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 | (7*10^218644+17)/3 | 218645 | Robert Price | 06/2023 |
| 2252 | 2^725534-2791931 | 218408 | Enzo Doria | 02/2016 |
| 2253 | Phi(220531,10)/2686456812680882641 | 217774 | Makoto Kamada | 10/2020 |
| 2254 | 2^722184+1877821 | 217400 | Enzo Doria | 08/2016 |
| 2255 | (109*10^217360-1)/9 | 217362 | Serge Batalov | 12/2014 |
| 2256 | 2^721721-4453 | 217260 | Yves Minet | 03/2021 |
| 2257 | 10^216950+49 | 216951 | Robert Price | 02/2023 |
| 2258 | 281*499979#/46410-2702372 | 216849 | Robert Smith | 08/2016 |
| 2259 | 281*499979#/46410+2400766 | 216849 | Robert Smith | 08/2016 |
| 2260 | Phi(83733,-13#) | 216643 | Henri Lifchitz | 02/2026 |
| 2261 | tau(311^15786) | 216429 | Nik Lygeros / Olivier Rozier / LR team | 10/2013 |
| 2262 | 2^718756-114107 | 216368 | Enzo Doria | 12/2014 |
| 2263 | 2^717672+121 | 216041 | Stefano Morozzi | 05/2021 |
| 2264 | 2^717305+80327 | 215931 | Enzo Doria | 07/2016 |
| 2265 | Phi(358640,2^5) | 215875 | Henri Lifchitz | 12/2025 |
| 2266 | 2^717069-59773 | 215860 | Enzo Doria | 10/2015 |
| 2267 | 10^215802+33 | 215803 | Robert Price | 08/2023 |
| 2268 | 30^146021-29^146021 | 215691 | Jean-Louis Charton | 09/2018 |
| 2269 | 277^88301-276^88301 | 215674 | Jean-Louis Charton | 06/2012 |
| 2270 | 2^716428+215011 | 215667 | Enzo Doria | 11/2023 |
| 2271 | (13*10^215592-43)/3 | 215593 | Robert Price | 08/2023 |
| 2272 | p(41292)#+p(41292+1) | 215450 | Henri Lifchitz | 11/2024 |
| 2273 | (29^147319-1)/466757843690852 | 215425 | Paul Vanderveen | 06/2025 |
| 2274 | 227^91413-40 | 215372 | Enzo Doria | 04/2015 |
| 2275 | (2^715008-21)/5 | 215239 | Stefano Morozzi | 08/2022 |
| 2276 | 2^714717+782897 | 215152 | Enzo Doria | 11/2016 |
| 2277 | (19^168013-1)/80910356454 | 214837 | Paul Vanderveen | 05/2025 |
| 2278 | tau(373^15186) | 214796 | Nik Lygeros / Olivier Rozier / LR team | 10/2013 |
| 2279 | 2^713241+1879157 | 214707 | Enzo Doria | 08/2016 |
| 2280 | (23*10^214633+91)/3 | 214634 | Robert Price | 03/2023 |
| 2281 | 11^206081-10^206081 | 214612 | Jean-Louis Charton | 10/2011 |
| 2282 | 2^712801-69553 | 214575 | Enzo Doria | 01/2016 |
| 2283 | 2^712603-25357 | 214515 | Enzo Doria | 09/2013 |
| 2284 | 2^711721-1846723 | 214250 | Enzo Doria | 07/2015 |
| 2285 | 2^710730-396765 | 213952 | Enzo Doria | 09/2013 |
| 2286 | (19*10^213934-37)/9 | 213935 | Alfred Reich | 12/2023 |
| 2287 | (19*10^213730-37)/9 | 213731 | Alfred Reich | 12/2023 |
| 2288 | (713^74897-1)/712 | 213685 | Jinyuan Wang | 08/2023 |
| 2289 | 2^709773+25907 | 213663 | Enzo Doria | 12/2023 |
| 2290 | 2^708468-114329 | 213271 | Enzo Doria | 02/2015 |
