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 | 234178^9+9^234178 | 223463 | Anatoly F. Selevich | 07/2011 |
| 2252 | 47747^47747-2512^2512 | 223406 | Henri Lifchitz | 10/2024 |
| 2253 | 2^741651-461197 | 223260 | Enzo Doria | 07/2015 |
| 2254 | 10^223236-1001 | 223236 | Robert Price | 10/2022 |
| 2255 | 2^741362-1845251 | 223173 | Enzo Doria | 07/2015 |
| 2256 | 3^467546-5*2^467546 | 223077 | Jon Grantham | 08/2023 |
| 2257 | 2^740455-1863877 | 222900 | Enzo Doria | 12/2015 |
| 2258 | 2^740274+217519 | 222845 | Enzo Doria | 01/2024 |
| 2259 | (14*10^222718-41)/9 | 222719 | Serge Batalov | 01/2023 |
| 2260 | 2^739636-2792219 | 222653 | Enzo Doria | 02/2016 |
| 2261 | 11^213654-180 | 222498 | Enzo Doria | 01/2013 |
| 2262 | 2^738957-1859743 | 222449 | Enzo Doria | 11/2015 |
| 2263 | 4*10^222253-21 | 222254 | Robert Price | 12/2022 |
| 2264 | 2^737825+57 | 222108 | Stefano Morozzi | 05/2021 |
| 2265 | (54^128189+1)/55 | 222073 | Paul Bourdelais | 11/2018 |
| 2266 | 3^232689+1^232689+4^232689+1^232689+5^232689+9^232689 | 222042 | Henri Lifchitz | 03/2025 |
| 2267 | 2^737166+220099 | 221910 | Enzo Doria | 03/2024 |
| 2268 | 394^85431+393 | 221736 | Alfred Reich | 03/2026 |
| 2269 | (10^221654+179)/9 | 221654 | Serge Batalov | 12/2014 |
| 2270 | 2^736281+79817 | 221643 | Enzo Doria | 06/2016 |
| 2271 | 10^221631+247617 | 221632 | Patrick De Geest | 10/2013 |
| 2272 | 10^221631-9 | 221631 | Alexander Gramolin | 02/2011 |
| 2273 | 10^221628+7 | 221629 | Alfred Reich | 04/2021 |
| 2274 | 2^735970-1839821 | 221550 | Enzo Doria | 06/2015 |
| 2275 | 2^735367+60293 | 221368 | Enzo Doria | 03/2016 |
| 2276 | 77*10^221343+3 | 221345 | Robert Price | 11/2023 |
| 2277 | 299^299^299-582 | 221328 | Henri Lifchitz | 03/2025 |
| 2278 | (241^92821-1)/240 | 221099 | Anonymous | 04/2024 |
| 2279 | (202*10^221092-1)/3 | 221094 | Robert Price | 06/2023 |
| 2280 | (5^316297-1)/220142716 | 221074 | Paul Vanderveen | 05/2025 |
| 2281 | (29^151153+1)/30 | 221045 | Paul Bourdelais | 09/2017 |
| 2282 | 2^734228+24751 | 221025 | Enzo Doria | 10/2023 |
| 2283 | (28*10^220800+173)/3 | 220801 | Robert Price | 07/2024 |
| 2284 | 2^733264-2784089 | 220735 | Enzo Doria | 10/2015 |
| 2285 | 2^733114-24555 | 220690 | Enzo Doria | 09/2013 |
| 2286 | 2^731891-636259 | 220322 | Enzo Doria | 12/2013 |
| 2287 | 98*10^220185-9 | 220187 | Robert Price | 05/2023 |
| 2288 | 418319^39164+418318 | 220161 | Alfred Reich | 11/2023 |
| 2289 | 2^4^182829+182829^4^2 | 220149 | Henri Lifchitz | 03/2025 |
| 2290 | 2^731124-25539 | 220091 | Enzo Doria | 09/2013 |
| 2291 | 2^730972-462029 | 220045 | Enzo Doria | 07/2015 |
