PRP Records

Probable Primes Top 10000

(301678 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 ?
1251111443^516+516^111443302306Hans Havermann12/2021
125267638^29387+29387^67638302218Hans Havermann11/2021
12532^1003494+1874899302082Enzo Doria06/2016
125475189^10400+10400^75189302037Hans Havermann12/2021
125567237^31042+31042^67237302026Hans Havermann12/2021
125664540^47791+47791^64540302005Hans Havermann11/2021
12572^1003046+60529301947Enzo Doria04/2016
125883278^4209+4209^83278301815Hans Havermann09/2021
125964431^48250+48250^64431301763Hans Havermann09/2021
126067237^30714+30714^67237301716Hans Havermann09/2021
12612^1002144+235861301676Enzo Doria05/2025
126264641^46288+46288^64641301581Hans Havermann09/2021
126371513^16482+16482^71513301572Hans Havermann10/2021
126472017^15396+15396^72017301565Hans Havermann09/2021
126565534^39927+39927^65534301540Hans Havermann10/2021
1266(23^221411-1)/22301501Paul Bourdelais08/2020
126763169^59152+59152^63169301441Hans Havermann09/2021
126875055^10348+10348^75055301336Hans Havermann09/2021
12692^1000647+1881353301225Enzo Doria11/2016
127083686^3961+3961^83686301086Hans Havermann10/2021
127168529^24742+24742^68529301078Hans Havermann09/2021
127265207^41416+41416^65207301072Hans Havermann10/2021
12742^1000000+821751301030Tony Prest / Never Odd Or Even10/2015
12732^999999+77151301030Norman Luhn09/2023
127590762^2071+2071^90762300984Hans Havermann06/2021
127663909^51142+51142^63909300934Hans Havermann08/2021
12772^999646+1874029300924Enzo Doria06/2016
127866280^34607+34607^66280300856Hans Havermann06/2021
127965534^38925+38925^65534300817Hans Havermann07/2021
128063296^56517+56517^63296300794Hans Havermann06/2021
1281110610^523+523^110610300694Hans Havermann06/2021
128266428^33609+33609^66428300684Hans Havermann06/2021
128374247^11210+11210^74247300672Hans Havermann06/2021
1284(59^169777-1)/58300649Paul Bourdelais08/2020
128510^300476+3300477Ed Trice10/2012
128610^300476-530913300476Patrick De Geest03/2016
128766703^31960+31960^66703300471Hans Havermann06/2021
128863722^51915+51915^63722300468Hans Havermann06/2021
12892^998053+1879667300444Enzo Doria09/2016
129077018^7959+7959^77018300437Hans Havermann07/2021
1291314738^9+9^314738300337Anatoly F. Selevich02/2011
12922^997689+217787300335Enzo Doria01/2024
129369478^20987+20987^69478300281Hans Havermann07/2021
129464088^48393+48393^64088300239Hans Havermann07/2021
12952^997369+237917300238Enzo Doria06/2025
129664605^44146+44146^64605300084Hans Havermann08/2021
12972^996845+29027300081Enzo Doria02/2024
12987^355039-6^355039300043Jean-Louis Charton05/2011
129967594^27465+27465^67594300035Hans Havermann06/2021
130010^300000+287389300001Patrick De Geest10/2019
130110^300000-83657300000Patrick De Geest10/2019
130270599^17756+17756^70599300000Hans Havermann06/2021
1303numbpart(72526161452)299999Serge Batalov04/2017
13042^996182-114431299881Enzo Doria02/2015
13053*2^996126+5299865Jon Grantham07/2023
13062^996034-17299837Stefano Morozzi07/2022
13072^995793+36587299764Enzo Doria09/2024
