021
317466*10^136894+7136896Robert Price07/2020
31752^454675-1777136871Yves Minet10/2011
317631676^20931+20931^31676136866Hans Havermann05/2021
31773*10^136829+29136830Robert Price05/2018
31784*10^136813-57136814Robert Price10/2018
3179(6092*28^94536-143)/9136812Curtis Bright05/2015
318037359^4588+4588^37359136795Hans Havermann05/2021
31812^454348-53136773Lelio R Paula09/2017
318231^91680-2136729Lelio R Paula05/2017
31832^454199-113697136728Enzo Doria09/2014
318430785^27622+27622^30785136725Hans Havermann05/2021
318532973^14014+14014^32973136725Hans Havermann05/2021
31877*10^136716+69136717Robert Price07/2019
318636002^6273+6273^36002136717Hans Havermann05/2021
31886*10^136692+53136693Robert Price05/2020
3189(13*10^136687+47)/3136688Robert Price10/2018
31902^453935-2791357136649Enzo Doria01/2016
31912^453906-69131136640Enzo Doria11/2015
319233232^12915+12915^33232136620Hans Havermann05/2021
31932^453791+1873913136605Enzo Doria06/2016
319434166^9951+9951^34166136592Hans Havermann05/2021
3195(21*2^453740-1)/2735136588Lelio R Paula07/2015
319631102^24635+24635^31102136587Hans Havermann05/2021
3197580^49413+49413^580136550Norbert Schneider02/2019
31982^453503-2788297136519Enzo Doria11/2015
319934989^7958+7958^34989136486Hans Havermann12/2020
3200(2*10^136484+187)/9136484Robert Price06/2022
320131007^25158+25158^31007136452Hans Havermann11/2020
32022^453267-113827136447Enzo Doria09/2014
320332234^17085+17085^32234136435Hans Havermann12/2020
32042^453102+1877629136398Enzo Doria08/2016
320531016^24981+24981^31016136397Hans Havermann12/2020
3206(62*10^136384-791)/9136385Robert Price06/2019
320734171^9798+9798^34171136382Hans Havermann12/2020
3208(17*10^136354-113)/3136355Robert Price06/2021
320932756^14541+14541^32756136350Hans Havermann11/2020
321032205^17086+17086^32205136313Hans Havermann12/2020
3211(25*10^136303+161)/3136304Robert Price09/2019
321235337^7196+7196^35337136299Hans Havermann12/2020
3213(182*10^136291+1)/3136293Robert Price02/2020
3214(88*10^136234+83)/9136235Robert Price03/2022
321523*10^136225-7136227Robert Price02/2020
3216L(651821)136223Henri Lifchitz09/2008
32172^452460+77701136205Enzo Doria05/2016
32182^452440-114755136199Enzo Doria04/2015
321932286^16489+16489^32286136157Hans Havermann11/2020
3220(47*10^136141+493)/9136142Robert Price03/2019
322140392^2339+2339^40392136082Hans Havermann12/2020
32222*10^136057-43136058Robert Price04/2018
3223(2^451956-5)/181136051Lelio R Paula07/2015
32242^451947-22165136050Enzo Doria07/2013
32252^451787-21805136002Enzo Doria07/2013
32262^451734-112817135986Enzo Doria06/2014
3227(11*2^451714+1)/75135979Lelio R Paula07/2015
32282^451705-21879135977Enzo Doria07/2013
32292^451560-112349135934Enzo Doria06/2014
32302^451530+45135925Lelio R Paula08/2017
323131622^19875+19875^31622135922Hans Havermann11/2020
3232(25*10^135906-73)/3135907Robert Price09/2019
32332^451450-21743135900Enzo Doria07/2013
3234(7*10^135879+11)/9135879Tyler Busby01/2023
323535218^7199+7199^35218135846Hans Havermann11/2020
323635661^6446+6446^35661135844Hans Havermann11/2020
323731869^18248+18248^31869135801Hans Havermann12/2020
3238(77*10^135789+157)/9135790Robert Price05/2022
32392^450805+65135706Lelio R Paula08/2017
324030761^25728+25728^30761135669Hans Havermann12/2020
32412*10^135663+69135664Robert Price06/2020
324233962^9867+9867^33962135651Hans Havermann11/2020
324334474^8605+8605^34474135647Hans Havermann11/2020
324434501^8508+8508^34501135583Hans Havermann12/2020
324535487^6614+6614^35487135577Hans Havermann12/2020
3246(13725^32768+1)/131074135573Lelio R Paula03/2012
3247(313007#+121876)/(2*30469*424867)135559Makoto Morimoto08/2020
3248(5^193939+1)/6135557Paul Bourdelais12/2008
3249(76*10^135553-49)/9135554Robert Price07/2022
3250(844*10^135527-7)/9135529Robert Price05/2021


Find by discoverer :


Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: February, 02 2023 13:22 (Time in France)

Go back
Valid XHTML 1.0!    Valid CSS!