| 2292 | 2^730833+1868627 | 220003 | Enzo Doria | 04/2016 |
| 2293 | 2^730645-2787133 | 219947 | Enzo Doria | 11/2015 |
| 2294 | 2^730547-25581 | 219917 | Enzo Doria | 09/2013 |
| 2295 | (113*13^197420-5)/12 | 219916 | Anonymous | 11/2022 |
| 2296 | (13^197420*113-5)/12 | 219916 | Eric Chen | 10/2023 |
| 2297 | 2^730460+82291 | 219891 | Enzo Doria | 09/2016 |
| 2298 | (5*10^219847-101)/3 | 219848 | Robert Price | 08/2023 |
| 2299 | (2^730339+1)/(3*27839062003*7943469324347) | 219831 | Gord Palameta | 12/2018 |
| 2300 | L(1051849) | 219824 | Renaud Lifchitz | 03/2009 |
| 2301 | 3*2^730149+5 | 219798 | Jon Grantham | 07/2023 |
| 2302 | 8*10^219740-3 | 219741 | Serge Batalov | 01/2023 |
| 2303 | 11^210961-240 | 219694 | Enzo Doria | 01/2013 |
| 2304 | (26*10^219639-77)/3 | 219640 | Robert Price | 03/2023 |
| 2305 | 2^729611-113437 | 219635 | Enzo Doria | 08/2014 |
| 2306 | 7^259710-2 | 219481 | Paul Bourdelais | 01/2021 |
| 2307 | F(1049897) | 219416 | Henri Lifchitz | 10/2008 |
| 2308 | (1488^69151-1)/1487 | 219386 | Alexander Zhirkov | 02/2023 |
| 2309 | 2^728604+1879321 | 219332 | Enzo Doria | 10/2016 |
| 2310 | 33^144412+2 | 219292 | Robert Price | 04/2015 |
| 2311 | 2^728277-183313 | 219234 | Hans Havermann | 10/2018 |
| 2312 | 2^727998-1862711 | 219150 | Enzo Doria | 12/2015 |
| 2313 | (29*10^219124+91)/3 | 219125 | Robert Price | 12/2022 |
| 2314 | 2^727729-114073 | 219069 | Enzo Doria | 12/2014 |
| 2315 | 2^727496-1851809 | 218999 | Enzo Doria | 08/2015 |
| 2316 | 2^727025+25907 | 218857 | Enzo Doria | 12/2023 |
| 2317 | 2^726591+2793143 | 218726 | Enzo Doria | 02/2016 |
| 2318 | (7*10^218644+17)/3 | 218645 | Robert Price | 06/2023 |
| 2319 | 2^725534-2791931 | 218408 | Enzo Doria | 02/2016 |
| 2320 | Phi(220531,10)/2686456812680882641 | 217774 | Makoto Kamada | 10/2020 |
| 2321 | 2^722184+1877821 | 217400 | Enzo Doria | 08/2016 |
| 2322 | (109*10^217360-1)/9 | 217362 | Serge Batalov | 12/2014 |
| 2323 | 2^721721-4453 | 217260 | Yves Minet | 03/2021 |
| 2324 | 10^216950+49 | 216951 | Robert Price | 02/2023 |
| 2325 | 281*499979#/46410-2702372 | 216849 | Robert Smith | 08/2016 |
| 2326 | 281*499979#/46410+2400766 | 216849 | Robert Smith | 08/2016 |
| 2327 | Phi(83733,-13#) | 216643 | Henri Lifchitz | 02/2026 |
| 2328 | tau(311^15786) | 216429 | Nik Lygeros / Olivier Rozier / LR team | 10/2013 |
| 2329 | 2^718756-114107 | 216368 | Enzo Doria | 12/2014 |
| 2330 | 2^717672+121 | 216041 | Stefano Morozzi | 05/2021 |
| 2331 | 2^717305+80327 | 215931 | Enzo Doria | 07/2016 |
| 2332 | Phi(358640,2^5) | 215875 | Henri Lifchitz | 12/2025 |
| 2333 | 2^717069-59773 | 215860 | Enzo Doria | 10/2015 |