1308(19*10^299640+77)/3299641Robert Price03/2023
13092^995214-2788361299590Enzo Doria12/2015
13102^994791-114319299462Enzo Doria01/2015
13112^994490-1863791299372Enzo Doria01/2016
13122^993322+1885729299020Enzo Doria03/2017
13132^993227+230033298992Enzo Doria12/2024
1314(36395^65536+36393^65536)/2298913Kellen Shenton04/2022
13152^992711-2788807298836Enzo Doria12/2015
13162^992525-114199298780Enzo Doria12/2014
1317(7^353501-3^353501)/4298743Jon Grantham08/2023
13182^992329+1884707298721Enzo Doria02/2017
13192^992292+229801298710Enzo Doria12/2024
13202^992052+215491298638Enzo Doria11/2023
13212^991968-23298613Stefano Morozzi07/2022
13222^991715-19298536Stefano Morozzi07/2022
13232^991387+237383298438Enzo Doria06/2025
1324(10^298414+7)/191/823/56921/1334467298398Alfred Reich10/2021
13252^989562+25297888Stefano Morozzi05/2021
13262^988580+214051297593Enzo Doria10/2023
13272^988537+218837297580Enzo Doria03/2024
1328(19*10^297497+77)/3297498Robert Price03/2023
1329(2*10^297488-23)/3297488Robert Price10/2022
13302^987033+46427297127Enzo Doria05/2025
1331(2^986191+1)/3296873Vincent Diepeveen06/2008
13322^985217-114553296580Enzo Doria03/2015
1333(76^157649-1)/75296507Paul Bourdelais07/2019
13342^984650+21529296410Enzo Doria08/2023
13352^984131-1828009296253Enzo Doria01/2015
13362^983620+60451296100Phil Moore03/2008
13372^982721-2683295829Yves Minet02/2016
1338(23*10^295581+7)/3295582Robert Price05/2023
13392^981298-2788421295401Enzo Doria12/2015
13402^981163-2790967295360Enzo Doria12/2015
13412^981016-15295316Stefano Morozzi07/2022
13428*10^295160-13295161Robert Price08/2023
13432^979594+1865839294888Enzo Doria02/2016
13442^979502+221029294860Enzo Doria03/2024
13452*10^294527-91294528Robert Price02/2023
1346(49363^63001-1)/(49363^251-1)294511Ryan Propper11/2023
134710^294475+49294476Robert Price02/2023
13482^977896+234601294377Enzo Doria04/2025
1349(11*10^294308+91)/3294309Robert Price03/2023
13502^976760+1885021294035Enzo Doria02/2017
13513*2^976518+5293962Jon Grantham07/2023
13522^975798+218599293745Enzo Doria01/2024
13532^974441+1878407293336Enzo Doria08/2016
13542^974180+1876831293258Enzo Doria07/2016
13552^974170+453319293255Enzo Doria01/2017
1356(211^126023-1)/210292911Anonymous05/2024
13572^972744-114419292826Enzo Doria03/2015
135811^281143+6292781Paul Bourdelais03/2021
1359(4*10^292619-91)/3292620Robert Price12/2022
1360E(69468)/13247122135292549Sergey Batalov10/2023
1361CopelandErdos(292447)292447Mark Rodenkirch12/2015
13623*10^292344-97292345Robert Price01/2023
13632^970911+1873373292274Enzo Doria07/2016
13642^970670+383059292201Enzo Doria12/2016
13652^970141-100363292042Enzo Doria02/2014
13662^969945+1874717291983Enzo Doria06/2016
13672^969384+1880701291814Enzo Doria10/2016
1368(13*10^291721-43)/3291722Robert Price08/2023
1369(3^611333-2^611333)/(99035947*87109884549431)291659Mike Oakes02/2017
137010^(2*145126+1)-2*10^145126-1290253Robert Price03/2025
13713*2^963892+5290161Jon Grantham07/2023
1372(151*10^289877-1)/3289879Robert Price07/2023
13732^962194+60139289650Enzo Doria02/2016