| 2291 | 2^708293+27557 | 213218 | Enzo Doria | 01/2024 |
| 2292 | 379*10^213199+9 | 213202 | Jason Yuen | 01/2025 |
| 2293 | 2^707277+28997 | 212912 | Enzo Doria | 02/2024 |
| 2294 | (163*10^212779-1)/9 | 212781 | Serge Batalov | 12/2014 |
| 2295 | 2^706838-69041 | 212780 | Enzo Doria | 11/2015 |
| 2296 | 2^705653+25907 | 212423 | Enzo Doria | 12/2023 |
| 2297 | 22*10^212339+7 | 212341 | Robert Price | 10/2022 |
| 2298 | 2^704577-113871 | 212099 | Enzo Doria | 10/2014 |
| 2299 | (2^704548-19)/3 | 212090 | Stefano Morozzi | 08/2022 |
| 2300 | 2^704110-2792441 | 211959 | Enzo Doria | 02/2016 |
| 2301 | 2^704084+28531 | 211951 | Enzo Doria | 02/2024 |
| 2302 | 2^703943-1862947 | 211908 | Enzo Doria | 12/2015 |
| 2303 | (60^119083+1)/61 | 211746 | Paul Bourdelais | 10/2018 |
| 2304 | (184*10^211682-1)/3 | 211684 | Robert Price | 12/2022 |
| 2305 | (10^211610-91)/9 | 211610 | Serge Batalov | 12/2014 |
| 2306 | 227^89797+2 | 211565 | Lelio R Paula | 08/2012 |
| 2307 | 2^702194-3 | 211382 | Paul Bourdelais | 03/2012 |
| 2308 | 2^702064+1874911 | 211343 | Enzo Doria | 07/2016 |
| 2309 | 2^701968-113873 | 211314 | Enzo Doria | 10/2014 |
| 2310 | (14*10^211262-41)/9 | 211263 | Serge Batalov | 01/2023 |
| 2311 | 2^701713-113779 | 211237 | Enzo Doria | 09/2014 |
| 2312 | 2^701616-216803 | 211208 | Enzo Doria | 01/2024 |
| 2313 | 2^701449-25201 | 211158 | Enzo Doria | 09/2013 |
| 2314 | 2^701403-2786977 | 211144 | Enzo Doria | 11/2015 |
| 2315 | 2^701189-25423 | 211079 | Enzo Doria | 09/2013 |
| 2316 | 2^701162-459161 | 211071 | Enzo Doria | 05/2015 |
| 2317 | 2^700793+219407 | 210960 | Enzo Doria | 03/2024 |
| 2318 | (24^152783-1)/23 | 210872 | Paul Bourdelais | 04/2018 |
| 2319 | 2^700400+9385 | 210842 | Lelio R Paula | 01/2014 |
| 2320 | 2^700304-17 | 210813 | Stefano Morozzi | 07/2022 |
| 2321 | 2^700131+1874693 | 210761 | Enzo Doria | 06/2016 |
| 2322 | (2^700095+225414)/2 | 210750 | Stefano Morozzi | 04/2020 |
| 2323 | (2^700090+278254)/2 | 210748 | Stefano Morozzi | 04/2020 |
| 2324 | (2^700075+303666)/2 | 210744 | Stefano Morozzi | 04/2020 |
| 2325 | (2^700073+75882)/2 | 210743 | Stefano Morozzi | 04/2020 |
| 2326 | (2^700074+328890)/2 | 210743 | Stefano Morozzi | 04/2020 |
| 2327 | (2^700052+79162)/2 | 210737 | Stefano Morozzi | 04/2020 |
| 2328 | (2^700052+304458)/2 | 210737 | Stefano Morozzi | 04/2020 |
| 2329 | (2^700048+376578)/2 | 210736 | Stefano Morozzi | 04/2020 |
| 2330 | 11^202357-1140 | 210734 | Enzo Doria | 12/2012 |
| 2331 | (2^700021+25874)/2 | 210728 | Stefano Morozzi | 04/2020 |
| 2332 | (2^700018+377518)/2 | 210727 | Stefano Morozzi | 04/2020 |
| 2333 | 2^699999+300729 | 210721 | Norman Luhn | 09/2023 |