| 2334 | 10^215802+33 | 215803 | Robert Price | 08/2023 |
| 2335 | 30^146021-29^146021 | 215691 | Jean-Louis Charton | 09/2018 |
| 2336 | 277^88301-276^88301 | 215674 | Jean-Louis Charton | 06/2012 |
| 2337 | 2^716428+215011 | 215667 | Enzo Doria | 11/2023 |
| 2338 | (13*10^215592-43)/3 | 215593 | Robert Price | 08/2023 |
| 2339 | p(41292)#+p(41292+1) | 215450 | Henri Lifchitz | 11/2024 |
| 2340 | (29^147319-1)/466757843690852 | 215425 | Paul Vanderveen | 06/2025 |
| 2341 | 227^91413-40 | 215372 | Enzo Doria | 04/2015 |
| 2342 | (2^715008-21)/5 | 215239 | Stefano Morozzi | 08/2022 |
| 2343 | 2^714717+782897 | 215152 | Enzo Doria | 11/2016 |
| 2344 | (19^168013-1)/80910356454 | 214837 | Paul Vanderveen | 05/2025 |
| 2345 | tau(373^15186) | 214796 | Nik Lygeros / Olivier Rozier / LR team | 10/2013 |
| 2346 | 2^713241+1879157 | 214707 | Enzo Doria | 08/2016 |
| 2347 | (23*10^214633+91)/3 | 214634 | Robert Price | 03/2023 |
| 2348 | 11^206081-10^206081 | 214612 | Jean-Louis Charton | 10/2011 |
| 2349 | 2^712801-69553 | 214575 | Enzo Doria | 01/2016 |
| 2350 | 2^712603-25357 | 214515 | Enzo Doria | 09/2013 |
| 2351 | 2^711721-1846723 | 214250 | Enzo Doria | 07/2015 |
| 2352 | 999^71336+998 | 213978 | Alfred Reich | 04/2026 |
| 2353 | 2^710730-396765 | 213952 | Enzo Doria | 09/2013 |
| 2354 | (19*10^213934-37)/9 | 213935 | Alfred Reich | 12/2023 |
| 2355 | (19*10^213730-37)/9 | 213731 | Alfred Reich | 12/2023 |
| 2356 | (713^74897-1)/712 | 213685 | Jinyuan Wang | 08/2023 |
| 2357 | 2^709773+25907 | 213663 | Enzo Doria | 12/2023 |
| 2358 | 2^708468-114329 | 213271 | Enzo Doria | 02/2015 |
| 2359 | 2^708293+27557 | 213218 | Enzo Doria | 01/2024 |
| 2360 | 379*10^213199+9 | 213202 | Jason Yuen | 01/2025 |
| 2361 | 2^707277+28997 | 212912 | Enzo Doria | 02/2024 |
| 2362 | (163*10^212779-1)/9 | 212781 | Serge Batalov | 12/2014 |
| 2363 | 2^706838-69041 | 212780 | Enzo Doria | 11/2015 |
| 2364 | 2^705653+25907 | 212423 | Enzo Doria | 12/2023 |
| 2365 | 22*10^212339+7 | 212341 | Robert Price | 10/2022 |
| 2366 | 2^704577-113871 | 212099 | Enzo Doria | 10/2014 |
| 2367 | (2^704548-19)/3 | 212090 | Stefano Morozzi | 08/2022 |
| 2368 | 2^704110-2792441 | 211959 | Enzo Doria | 02/2016 |
| 2369 | 2^704084+28531 | 211951 | Enzo Doria | 02/2024 |
| 2370 | 2^703943-1862947 | 211908 | Enzo Doria | 12/2015 |
| 2371 | (60^119083+1)/61 | 211746 | Paul Bourdelais | 10/2018 |
| 2372 | 163^95704-162 | 211716 | Norbert Schneider | 02/2026 |
| 2373 | (184*10^211682-1)/3 | 211684 | Robert Price | 12/2022 |
| 2374 | (10^211610-91)/9 | 211610 | Serge Batalov | 12/2014 |
