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
| Rank |
Probable prime |
Digits (> 50000) |
Who ? |
When ? |
| 2251 | 2^675327-107469 | 203294 | Stefano Morozzi | 07/2025 |
| 2252 | 2^675327-55159 | 203294 | Stefano Morozzi | 07/2025 |
| 2253 | 2^675328-92097 | 203294 | Stefano Morozzi | 07/2025 |
| 2254 | 2^675323-197989 | 203293 | Stefano Morozzi | 07/2025 |
| 2255 | 2^675315-104421 | 203291 | Stefano Morozzi | 07/2025 |
| 2256 | 2^675316-155007 | 203291 | Stefano Morozzi | 07/2025 |
| 2257 | 2^675317-30613 | 203291 | Stefano Morozzi | 07/2025 |
| 2258 | 2^675318-116925 | 203291 | Stefano Morozzi | 07/2025 |
| 2259 | 2^675312-135209 | 203290 | Stefano Morozzi | 06/2025 |
| 2260 | 2^675313-131635 | 203290 | Stefano Morozzi | 06/2025 |
| 2261 | 2^675314-187365 | 203290 | Stefano Morozzi | 07/2025 |
| 2262 | 2^675305-75049 | 203288 | Stefano Morozzi | 06/2025 |
| 2263 | 2^675308-198257 | 203288 | Stefano Morozzi | 06/2025 |
| 2264 | 2^675308-80475 | 203288 | Stefano Morozzi | 06/2025 |
| 2265 | 2^675302-68271 | 203287 | Stefano Morozzi | 06/2025 |
| 2266 | 2^675304-74217 | 203287 | Stefano Morozzi | 06/2025 |
| 2267 | 2^675299-103321 | 203286 | Stefano Morozzi | 06/2025 |
| 2268 | 2^675292-125489 | 203284 | Stefano Morozzi | 06/2025 |
| 2269 | 2^675289-140833 | 203283 | Stefano Morozzi | 06/2025 |
| 2270 | 2^675291-141087 | 203283 | Stefano Morozzi | 06/2025 |
| 2271 | 2^675285-177525 | 203282 | Stefano Morozzi | 06/2025 |
| 2272 | 2^675288-133227 | 203282 | Stefano Morozzi | 06/2025 |
| 2273 | 2^675282-24717 | 203281 | Stefano Morozzi | 06/2025 |
| 2274 | 2^675279-113179 | 203280 | Stefano Morozzi | 06/2025 |
| 2275 | 2^675266-25557 | 203276 | Stefano Morozzi | 06/2025 |
| 2276 | 2^675267-112125 | 203276 | Stefano Morozzi | 06/2025 |
| 2277 | 2^675263-164881 | 203275 | Stefano Morozzi | 06/2025 |
| 2278 | 2^675261-4885 | 203274 | Stefano Morozzi | 06/2025 |
| 2279 | 2^675261-9489 | 203274 | Stefano Morozzi | 06/2025 |
| 2280 | 2^675255-100321 | 203273 | Stefano Morozzi | 06/2025 |
| 2281 | 2^675256-41439 | 203273 | Stefano Morozzi | 06/2025 |
| 2282 | 2^675257-34623 | 203273 | Stefano Morozzi | 06/2025 |
| 2283 | 2^675254-132177 | 203272 | Stefano Morozzi | 06/2025 |
| 2284 | 2^675254-58053 | 203272 | Stefano Morozzi | 06/2025 |
| 2285 | 2^675242-117707 | 203269 | Stefano Morozzi | 06/2025 |
| 2286 | 2^675243-156531 | 203269 | Stefano Morozzi | 06/2025 |
| 2287 | 2^675243-56595 | 203269 | Stefano Morozzi | 06/2025 |
| 2288 | 2^675239-90471 | 203268 | Stefano Morozzi | 06/2025 |
| 2289 | 2^675240-34863 | 203268 | Stefano Morozzi | 06/2025 |
| 2290 | 2^675234-71207 | 203266 | Stefano Morozzi | 06/2025 |