| 2334 | (238*10^210712-1)/3 | 210714 | Robert Price | 09/2023 |
| 2335 | 2^699740+25 | 210643 | Stefano Morozzi | 05/2021 |
| 2336 | (23*10^210525-143)/3 | 210526 | Robert Price | 12/2023 |
| 2337 | 2^698929-2788423 | 210399 | Enzo Doria | 11/2015 |
| 2338 | (5^300893+4^300893)/9 | 210315 | Jean-Louis Charton | 11/2011 |
| 2339 | 2^698316+1878601 | 210215 | Enzo Doria | 08/2016 |
| 2340 | 34*10^210097-9 | 210099 | Robert Price | 05/2023 |
| 2341 | (19*10^210011-49)/3 | 210012 | Robert Price | 06/2023 |
| 2342 | 6*10^209846-91 | 209847 | Robert Price | 05/2023 |
| 2343 | 2^697036+1878751 | 209829 | Enzo Doria | 08/2016 |
| 2344 | 2^696813+28607 | 209762 | Enzo Doria | 02/2024 |
| 2345 | (238*10^209715-1)/3 | 209717 | Robert Price | 09/2023 |
| 2346 | 6^269407+5 | 209640 | Paul Bourdelais | 02/2021 |
| 2347 | (2^696343-1)/11141489/36009913139329 | 209600 | Tony Prest / Never Odd Or Even | 02/2014 |
| 2348 | 2^696254-115151 | 209594 | Enzo Doria | 06/2015 |
| 2349 | 2^695841+225 | 209470 | Henri Lifchitz | 01/2025 |
| 2350 | (35^135623+1)/36 | 209410 | Paul Bourdelais | 07/2018 |
| 2351 | 7*10^209161+39 | 209162 | Robert Price | 01/2023 |
| 2352 | 2^694633+1887257 | 209106 | Enzo Doria | 05/2017 |
| 2353 | fibonacci(999790)-4 | 208944 | Jon Grantham | 08/2023 |
| 2354 | 2^693959+180923 | 208903 | Enzo Doria | 07/2016 |
| 2355 | (2^693747-11)/3 | 208839 | Stefano Morozzi | 08/2022 |
| 2356 | 2^693462-1847561 | 208753 | Enzo Doria | 07/2015 |
| 2357 | 2^690890-59981 | 207979 | Enzo Doria | 11/2015 |
| 2358 | (38^131591+1)/39 | 207884 | Paul Bourdelais | 07/2018 |
| 2359 | 3*2^690484+5 | 207857 | Jon Grantham | 07/2023 |
| 2360 | 2^690163+1877063 | 207760 | Enzo Doria | 07/2016 |
| 2361 | Phi(64773,-64773) | 207680 | Henri Lifchitz | 06/2025 |
| 2362 | 7^245608-2 | 207563 | Paul Bourdelais | 01/2021 |
| 2363 | (67*10^207556+23)/9 | 207557 | Serge Batalov | 01/2023 |
| 2364 | 2^689286-29381 | 207496 | Enzo Doria | 08/2015 |
| 2365 | 2^689122-114521 | 207447 | Enzo Doria | 04/2015 |
| 2366 | 9*10^207254-89 | 207255 | Robert Price | 02/2023 |
| 2367 | 2^688373+6077 | 207221 | Enzo Doria | 02/2016 |
| 2368 | 2^688201+1875527 | 207170 | Enzo Doria | 07/2016 |
| 2369 | (42^127609+1)/43 | 207140 | Paul Bourdelais | 07/2018 |
| 2370 | 2^687938+213589 | 207090 | Enzo Doria | 10/2023 |
| 2371 | 2^687619+81563 | 206994 | Enzo Doria | 08/2016 |
| 2372 | 3*10^206927+37 | 206928 | Robert Price | 08/2023 |
| 2373 | 2^687383+21803 | 206923 | Enzo Doria | 09/2023 |
| 2374 | (11*10^206688+19)/3 | 206689 | Robert Price | 07/2024 |
| 2375 | 2^686572-1845299 | 206679 | Enzo Doria | 07/2015 |
