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
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| Rank |
Probable prime |
Digits (> 50000) |
Who ? |
When ? |
| 2251 | 2^675047-100299 | 203210 | Stefano Morozzi | 01/2025 |
| 2252 | 2^675048-97313 | 203210 | Stefano Morozzi | 01/2025 |
| 2253 | 2^675046+118119 | 203210 | Stefano Morozzi | 02/2025 |
| 2254 | 2^675048+128941 | 203210 | Stefano Morozzi | 02/2025 |
| 2255 | 2^675049+136359 | 203210 | Stefano Morozzi | 02/2025 |
| 2256 | 2^675044-81087 | 203209 | Stefano Morozzi | 01/2025 |
| 2257 | 2^675042-179811 | 203208 | Stefano Morozzi | 01/2025 |
| 2258 | 2^675036-192939 | 203207 | Stefano Morozzi | 01/2025 |
| 2259 | 2^675037-17853 | 203207 | Stefano Morozzi | 01/2025 |
| 2260 | 2^675036+47101 | 203207 | Stefano Morozzi | 02/2025 |
| 2261 | 2^675038+189589 | 203207 | Stefano Morozzi | 02/2025 |
| 2262 | 2^675034-169727 | 203206 | Stefano Morozzi | 01/2025 |
| 2263 | 2^675035-173055 | 203206 | Stefano Morozzi | 01/2025 |
| 2264 | 2^675035-73551 | 203206 | Stefano Morozzi | 01/2025 |
| 2265 | 2^675033+79109 | 203206 | Stefano Morozzi | 02/2025 |
| 2266 | 2^675034+154057 | 203206 | Stefano Morozzi | 02/2025 |
| 2267 | 2^675030+109245 | 203205 | Stefano Morozzi | 01/2025 |
| 2268 | 2^675030-160047 | 203205 | Stefano Morozzi | 01/2025 |
| 2269 | 2^675027+106733 | 203204 | Stefano Morozzi | 01/2025 |
| 2270 | 2^675026-67377 | 203204 | Stefano Morozzi | 01/2025 |
| 2271 | 2^675021+13335 | 203202 | Stefano Morozzi | 01/2025 |
| 2272 | 2^675020-180497 | 203202 | Stefano Morozzi | 01/2025 |
| 2273 | 2^675016+174777 | 203201 | Stefano Morozzi | 01/2025 |
| 2274 | 2^675017+128379 | 203201 | Stefano Morozzi | 01/2025 |
| 2275 | 2^675017+171249 | 203201 | Stefano Morozzi | 01/2025 |
| 2276 | 2^675018+86517 | 203201 | Stefano Morozzi | 01/2025 |
| 2277 | 2^675019+125891 | 203201 | Stefano Morozzi | 01/2025 |
| 2278 | 2^675019+163251 | 203201 | Stefano Morozzi | 01/2025 |
| 2279 | 2^675016-170847 | 203201 | Stefano Morozzi | 01/2025 |
| 2280 | 2^675019-44755 | 203201 | Stefano Morozzi | 01/2025 |
| 2281 | 2^675015+120225 | 203200 | Stefano Morozzi | 01/2025 |
| 2282 | 2^675013-69831 | 203200 | Stefano Morozzi | 01/2025 |
| 2283 | 2^675014-3897 | 203200 | Stefano Morozzi | 01/2025 |
| 2284 | 2^675006+75357 | 203198 | Stefano Morozzi | 01/2025 |
| 2285 | 2^675008+112231 | 203198 | Stefano Morozzi | 01/2025 |
| 2286 | 2^675007-123309 | 203198 | Stefano Morozzi | 01/2025 |
| 2287 | 2^675003+52529 | 203197 | Stefano Morozzi | 01/2025 |
| 2288 | 2^675002+50595 | 203196 | Stefano Morozzi | 01/2025 |
| 2289 | 2^674627-25161 | 203083 | Enzo Doria | 09/2013 |
| 2290 | 2^674603-69337 | 203076 | Enzo Doria | 12/2015 |