| 2375 | 227^89797+2 | 211565 | Lelio R Paula | 08/2012 |
| 2376 | 2^702194-3 | 211382 | Paul Bourdelais | 03/2012 |
| 2377 | 2^702064+1874911 | 211343 | Enzo Doria | 07/2016 |
| 2378 | 2^701968-113873 | 211314 | Enzo Doria | 10/2014 |
| 2379 | (14*10^211262-41)/9 | 211263 | Serge Batalov | 01/2023 |
| 2380 | 2^701713-113779 | 211237 | Enzo Doria | 09/2014 |
| 2381 | 2^701616-216803 | 211208 | Enzo Doria | 01/2024 |
| 2382 | 2^701449-25201 | 211158 | Enzo Doria | 09/2013 |
| 2383 | 2^701403-2786977 | 211144 | Enzo Doria | 11/2015 |
| 2384 | 2^701189-25423 | 211079 | Enzo Doria | 09/2013 |
| 2385 | 2^701162-459161 | 211071 | Enzo Doria | 05/2015 |
| 2386 | 2^700793+219407 | 210960 | Enzo Doria | 03/2024 |
| 2387 | (24^152783-1)/23 | 210872 | Paul Bourdelais | 04/2018 |
| 2388 | 2^700400+9385 | 210842 | Lelio R Paula | 01/2014 |
| 2389 | 2^700304-17 | 210813 | Stefano Morozzi | 07/2022 |
| 2390 | 2^700131+1874693 | 210761 | Enzo Doria | 06/2016 |
| 2391 | (2^700095+225414)/2 | 210750 | Stefano Morozzi | 04/2020 |
| 2392 | (2^700090+278254)/2 | 210748 | Stefano Morozzi | 04/2020 |
| 2393 | (2^700075+303666)/2 | 210744 | Stefano Morozzi | 04/2020 |
| 2394 | (2^700073+75882)/2 | 210743 | Stefano Morozzi | 04/2020 |
| 2395 | (2^700074+328890)/2 | 210743 | Stefano Morozzi | 04/2020 |
| 2396 | (2^700052+79162)/2 | 210737 | Stefano Morozzi | 04/2020 |
| 2397 | (2^700052+304458)/2 | 210737 | Stefano Morozzi | 04/2020 |
| 2398 | (2^700048+376578)/2 | 210736 | Stefano Morozzi | 04/2020 |
| 2399 | 11^202357-1140 | 210734 | Enzo Doria | 12/2012 |
| 2400 | (2^700021+25874)/2 | 210728 | Stefano Morozzi | 04/2020 |
| 2401 | (2^700018+377518)/2 | 210727 | Stefano Morozzi | 04/2020 |
| 2402 | 2^699999+300729 | 210721 | Norman Luhn | 09/2023 |
| 2403 | (238*10^210712-1)/3 | 210714 | Robert Price | 09/2023 |
| 2404 | 2^699740+25 | 210643 | Stefano Morozzi | 05/2021 |
| 2405 | (23*10^210525-143)/3 | 210526 | Robert Price | 12/2023 |
| 2406 | 2^698929-2788423 | 210399 | Enzo Doria | 11/2015 |
| 2407 | (5^300893+4^300893)/9 | 210315 | Jean-Louis Charton | 11/2011 |
| 2408 | 2^698316+1878601 | 210215 | Enzo Doria | 08/2016 |
| 2409 | 34*10^210097-9 | 210099 | Robert Price | 05/2023 |
| 2410 | (19*10^210011-49)/3 | 210012 | Robert Price | 06/2023 |
| 2411 | 6*10^209846-91 | 209847 | Robert Price | 05/2023 |
| 2412 | 2^697036+1878751 | 209829 | Enzo Doria | 08/2016 |
| 2413 | 2^696813+28607 | 209762 | Enzo Doria | 02/2024 |
| 2414 | (238*10^209715-1)/3 | 209717 | Robert Price | 09/2023 |
| 2415 | 6^269407+5 | 209640 | Paul Bourdelais | 02/2021 |
| 2416 | (2^696343-1)/11141489/36009913139329 | 209600 | Tony Prest / Never Odd Or Even | 02/2014 |