| 2291 | 2^675235-195175 | 203266 | Stefano Morozzi | 06/2025 |
| 2292 | 2^675235-199855 | 203266 | Stefano Morozzi | 06/2025 |
| 2293 | 2^675229-71601 | 203265 | Stefano Morozzi | 06/2025 |
| 2294 | 2^675219-66709 | 203262 | Stefano Morozzi | 06/2025 |
| 2295 | 2^675220-98999 | 203262 | Stefano Morozzi | 06/2025 |
| 2296 | 2^675221-149589 | 203262 | Stefano Morozzi | 06/2025 |
| 2297 | 2^675211-198405 | 203259 | Stefano Morozzi | 04/2025 |
| 2298 | 2^675208-131505 | 203258 | Stefano Morozzi | 04/2025 |
| 2299 | 2^675202-14823 | 203257 | Stefano Morozzi | 04/2025 |
| 2300 | 2^675202-35967 | 203257 | Stefano Morozzi | 04/2025 |
| 2301 | 2^675202-54681 | 203257 | Stefano Morozzi | 04/2025 |
| 2302 | 2^675205-107845 | 203257 | Stefano Morozzi | 04/2025 |
| 2303 | 2^675199-131397 | 203256 | Stefano Morozzi | 04/2025 |
| 2304 | 2^675199-34219 | 203256 | Stefano Morozzi | 04/2025 |
| 2305 | 2^675199-56175 | 203256 | Stefano Morozzi | 04/2025 |
| 2306 | 2^675198-106925 | 203255 | Stefano Morozzi | 04/2025 |
| 2307 | 2^675192-192243 | 203254 | Stefano Morozzi | 04/2025 |
| 2308 | 2^675189-37383 | 203253 | Stefano Morozzi | 04/2025 |
| 2309 | 2^675190-68711 | 203253 | Stefano Morozzi | 04/2025 |
| 2310 | 2^675191-114549 | 203253 | Stefano Morozzi | 04/2025 |
| 2311 | 2^675191-29445 | 203253 | Stefano Morozzi | 04/2025 |
| 2312 | 2^675186-24563 | 203252 | Stefano Morozzi | 04/2025 |
| 2313 | 2^675187-185041 | 203252 | Stefano Morozzi | 04/2025 |
| 2314 | 2^675188-121613 | 203252 | Stefano Morozzi | 04/2025 |
| 2315 | 2^675183-43587 | 203251 | Stefano Morozzi | 04/2025 |
| 2316 | 2^675184-60563 | 203251 | Stefano Morozzi | 04/2025 |
| 2317 | 10247^50678-50678^10247 | 203250 | Norbert Schneider | 03/2022 |
| 2318 | 2^675177-30495 | 203249 | Stefano Morozzi | 04/2025 |
| 2319 | 2^675170-170651 | 203247 | Stefano Morozzi | 04/2025 |
| 2320 | 2^675171-21231 | 203247 | Stefano Morozzi | 04/2025 |
| 2321 | 2^675166-116351 | 203246 | Stefano Morozzi | 04/2025 |
| 2322 | 2^675166-63465 | 203246 | Stefano Morozzi | 04/2025 |
| 2323 | 2^675167-11047 | 203246 | Stefano Morozzi | 04/2025 |
| 2324 | 2^675168-197307 | 203246 | Stefano Morozzi | 04/2025 |
| 2325 | 2^675168-89379 | 203246 | Stefano Morozzi | 04/2025 |
| 2326 | 2^675166+23097 | 203246 | Stefano Morozzi | 07/2025 |
| 2327 | 2^675167+7725 | 203246 | Stefano Morozzi | 07/2025 |
| 2328 | 2^675167+35999 | 203246 | Stefano Morozzi | 07/2025 |
| 2329 | 2^675162-24471 | 203245 | Stefano Morozzi | 04/2025 |
| 2330 | 2^675163-4971 | 203245 | Stefano Morozzi | 04/2025 |
| 2331 | 2^675163-69489 | 203245 | Stefano Morozzi | 04/2025 |
| 2332 | 2^675165-153541 | 203245 | Stefano Morozzi | 04/2025 |