| 2291 | (182*10^203048+1)/3 | 203050 | Robert Price | 09/2023 |
| 2292 | 2^674459+74213 | 203033 | Enzo Doria | 04/2016 |
| 2293 | 2^674116-458879 | 202930 | Enzo Doria | 04/2015 |
| 2294 | 2^674076-114755 | 202918 | Enzo Doria | 04/2015 |
| 2295 | 5^289937-4^289937 | 202658 | Jean-Louis Charton | 03/2013 |
| 2296 | 5^289926-289926^5 | 202650 | Henri Lifchitz | 07/2024 |
| 2297 | (2^673184-7)/3 | 202649 | Stefano Morozzi | 08/2022 |
| 2298 | (467617#+14534)/(2^2*13*43) | 202603 | Makoto Morimoto | 06/2019 |
| 2299 | (155^92479-1)/154 | 202558 | Anonymous | 06/2024 |
| 2300 | 2^672773+219407 | 202525 | Enzo Doria | 03/2024 |
| 2301 | 1374^64531-64531^1374 | 202498 | Henri Lifchitz | 10/2024 |
| 2302 | 2^672556-1835519 | 202460 | Enzo Doria | 04/2015 |
| 2303 | (7*10^202267+179)/3 | 202268 | Robert Price | 02/2023 |
| 2304 | 2^671446-351401 | 202126 | Enzo Doria | 07/2015 |
| 2305 | 2^671373+77747 | 202104 | Enzo Doria | 05/2016 |
| 2306 | (2*10^202059+7)/9 | 202059 | Rytis Slatkevicius | 01/2023 |
| 2307 | 98*10^202021-9 | 202023 | Robert Price | 05/2023 |
| 2308 | 2^670726-114845 | 201909 | Enzo Doria | 05/2015 |
| 2309 | 2^670539-25045 | 201853 | Enzo Doria | 09/2013 |
| 2310 | 10^201801-93 | 201801 | Robert Price | 02/2023 |
| 2311 | 43284^43519-43519^43284 | 201769 | Norbert Schneider | 08/2018 |
| 2312 | 2^670213+282317 | 201755 | Enzo Doria | 09/2016 |
| 2313 | 2^670133+89 | 201731 | Stefano Morozzi | 05/2021 |
| 2314 | 2^669854-113501 | 201647 | Enzo Doria | 08/2014 |
| 2315 | 2^669718+81619 | 201606 | Enzo Doria | 08/2016 |
| 2316 | (299*10^201547-17)/3 | 201549 | Robert Price | 02/2023 |
| 2317 | (145*10^201504-1)/9 | 201506 | Serge Batalov | 12/2014 |
| 2318 | 2^668938-1839821 | 201371 | Enzo Doria | 06/2015 |
| 2319 | (198^87623-1)/197 | 201239 | Anonymous | 06/2024 |
| 2320 | 2^668492+1879303 | 201237 | Enzo Doria | 08/2016 |
| 2321 | 7*10^201140-87 | 201141 | Robert Price | 03/2023 |
| 2322 | 6^258413-5^258413 | 201085 | Jean-Louis Charton | 03/2013 |
| 2323 | 10194^50161-50161^10194 | 201063 | Norbert Schneider | 09/2020 |
| 2324 | 2^667894+1875589 | 201057 | Enzo Doria | 06/2016 |
| 2325 | 2^667569-1836559 | 200959 | Enzo Doria | 05/2015 |
| 2326 | (172*10^200746-1)/9 | 200748 | Serge Batalov | 12/2014 |
| 2327 | (166^90407-1)/165 | 200712 | Anonymous | 06/2024 |
| 2328 | 2^666430+782569 | 200616 | Enzo Doria | 10/2016 |
| 2329 | (13*10^200610-43)/3 | 200611 | Robert Price | 08/2023 |
| 2330 | (8*10^200408-11)/3 | 200409 | Robert Price | 07/2023 |
| 2331 | p(38635)#-p(38635+1) | 200356 | Henri Lifchitz | 11/2024 |
| 2332 | (19*10^200260+101)/3 | 200261 | Robert Price | 06/2023 |
| 2333 | 43183^43183+4^4 | 200167 | Serge Batalov | 04/2024 |