| 2417 | 2^696254-115151 | 209594 | Enzo Doria | 06/2015 |
| 2418 | 2^695841+225 | 209470 | Henri Lifchitz | 01/2025 |
| 2419 | (35^135623+1)/36 | 209410 | Paul Bourdelais | 07/2018 |
| 2420 | 7*10^209161+39 | 209162 | Robert Price | 01/2023 |
| 2421 | 2^694633+1887257 | 209106 | Enzo Doria | 05/2017 |
| 2422 | fibonacci(999790)-4 | 208944 | Jon Grantham | 08/2023 |
| 2423 | 2^693959+180923 | 208903 | Enzo Doria | 07/2016 |
| 2424 | (2^693747-11)/3 | 208839 | Stefano Morozzi | 08/2022 |
| 2425 | 2^693462-1847561 | 208753 | Enzo Doria | 07/2015 |
| 2426 | 2^690890-59981 | 207979 | Enzo Doria | 11/2015 |
| 2427 | (38^131591+1)/39 | 207884 | Paul Bourdelais | 07/2018 |
| 2428 | 3*2^690484+5 | 207857 | Jon Grantham | 07/2023 |
| 2429 | 2^690163+1877063 | 207760 | Enzo Doria | 07/2016 |
| 2430 | Phi(64773,-64773) | 207680 | Henri Lifchitz | 06/2025 |
| 2431 | 7^245608-2 | 207563 | Paul Bourdelais | 01/2021 |
| 2432 | (67*10^207556+23)/9 | 207557 | Serge Batalov | 01/2023 |
| 2433 | 2^689286-29381 | 207496 | Enzo Doria | 08/2015 |
| 2434 | 2^689122-114521 | 207447 | Enzo Doria | 04/2015 |
| 2435 | 9*10^207254-89 | 207255 | Robert Price | 02/2023 |
| 2436 | 2^688373+6077 | 207221 | Enzo Doria | 02/2016 |
| 2437 | 2^688201+1875527 | 207170 | Enzo Doria | 07/2016 |
| 2438 | (42^127609+1)/43 | 207140 | Paul Bourdelais | 07/2018 |
| 2439 | 2^687938+213589 | 207090 | Enzo Doria | 10/2023 |
| 2440 | 2^687619+81563 | 206994 | Enzo Doria | 08/2016 |
| 2441 | 3*10^206927+37 | 206928 | Robert Price | 08/2023 |
| 2442 | 2^687383+21803 | 206923 | Enzo Doria | 09/2023 |
| 2443 | (11*10^206688+19)/3 | 206689 | Robert Price | 07/2024 |
| 2444 | 2^686572-1845299 | 206679 | Enzo Doria | 07/2015 |
| 2445 | (21^156217-1)/20 | 206552 | Paul Bourdelais | 04/2010 |
| 2446 | 2^685970+39415 | 206498 | Enzo Doria | 11/2024 |
| 2447 | (2^685739+1)/(3*87774593) | 206420 | Gord Palameta | 08/2018 |
| 2448 | 2^685578+3 | 206380 | Paul Bourdelais | 04/2012 |
| 2449 | 2^685078+218599 | 206230 | Enzo Doria | 01/2024 |
| 2450 | 2^684836-49349 | 206157 | Enzo Doria | 10/2015 |
| 2451 | (73^110603-1)/72 | 206088 | Paul Bourdelais | 06/2018 |
| 2452 | 2^684163-2790967 | 205954 | Enzo Doria | 12/2015 |
| 2453 | 326^81943-325^81943 | 205941 | Jean-Louis Charton | 07/2012 |
| 2454 | (2^684127-1)/23765203727 | 205933 | Jens K. Andersen | 04/2009 |
| 2455 | (68*10^205510+13)/9 | 205511 | Serge Batalov | 01/2023 |
| 2456 | 4^341233-3^341233 | 205443 | Jean-Louis Charton | 01/2006 |
| 2457 | 2^682414+215029 | 205428 | Enzo Doria | 11/2023 |
| 2458 | (963^68821-1)/962 | 205334 | Jinyuan Wang | 01/2024 |