| 2376 | (21^156217-1)/20 | 206552 | Paul Bourdelais | 04/2010 |
| 2377 | 2^685970+39415 | 206498 | Enzo Doria | 11/2024 |
| 2378 | (2^685739+1)/(3*87774593) | 206420 | Gord Palameta | 08/2018 |
| 2379 | 2^685578+3 | 206380 | Paul Bourdelais | 04/2012 |
| 2380 | 2^685078+218599 | 206230 | Enzo Doria | 01/2024 |
| 2381 | 2^684836-49349 | 206157 | Enzo Doria | 10/2015 |
| 2382 | (73^110603-1)/72 | 206088 | Paul Bourdelais | 06/2018 |
| 2383 | 2^684163-2790967 | 205954 | Enzo Doria | 12/2015 |
| 2384 | 326^81943-325^81943 | 205941 | Jean-Louis Charton | 07/2012 |
| 2385 | (2^684127-1)/23765203727 | 205933 | Jens K. Andersen | 04/2009 |
| 2386 | (68*10^205510+13)/9 | 205511 | Serge Batalov | 01/2023 |
| 2387 | 4^341233-3^341233 | 205443 | Jean-Louis Charton | 01/2006 |
| 2388 | 2^682414+215029 | 205428 | Enzo Doria | 11/2023 |
| 2389 | (963^68821-1)/962 | 205334 | Jinyuan Wang | 01/2024 |
| 2390 | (43*10^205183-421)/9 | 205184 | Robert Price | 10/2023 |
| 2391 | 2^681545+467 | 205166 | Lelio R Paula | 11/2013 |
| 2392 | 2^681306+81049 | 205094 | Enzo Doria | 07/2016 |
| 2393 | 2^680697+1877057 | 204911 | Enzo Doria | 07/2016 |
| 2394 | 2^680415+71783 | 204826 | Enzo Doria | 04/2016 |
| 2395 | 10^204764-8001 | 204764 | Robert Price | 03/2023 |
| 2396 | (26*10^204730-77)/3 | 204731 | Robert Price | 03/2023 |
| 2397 | 2^679860-459995 | 204659 | Enzo Doria | 06/2015 |
| 2398 | 2^679593+1879547 | 204578 | Enzo Doria | 09/2016 |
| 2399 | 2^678899+220073 | 204369 | Enzo Doria | 03/2024 |
| 2400 | 2^678753+21677 | 204326 | Enzo Doria | 08/2023 |
| 2401 | 2^678651+1875023 | 204295 | Enzo Doria | 07/2016 |
| 2402 | 2^678561+678561 | 204268 | Henri Lifchitz | 05/2006 |
| 2403 | 5*3^427884+2^427884 | 204154 | Jon Grantham | 08/2023 |
| 2404 | 2^678101-114043 | 204129 | Enzo Doria | 11/2014 |
| 2405 | 2^678028+1875631 | 204107 | Enzo Doria | 06/2016 |
| 2406 | 2^677721+28607 | 204015 | Enzo Doria | 01/2024 |
| 2407 | (19*10^203798-7)/3 | 203799 | Robert Price | 12/2023 |
| 2408 | 2^676992-59783 | 203795 | Enzo Doria | 10/2015 |
| 2409 | 2^676972+1866871 | 203789 | Enzo Doria | 03/2016 |
| 2410 | 2^676815+22583 | 203742 | Enzo Doria | 09/2023 |
| 2411 | 2^676761-9 | 203726 | Robert Price | 01/2017 |
| 2412 | 2^676592-23 | 203675 | Stefano Morozzi | 07/2022 |
| 2413 | 2^676563-2792407 | 203666 | Enzo Doria | 02/2016 |
| 2414 | 2^676306-114713 | 203589 | Enzo Doria | 04/2015 |
| 2415 | (2^675977-1)/(1686378749257*7171117283326998925471) | 203456 | Dario Alpern | 07/2015 |
| 2416 | 6*10^203365+53 | 203366 | Robert Price | 09/2023 |
| 2417 | 2^675433-118231 | 203326 | Stefano Morozzi | 09/2025 |