| 2334 | (86^103471+1)/87 | 200163 | Paul Bourdelais | 05/2018 |
| 2335 | (10^(2*100072+1)+36*10^100072-1)/9 | 200145 | Robert Price | 09/2023 |
| 2336 | 2^664778+34789 | 200119 | Enzo Doria | 07/2024 |
| 2337 | 103*(10^100000+20110)^2-4707*(10^100000+20110)+50383 | 200003 | Robert Price | 05/2017 |
| 2338 | 103*(10^100000+33798)^2-4707*(10^100000+33798)+50383 | 200003 | Robert Price | 01/2018 |
| 2339 | numbpart(32235776596) | 200002 | Serge Batalov | 04/2017 |
| 2340 | (10^200001+149)/3 | 200001 | Serge Batalov | 12/2014 |
| 2341 | 10^200000+571791 | 200001 | Patrick De Geest | 08/2019 |
| 2342 | (3^419180-621444)/3 | 200000 | Stefano Morozzi | 06/2019 |
| 2343 | (3^419180-1941384)/3 | 200000 | Stefano Morozzi | 08/2019 |
| 2344 | 10^200000-45557 | 200000 | Patrick De Geest | 08/2019 |
| 2346 | (10^200000-1)/9-10^58838 | 200000 | Akihiko Yoshida | 04/2020 |
| 2345 | 2593604092947240127723272^8192+2593604092947240127722755^8192 | 200000 | Youcef Lemsafer | 01/2023 |
| 2347 | (2593604092947240127723019^8192+2593604092947240127723011^8192)/2 | 199999 | Youcef Lemsafer | 01/2023 |
| 2348 | (2593604092947240127723087^8192+2593604092947240127722984^8192)/147457 | 199994 | Youcef Lemsafer | 01/2023 |
| 2349 | (2593604092947240127723229^8192+2593604092947240127723171^8192)/15032745986 | 199989 | Youcef Lemsafer | 01/2023 |
| 2350 | (2593604092947240127723215^8192+2593604092947240127722938^8192)/12728329863169 | 199986 | Youcef Lemsafer | 01/2023 |
| 2351 | 92*10^199980-9 | 199982 | Robert Price | 12/2021 |
| 2352 | (2593604092947240127723216^8192+2593604092947240127723163^8192)/20172788859482903707649 | 199977 | Youcef Lemsafer | 01/2023 |
| 2353 | (85*10^199951-139)/9 | 199952 | Robert Price | 08/2021 |
| 2354 | (10^199926+7)/29/373/2339 | 199919 | Alfred Reich | 08/2021 |
| 2355 | 2^663838+25819 | 199836 | Enzo Doria | 11/2023 |
| 2356 | 23*10^199833-9 | 199835 | Robert Price | 10/2021 |
| 2357 | fibonacci(956176)-4 | 199829 | Jon Grantham | 08/2023 |
| 2358 | (299*10^199801-17)/3 | 199803 | Robert Price | 04/2020 |
| 2359 | 6*10^199788+77 | 199789 | Robert Price | 06/2020 |
| 2360 | (2^663604+1)/270750449 | 199757 | Anonymous | 10/2024 |
| 2361 | (23*10^199615+37)/3 | 199616 | Robert Price | 02/2022 |
| 2362 | (17*10^199607-167)/3 | 199608 | Robert Price | 05/2022 |
| 2363 | 2^663020-933075 | 199589 | Paul Bourdelais | 06/2021 |
| 2364 | 2^663007+29963 | 199585 | Enzo Doria | 03/2024 |
| 2365 | 3*2^662703-5 | 199494 | Jon Grantham | 07/2023 |
| 2366 | (14*10^199447+73)/3 | 199448 | Robert Price | 12/2018 |
| 2367 | (2^662424-15)/7 | 199409 | Stefano Morozzi | 08/2022 |
| 2368 | 2^662194+22189 | 199341 | Enzo Doria | 09/2023 |
| 2369 | 2^662103-29287 | 199313 | Enzo Doria | 08/2015 |