13742^961409+44267289413Enzo Doria04/2025
13752^959307-1861507288781Enzo Doria11/2015
1376(17*10^288692+31)/3288693Robert Price04/2023
137714^251797-3288592Paul Bourdelais12/2020
1378(8745^73441-1)/(8745^271-1)288419Ryan Propper11/2023
1379(2*10^288371-23)/3288371Robert Price10/2022
1380(31*10^288238-1)/3288240Robert Price02/2023
1381(7^341063-2^341063)/5288231Jon Grantham08/2023
13822^957372+283531288198Enzo Doria02/2017
13832^957192-1864049288144Enzo Doria01/2016
1384(95774^58081-1)/(95774^241-1)288116Ryan Propper11/2023
13852^956446+1875199287919Enzo Doria06/2016
13862^956283+219143287870Enzo Doria02/2024
13877*10^287854+39287855Robert Price01/2023
13882^956082+28309287810Enzo Doria02/2024
1389(17^233689+1)/18287542Paul Bourdelais09/2013
13902^955178+1883587287538Enzo Doria12/2016
13912^954127-954127^2287221Henri Lifchitz01/2021
13922^954001+1875257287183Enzo Doria07/2016
13932*10^287175-49287176Robert Price05/2023
1394(22*10^287085-19)/3287086Robert Price07/2023
13952^953667+38573287083Enzo Doria11/2024
13962^953488+22411287029Enzo Doria09/2023
1397(23891^65536+1)/2286932Serge Batalov03/2018
13985*3^601336-2^601336286911Jon Grantham08/2023
13992^952268+1878601286662Enzo Doria09/2016
14002^950801+81557286220Enzo Doria08/2016
14012^949403+217523285799Enzo Doria01/2024
140222845^65536+22844^65536285658Kellen Shenton03/2021
1403(19*10^285615+53)/9285616Rytis Slatkevicius12/2024
1404(11*2^948635-13)/15285568Renaud Lifchitz11/2011
1405(54^164839+1)/55285565Paul Bourdelais07/2019
14062^948510+782569285530Enzo Doria10/2016
14072^948374-114137285490Enzo Doria01/2015
14082^947739+1872923285298Enzo Doria06/2016
14092^946274+218407284857Enzo Doria03/2024
14107*10^284751+9284752Robert Price04/2023
14112^944561-21284342Stefano Morozzi07/2022
1412(4*10^284330-31)/9284330Serge Batalov11/2022
1413(32*10^283826-23)/9283827Serge Batalov01/2023
14142^942533+82067283731Enzo Doria09/2016
14152^941469+39283411Jon Grantham08/2023
1416(10^283342-31)/3283342Robert Price03/2023
14172^940950+1874989283255Enzo Doria06/2016
14182^940426-2786141283097Enzo Doria11/2015
14192^940155+226973283015Enzo Doria09/2024
1420(2*10^282948-11)/9282948Serge Batalov11/2022
14212^939881-114115282933Enzo Doria12/2014
1422(14*10^282673-143)/3282674Robert Price05/2023
142310^282493+632551282494Patrick De Geest02/2017
142510^282493-9^282493282493Jean-Louis Charton03/2007
142410^282493-132327282493Patrick De Geest02/2017
14263^591827-2^591827282374Mike Oakes08/2009
1427Tau(509^18946)282048Nik Lygeros / Olivier Rozier05/2015
14282^936716-1835519281980Enzo Doria04/2015
14292^936588+79411281942Enzo Doria06/2016
14302^936047+1877423281779Enzo Doria08/2016
14312^935713+1869377281678Enzo Doria05/2016
14322^933082+1877059280886Enzo Doria08/2016
1433(5*10^280710+1)/3280711Serge Batalov10/2014
14342^932443+225893280694Enzo Doria08/2024
14352^932064+26521280580Enzo Doria12/2023
14362^931976+25280553Stefano Morozzi05/2021
1437(42^172663+1)/43280274Paul Bourdelais07/2019
1438(10^279978+11)/3279978Serge Batalov07/2015
14392^929524-1864829279815Enzo Doria01/2016