| 2418 | 2^675433-138811 | 203326 | Stefano Morozzi | 09/2025 |
| 2419 | 2^675430-133685 | 203325 | Stefano Morozzi | 09/2025 |
| 2420 | 2^675430-29937 | 203325 | Stefano Morozzi | 09/2025 |
| 2421 | 2^675430-57281 | 203325 | Stefano Morozzi | 09/2025 |
| 2422 | 2^675422-99827 | 203323 | Stefano Morozzi | 09/2025 |
| 2423 | 2^675424-130715 | 203323 | Stefano Morozzi | 09/2025 |
| 2424 | 2^675420-36699 | 203322 | Stefano Morozzi | 09/2025 |
| 2425 | 2^675421-65269 | 203322 | Stefano Morozzi | 09/2025 |
| 2426 | 2^675417-43003 | 203321 | Stefano Morozzi | 09/2025 |
| 2427 | 2^675412-151665 | 203320 | Stefano Morozzi | 09/2025 |
| 2428 | 2^675413-124789 | 203320 | Stefano Morozzi | 09/2025 |
| 2429 | 2^675413-186285 | 203320 | Stefano Morozzi | 09/2025 |
| 2430 | 2^675409-163929 | 203319 | Stefano Morozzi | 09/2025 |
| 2431 | 2^675409-5841 | 203319 | Stefano Morozzi | 09/2025 |
| 2432 | 2^675411-100471 | 203319 | Stefano Morozzi | 09/2025 |
| 2433 | 2^675411-13075 | 203319 | Stefano Morozzi | 09/2025 |
| 2434 | 2^675406-8877 | 203318 | Stefano Morozzi | 09/2025 |
| 2435 | 2^675407-176385 | 203318 | Stefano Morozzi | 09/2025 |
| 2436 | 2^675402-188523 | 203317 | Stefano Morozzi | 09/2025 |
| 2437 | 2^675398-150683 | 203316 | Stefano Morozzi | 08/2025 |
| 2438 | 2^675399-132069 | 203316 | Stefano Morozzi | 08/2025 |
| 2439 | 2^675401-130593 | 203316 | Stefano Morozzi | 08/2025 |
| 2440 | 2^675397-134749 | 203315 | Stefano Morozzi | 08/2025 |
| 2441 | 2^675385-169051 | 203312 | Stefano Morozzi | 08/2025 |
| 2442 | 2^675383-97737 | 203311 | Stefano Morozzi | 08/2025 |
| 2443 | 2^675380-94305 | 203310 | Stefano Morozzi | 08/2025 |
| 2444 | 2^675381-78495 | 203310 | Stefano Morozzi | 08/2025 |
| 2445 | 2^675373-1039 | 203308 | Stefano Morozzi | 08/2025 |
| 2446 | 2^675374-190163 | 203308 | Stefano Morozzi | 08/2025 |
| 2447 | 2^675374-9177 | 203308 | Stefano Morozzi | 08/2025 |
| 2448 | 2^675368-144215 | 203307 | Stefano Morozzi | 08/2025 |
| 2449 | 2^675369-44433 | 203307 | Stefano Morozzi | 08/2025 |
| 2450 | 2^675370-118025 | 203307 | Stefano Morozzi | 08/2025 |
| 2451 | 2^675370-190293 | 203307 | Stefano Morozzi | 08/2025 |
| 2452 | 2^675366-150243 | 203306 | Stefano Morozzi | 08/2025 |
| 2453 | 2^675362-131235 | 203305 | Stefano Morozzi | 08/2025 |
| 2454 | 2^675362-161171 | 203305 | Stefano Morozzi | 08/2025 |
| 2455 | 2^675363-189607 | 203305 | Stefano Morozzi | 08/2025 |
| 2456 | 2^675364-20763 | 203305 | Stefano Morozzi | 08/2025 |
| 2457 | 2^675357-45801 | 203303 | Stefano Morozzi | 07/2025 |
| 2458 | 2^675354-109623 | 203302 | Stefano Morozzi | 07/2025 |
| 2459 | 2^675350-124911 | 203301 | Stefano Morozzi | 07/2025 |