| 2370 | (2*10^199283+457)/9 | 199283 | Robert Price | 01/2018 |
| 2371 | (10^199248-19)/9 | 199248 | Robert Price | 01/2018 |
| 2372 | (83*10^199213+529)/9 | 199214 | Robert Price | 12/2021 |
| 2373 | (194*10^199146-17)/3 | 199148 | Robert Price | 09/2020 |
| 2374 | (151*10^199003-1)/3 | 199005 | Robert Price | 03/2020 |
| 2375 | 9*10^198946-73 | 198947 | Robert Price | 01/2021 |
| 2376 | 45*10^198931-7 | 198933 | Robert Price | 07/2020 |
| 2377 | 2^660482-2891 | 198825 | Yves Minet | 05/2016 |
| 2378 | 2^659594+37729 | 198558 | Enzo Doria | 10/2024 |
| 2379 | 2^659589-21 | 198557 | Stefano Morozzi | 07/2022 |
| 2380 | 2^659583+1879223 | 198555 | Enzo Doria | 08/2016 |
| 2381 | (53*10^198529+1)/9 | 198530 | Serge Batalov | 07/2010 |
| 2382 | (49*10^198403+311)/9 | 198404 | Robert Price | 06/2019 |
| 2383 | 96*10^198376-7 | 198378 | Robert Price | 03/2021 |
| 2384 | (10^198375+7)/59/1201/87589 | 198366 | Alfred Reich | 08/2021 |
| 2385 | 2^658828-29819 | 198327 | Enzo Doria | 08/2015 |
| 2386 | 2^658776-2791229 | 198312 | Enzo Doria | 01/2016 |
| 2387 | (35*10^198294-377)/9 | 198295 | Robert Price | 07/2018 |
| 2388 | (4*10^198268+137)/3 | 198269 | Robert Price | 03/2018 |
| 2389 | 2^658544-1854029 | 198242 | Enzo Doria | 09/2015 |
| 2390 | (62*10^198229-233)/9 | 198230 | Robert Price | 02/2022 |
| 2391 | (26*10^198200-41)/3 | 198201 | Robert Price | 02/2022 |
| 2392 | (157^90239-1)/156 | 198154 | Alexander Zhirkov | 06/2016 |
| 2393 | 2^657815+26213 | 198023 | Enzo Doria | 12/2023 |
| 2394 | 2*10^197959-37 | 197960 | Robert Price | 11/2021 |
| 2395 | (29*10^197941-41)/3 | 197942 | Tyler Busby | 03/2024 |
| 2396 | (232*10^197897+17)/3 | 197899 | Robert Price | 04/2021 |
| 2397 | (4*10^197778+173)/3 | 197779 | Robert Price | 02/2018 |
| 2398 | 2^656964+6561 | 197766 | Henri Lifchitz | 01/2025 |
| 2399 | 2^656763+211373 | 197706 | Enzo Doria | 08/2023 |
| 2400 | 78*10^197702-7 | 197704 | Robert Price | 10/2020 |
| 2401 | (17*10^197640-23)/3 | 197641 | Robert Price | 03/2021 |
| 2402 | (29*10^197629-77)/3 | 197630 | Robert Price | 02/2020 |
| 2403 | 2^656462+1874419 | 197615 | Enzo Doria | 06/2016 |
| 2404 | (89^101363+1)/90 | 197595 | Paul Bourdelais | 11/2017 |
| 2405 | 2^656172+229051 | 197528 | Enzo Doria | 11/2024 |
| 2406 | 2^655893-344563 | 197444 | Enzo Doria | 07/2015 |
| 2407 | 2^655875+71333 | 197439 | Enzo Doria | 04/2016 |
| 2408 | 2^655845-9 | 197430 | Robert Price | 01/2017 |
| 2409 | (299*10^197426+1)/3 | 197428 | Robert Price | 04/2020 |
| 2410 | 2^655682-1849121 | 197380 | Enzo Doria | 08/2015 |
| 2411 | 4*10^197268-89 | 197269 | Robert Price | 11/2018 |
| 2412 | (11*10^197198-89)/3 | 197199 | Robert Price | 05/2021 |
| 2413 | 2^655045-49603 | 197189 | Enzo Doria | 10/2015 |