| 2459 | (43*10^205183-421)/9 | 205184 | Robert Price | 10/2023 |
| 2460 | 2^681545+467 | 205166 | Lelio R Paula | 11/2013 |
| 2461 | 2^681306+81049 | 205094 | Enzo Doria | 07/2016 |
| 2462 | 2^680697+1877057 | 204911 | Enzo Doria | 07/2016 |
| 2463 | 2^680415+71783 | 204826 | Enzo Doria | 04/2016 |
| 2464 | 10^204764-8001 | 204764 | Robert Price | 03/2023 |
| 2465 | (26*10^204730-77)/3 | 204731 | Robert Price | 03/2023 |
| 2466 | 2^679860-459995 | 204659 | Enzo Doria | 06/2015 |
| 2467 | 2^679593+1879547 | 204578 | Enzo Doria | 09/2016 |
| 2468 | 2^678899+220073 | 204369 | Enzo Doria | 03/2024 |
| 2469 | 2^678753+21677 | 204326 | Enzo Doria | 08/2023 |
| 2470 | 2^678651+1875023 | 204295 | Enzo Doria | 07/2016 |
| 2471 | 2^678561+678561 | 204268 | Henri Lifchitz | 05/2006 |
| 2472 | 5*3^427884+2^427884 | 204154 | Jon Grantham | 08/2023 |
| 2473 | 2^678101-114043 | 204129 | Enzo Doria | 11/2014 |
| 2474 | 2^678028+1875631 | 204107 | Enzo Doria | 06/2016 |
| 2475 | 2^677721+28607 | 204015 | Enzo Doria | 01/2024 |
| 2476 | (19*10^203798-7)/3 | 203799 | Robert Price | 12/2023 |
| 2477 | 2^676992-59783 | 203795 | Enzo Doria | 10/2015 |
| 2478 | 2^676972+1866871 | 203789 | Enzo Doria | 03/2016 |
| 2479 | 2^676815+22583 | 203742 | Enzo Doria | 09/2023 |
| 2480 | 2^676761-9 | 203726 | Robert Price | 01/2017 |
| 2481 | 2^676592-23 | 203675 | Stefano Morozzi | 07/2022 |
| 2482 | 2^676563-2792407 | 203666 | Enzo Doria | 02/2016 |
| 2483 | 2^676306-114713 | 203589 | Enzo Doria | 04/2015 |
| 2484 | (2^675977-1)/(1686378749257*7171117283326998925471) | 203456 | Dario Alpern | 07/2015 |
| 2485 | 6*10^203365+53 | 203366 | Robert Price | 09/2023 |
| 2486 | 2^675433-118231 | 203326 | Stefano Morozzi | 09/2025 |
| 2487 | 2^675433-138811 | 203326 | Stefano Morozzi | 09/2025 |
| 2488 | 2^675430-133685 | 203325 | Stefano Morozzi | 09/2025 |
| 2489 | 2^675430-29937 | 203325 | Stefano Morozzi | 09/2025 |
| 2490 | 2^675430-57281 | 203325 | Stefano Morozzi | 09/2025 |
| 2491 | 2^675422-99827 | 203323 | Stefano Morozzi | 09/2025 |
| 2492 | 2^675424-130715 | 203323 | Stefano Morozzi | 09/2025 |
| 2493 | 2^675420-36699 | 203322 | Stefano Morozzi | 09/2025 |
| 2494 | 2^675421-65269 | 203322 | Stefano Morozzi | 09/2025 |
| 2495 | 2^675417-43003 | 203321 | Stefano Morozzi | 09/2025 |
| 2496 | 2^675412-151665 | 203320 | Stefano Morozzi | 09/2025 |
| 2497 | 2^675413-124789 | 203320 | Stefano Morozzi | 09/2025 |
| 2498 | 2^675413-186285 | 203320 | Stefano Morozzi | 09/2025 |
| 2499 | 2^675409-163929 | 203319 | Stefano Morozzi | 09/2025 |
| 2500 | 2^675409-5841 | 203319 | Stefano Morozzi | 09/2025 |