14402^929329+22697279756Enzo Doria09/2023
14412^929152+60181279703Enzo Doria02/2016
14422^928621-2787883279543Enzo Doria11/2015
1443(2^927763+lucasV(-1,2,927763)+1)/2279285Mike Oakes04/2017
14443*10^279271+77279272Robert Price06/2024
14452^927429+1882277279184Enzo Doria12/2016
14462^926766-11278985Stefano Morozzi07/2022
1447(71^150697-1)/70278978Paul Bourdelais07/2019
1448(33^183661-1)/32278891Paul Bourdelais12/2018
1449(166*10^278633-7)/3278635Robert Price02/2023
1450(2^925391+lucasV(-1,2,925391)+1)/2278571Mike Oakes03/2017
14512^925330-1301278553Yves Minet06/2015
1452(299*10^278546+1)/3278548Robert Price01/2023
14532^925299+216053278543Enzo Doria11/2023
1455(21^210599+1)/22278457Paul Bourdelais08/2013
1454(79^146749-1)/6395645198026062186278457Paul Vanderveen06/2025
1456(266*10^278325+1)/3278327Robert Price01/2023
14572^923261-69175277930Enzo Doria11/2015
1458757^96487-756^96487277796Jean-Louis Charton12/2012
14592^922301+57277641Stefano Morozzi05/2021
14607*10^277478-39277479Robert Price07/2023
1461((((((((((((((291487327^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2277369Serge Batalov07/2016
1462(5^396413-1)/4277081Paul Bourdelais06/2010
14632^920318+2792299277044Enzo Doria02/2016
1464(16*10^276537-31)/3276538Robert Price03/2023
14652^918596-2786939276525Enzo Doria11/2015
14662^917910+28369276319Enzo Doria01/2024
14672^917328+228571276144Enzo Doria11/2024
1468(6737^72361-1)/(6737^269-1)276002Ryan Propper11/2023
14692^916639+60563275936Enzo Doria04/2016
1470(2*10^275922+1)/3275922Serge Batalov11/2022
14712^916385-2786383275860Enzo Doria11/2015
14722^915928+82081275722Enzo Doria09/2016
1473(4*10^275671+11)/3275672Tyler Busby02/2023
14742^915576-114137275616Enzo Doria01/2015
14752^914828+1876741275391Enzo Doria07/2016
14762^914757-2203275370Yves Minet12/2015
14777*10^275157-27275158Robert Price11/2022
14782^912744+20011274764Enzo Doria06/2023
14792^911900+1871245274510Enzo Doria05/2016
1480(16*10^274251-91)/3274252Robert Price11/2022
14812^910999+9274239Stefano Morozzi05/2021
1482(2^910869-7)/5274199Stefano Morozzi08/2022
14832^910490+283429274085Enzo Doria01/2017
14847*10^273983+39273984Robert Price01/2023
14852^909988-1862249273934Enzo Doria12/2015
14862^909901+378567273908Boyan Hu08/2024
14872^909297+1879157273726Enzo Doria08/2016
14882^909257-1864423273714Enzo Doria01/2016
14892^909254+31309273713Enzo Doria03/2024
14902^908739-7273558Stefano Morozzi07/2022
14912^908579-1861747273510Enzo Doria12/2015
14923*2^908005-5273338Jon Grantham07/2023
14932^907635-2791597273226Enzo Doria01/2016
14942^907059+211193273052Enzo Doria08/2023
1495(53^158341+1)/54273022Paul Bourdelais07/2019
14962^906594-113201272912Enzo Doria08/2014
14979*10^272800+91272801Robert Price05/2023
14982*10^272710-49272711Robert Price05/2023
14992*10^272403-91272404Robert Price02/2023
15002^904773+1872167272364Enzo Doria06/2016


Find by discoverer :


Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: June, 28 2025 10:26 (Time in France)

Go back
Valid XHTML 1.0!    Valid CSS!