| 2414 | 2^655000-2784089 | 197175 | Enzo Doria | 10/2015 |
| 2415 | (18^157051-1)/17 | 197141 | Paul Bourdelais | 03/2010 |
| 2416 | (4*10^197061+41)/9 | 197061 | Serge Batalov | 11/2022 |
| 2417 | (154*10^197005+17)/9 | 197007 | Robert Price | 06/2022 |
| 2418 | 2^654400-39719 | 196995 | Enzo Doria | 09/2015 |
| 2419 | (5^281807-2^281807)/3 | 196975 | Jon Grantham | 08/2023 |
| 2420 | (14*10^196965-221)/9 | 196966 | Robert Price | 04/2018 |
| 2421 | 2^654216-459995 | 196939 | Enzo Doria | 06/2015 |
| 2422 | (17*10^196921+31)/3 | 196922 | Robert Price | 01/2019 |
| 2423 | (14*10^196885-89)/3 | 196886 | Robert Price | 05/2020 |
| 2424 | 3*10^196881-59 | 196882 | Robert Price | 09/2018 |
| 2425 | 2^653851+82295 | 196829 | Enzo Doria | 09/2016 |
| 2426 | (38*10^196792+691)/9 | 196793 | Robert Price | 10/2018 |
| 2427 | (65*10^196768+493)/9 | 196769 | Robert Price | 08/2021 |
| 2429 | 2^653636-29429 | 196765 | Enzo Doria | 08/2015 |
| 2428 | 2^653638-11 | 196765 | Stefano Morozzi | 07/2022 |
| 2430 | 2^653601-69673 | 196754 | Enzo Doria | 02/2016 |
| 2431 | (44*10^196684+1)/9 | 196685 | Serge Batalov | 07/2010 |
| 2432 | 2^652786-1852571 | 196509 | Enzo Doria | 08/2015 |
| 2433 | 2^652752-1325 | 196498 | Yves Minet | 07/2015 |
| 2434 | 2^652470-1859141 | 196414 | Enzo Doria | 10/2015 |
| 2435 | 2^652346+29329 | 196376 | Enzo Doria | 02/2024 |
| 2436 | 2^652307+1877483 | 196364 | Enzo Doria | 08/2016 |
| 2437 | 2^652293-115273 | 196360 | Enzo Doria | 06/2015 |
| 2438 | (47*10^196281+403)/9 | 196282 | Robert Price | 03/2019 |
| 2439 | 2^652025+218027 | 196280 | Enzo Doria | 01/2024 |
| 2440 | 2^652004+23961 | 196273 | Enzo Doria | 10/2023 |
| 2441 | (7*10^196125-31)/3 | 196126 | Robert Price | 12/2021 |
| 2442 | 33^129128+129128^33 | 196083 | Norbert Schneider | 06/2022 |
| 2443 | 6*10^196070+73 | 196071 | Robert Price | 04/2019 |
| 2444 | 2^651218-1868201 | 196037 | Enzo Doria | 04/2016 |
| 2445 | 2^651047-49687 | 195985 | Enzo Doria | 10/2015 |
| 2446 | 10^195968-700001 | 195968 | Robert Price | 08/2021 |
| 2447 | fibonacci(937485)+3 | 195923 | Jon Grantham | 08/2023 |
| 2448 | (29*10^195875-197)/3 | 195876 | Robert Price | 08/2021 |
| 2449 | (25*10^195808-97)/9 | 195809 | Robert Price | 01/2022 |
| 2450 | 2^650285-2785333 | 195756 | Enzo Doria | 10/2015 |
| 2451 | (10^195732+7)/18089/49605893 | 195721 | Alfred Reich | 08/2021 |
| 2452 | (29*10^195648-41)/3 | 195649 | Tyler Busby | 03/2024 |
| 2453 | (69^106397-1)/68 | 195647 | Paul Bourdelais | 10/2017 |
| 2454 | 2^649811+1877573 | 195613 | Enzo Doria | 08/2016 |
| 2455 | 2^649662-170531 | 195568 | Hans Havermann | 10/2018 |
| 2456 | 2^649586+182839 | 195545 | Enzo Doria | 11/2016 |