| 2460 | 2^675345-83365 | 203300 | Stefano Morozzi | 07/2025 |
| 2461 | 2^675347-160357 | 203300 | Stefano Morozzi | 07/2025 |
| 2462 | 2^675339-178989 | 203298 | Stefano Morozzi | 07/2025 |
| 2463 | 2^675337-135031 | 203297 | Stefano Morozzi | 07/2025 |
| 2464 | 2^675337-21693 | 203297 | Stefano Morozzi | 07/2025 |
| 2465 | 2^675334-194937 | 203296 | Stefano Morozzi | 07/2025 |
| 2466 | 2^675334-34313 | 203296 | Stefano Morozzi | 07/2025 |
| 2467 | 2^675330-167061 | 203295 | Stefano Morozzi | 07/2025 |
| 2468 | 2^675331-148659 | 203295 | Stefano Morozzi | 07/2025 |
| 2469 | 2^675326-178983 | 203294 | Stefano Morozzi | 07/2025 |
| 2470 | 2^675327-107469 | 203294 | Stefano Morozzi | 07/2025 |
| 2471 | 2^675327-55159 | 203294 | Stefano Morozzi | 07/2025 |
| 2472 | 2^675328-92097 | 203294 | Stefano Morozzi | 07/2025 |
| 2473 | 2^675323-197989 | 203293 | Stefano Morozzi | 07/2025 |
| 2474 | 2^675315-104421 | 203291 | Stefano Morozzi | 07/2025 |
| 2475 | 2^675316-155007 | 203291 | Stefano Morozzi | 07/2025 |
| 2476 | 2^675317-30613 | 203291 | Stefano Morozzi | 07/2025 |
| 2477 | 2^675318-116925 | 203291 | Stefano Morozzi | 07/2025 |
| 2478 | 2^675312-135209 | 203290 | Stefano Morozzi | 06/2025 |
| 2479 | 2^675313-131635 | 203290 | Stefano Morozzi | 06/2025 |
| 2480 | 2^675314-187365 | 203290 | Stefano Morozzi | 07/2025 |
| 2481 | 2^675305-75049 | 203288 | Stefano Morozzi | 06/2025 |
| 2482 | 2^675308-198257 | 203288 | Stefano Morozzi | 06/2025 |
| 2483 | 2^675308-80475 | 203288 | Stefano Morozzi | 06/2025 |
| 2484 | 2^675302-68271 | 203287 | Stefano Morozzi | 06/2025 |
| 2485 | 2^675304-74217 | 203287 | Stefano Morozzi | 06/2025 |
| 2486 | 2^675299-103321 | 203286 | Stefano Morozzi | 06/2025 |
| 2487 | 2^675292-125489 | 203284 | Stefano Morozzi | 06/2025 |
| 2488 | 2^675289-140833 | 203283 | Stefano Morozzi | 06/2025 |
| 2489 | 2^675291-141087 | 203283 | Stefano Morozzi | 06/2025 |
| 2490 | 2^675285-177525 | 203282 | Stefano Morozzi | 06/2025 |
| 2491 | 2^675288-133227 | 203282 | Stefano Morozzi | 06/2025 |
| 2492 | 2^675282-24717 | 203281 | Stefano Morozzi | 06/2025 |
| 2493 | 2^675279-113179 | 203280 | Stefano Morozzi | 06/2025 |
| 2494 | 2^675266-25557 | 203276 | Stefano Morozzi | 06/2025 |
| 2495 | 2^675267-112125 | 203276 | Stefano Morozzi | 06/2025 |
| 2496 | 2^675263-164881 | 203275 | Stefano Morozzi | 06/2025 |
| 2497 | 2^675261-4885 | 203274 | Stefano Morozzi | 06/2025 |
| 2498 | 2^675261-9489 | 203274 | Stefano Morozzi | 06/2025 |
| 2499 | 2^675255-100321 | 203273 | Stefano Morozzi | 06/2025 |
| 2500 | 2^675256-41439 | 203273 | Stefano Morozzi | 06/2025 |