| 2457 | 2^649537-1867363 | 195531 | Enzo Doria | 04/2016 |
| 2458 | 2^649536-1861499 | 195530 | Enzo Doria | 12/2015 |
| 2459 | 2^649493+25907 | 195517 | Enzo Doria | 11/2023 |
| 2460 | (103*10^195478-1)/3 | 195480 | Serge Batalov | 12/2014 |
| 2461 | 2^649102-59351 | 195400 | Enzo Doria | 10/2015 |
| 2462 | (2*10^195399+529)/9 | 195399 | Robert Price | 01/2018 |
| 2463 | (202*10^195383-13)/9 | 195385 | Robert Price | 01/2020 |
| 2464 | 2^648988+1178971 | 195365 | Enzo Doria | 06/2016 |
| 2465 | 2^648975-114319 | 195361 | Enzo Doria | 02/2015 |
| 2466 | (11*10^195350-137)/9 | 195351 | Robert Price | 01/2018 |
| 2467 | 2^648619-24835 | 195254 | Enzo Doria | 09/2013 |
| 2468 | 5*10^195250-21 | 195251 | Robert Price | 12/2021 |
| 2469 | (14*10^195234-83)/3 | 195235 | Robert Price | 12/2018 |
| 2470 | 5*10^195221+81 | 195222 | Robert Price | 03/2019 |
| 2471 | 10^195143-5001 | 195143 | Robert Price | 12/2021 |
| 2472 | 2^648190-24737 | 195125 | Enzo Doria | 09/2013 |
| 2473 | (57^111119+1)/58 | 195110 | Paul Bourdelais | 10/2017 |
| 2474 | (29*10^195098-197)/3 | 195099 | Robert Price | 08/2021 |
| 2475 | 10^195060+89701 | 195061 | Patrick De Geest | 02/2021 |
| 2477 | 10^195060-40000000001 | 195060 | Robert Price | 09/2020 |
| 2476 | 10^195060-110337 | 195060 | Patrick De Geest | 02/2021 |
| 2478 | 56*10^195032-3 | 195034 | Robert Price | 03/2020 |
| 2479 | 11^187185-90 | 194934 | Enzo Doria | 09/2012 |
| 2480 | 2^647545-25 | 194931 | Boyan Hu | 12/2024 |
| 2481 | 2^647468+220141 | 194908 | Enzo Doria | 03/2024 |
| 2482 | (86*10^194818-437)/9 | 194819 | Robert Price | 03/2021 |
| 2483 | 7^230492-230492^7 | 194789 | Henri Lifchitz | 07/2024 |
| 2484 | 2^647068+77281 | 194787 | Enzo Doria | 05/2016 |
| 2485 | 2*10^194716-93 | 194717 | Robert Price | 12/2021 |
| 2486 | 15^165559-14^165559 | 194713 | Jean-Louis Charton | 03/2011 |
| 2487 | F(931517) | 194676 | Henri Lifchitz | 09/2008 |
| 2488 | 4*10^194668+49 | 194669 | Robert Price | 01/2019 |
| 2489 | 2^646589+1179407 | 194643 | Enzo Doria | 06/2016 |
| 2490 | 2^646289-114621 | 194553 | Enzo Doria | 05/2015 |
| 2491 | 2^646236-39659 | 194537 | Enzo Doria | 09/2015 |
| 2492 | (16*10^194536+53)/3 | 194537 | Robert Price | 03/2019 |
| 2493 | 2^646161-59833 | 194514 | Enzo Doria | 11/2015 |
| 2494 | (17*10^194502+31)/3 | 194503 | Robert Price | 01/2019 |
| 2495 | (19*10^194428+287)/9 | 194429 | Robert Price | 10/2021 |
| 2496 | 2*10^194413+3 | 194414 | Robert Price | 07/2015 |
| 2497 | 2^645360-1848599 | 194273 | Enzo Doria | 08/2015 |
| 2498 | 22470^44641+44641^22470 | 194260 | Norbert Schneider | 08/2023 |
| 2499 | (112*10^194150-1)/3 | 194152 | Serge Batalov | 12/2014 |
| 2500 | Phi(293127,10) | 194041 | Makoto Kamada | 12/2023 |