| 2333 | 2^675159-107809 | 203244 | Stefano Morozzi | 04/2025 |
| 2334 | 2^675160+107463 | 203244 | Stefano Morozzi | 07/2025 |
| 2335 | 2^675160+174355 | 203244 | Stefano Morozzi | 07/2025 |
| 2336 | 2^675156-156785 | 203243 | Stefano Morozzi | 04/2025 |
| 2337 | 2^675157-177433 | 203243 | Stefano Morozzi | 04/2025 |
| 2338 | 2^675154-66563 | 203242 | Stefano Morozzi | 04/2025 |
| 2339 | 2^675153+21477 | 203242 | Stefano Morozzi | 07/2025 |
| 2340 | 2^675153+88607 | 203242 | Stefano Morozzi | 07/2025 |
| 2341 | 2^675154+7609 | 203242 | Stefano Morozzi | 07/2025 |
| 2342 | 2^675155+128255 | 203242 | Stefano Morozzi | 07/2025 |
| 2343 | 2^675148-71007 | 203240 | Stefano Morozzi | 04/2025 |
| 2344 | 2^675148-94815 | 203240 | Stefano Morozzi | 04/2025 |
| 2345 | 2^675146+28957 | 203240 | Stefano Morozzi | 06/2025 |
| 2346 | 2^675143+55865 | 203239 | Stefano Morozzi | 06/2025 |
| 2347 | 2^675143+100619 | 203239 | Stefano Morozzi | 06/2025 |
| 2348 | 2^675143+191895 | 203239 | Stefano Morozzi | 06/2025 |
| 2349 | 2^675144+34207 | 203239 | Stefano Morozzi | 06/2025 |
| 2350 | 2^675142+160903 | 203238 | Stefano Morozzi | 06/2025 |
| 2351 | 2^675138-52371 | 203237 | Stefano Morozzi | 04/2025 |
| 2352 | 2^675138+114979 | 203237 | Stefano Morozzi | 06/2025 |
| 2353 | 2^675133-7273 | 203236 | Stefano Morozzi | 04/2025 |
| 2354 | 2^675134-73473 | 203236 | Stefano Morozzi | 04/2025 |
| 2355 | 2^675129+146825 | 203235 | Stefano Morozzi | 06/2025 |
| 2356 | 2^675131+198275 | 203235 | Stefano Morozzi | 06/2025 |
| 2357 | 2^675132+156585 | 203235 | Stefano Morozzi | 06/2025 |
| 2358 | 2^675124-51675 | 203233 | Stefano Morozzi | 04/2025 |
| 2359 | 2^675124+3907 | 203233 | Stefano Morozzi | 06/2025 |
| 2360 | 2^675124+58711 | 203233 | Stefano Morozzi | 06/2025 |
| 2361 | 2^675124+115557 | 203233 | Stefano Morozzi | 06/2025 |
| 2362 | 2^675120-40809 | 203232 | Stefano Morozzi | 04/2025 |
| 2363 | 2^675120-50573 | 203232 | Stefano Morozzi | 04/2025 |
| 2364 | 2^675122+185715 | 203232 | Stefano Morozzi | 06/2025 |
| 2365 | 2^675116-109889 | 203231 | Stefano Morozzi | 04/2025 |
| 2366 | 2^675116+90607 | 203231 | Stefano Morozzi | 06/2025 |
| 2367 | 2^675113+69461 | 203230 | Stefano Morozzi | 06/2025 |
| 2368 | 2^675110+147825 | 203229 | Stefano Morozzi | 06/2025 |
| 2369 | 2^675110+179107 | 203229 | Stefano Morozzi | 06/2025 |
| 2370 | 2^675106-73241 | 203228 | Stefano Morozzi | 02/2025 |
| 2371 | 2^675103-188727 | 203227 | Stefano Morozzi | 02/2025 |
| 2372 | 2^675104-16199 | 203227 | Stefano Morozzi | 02/2025 |
| 2373 | 2^675104-195303 | 203227 | Stefano Morozzi | 02/2025 |
| 2374 | 2^675105-94521 | 203227 | Stefano Morozzi | 02/2025 |
| 2375 | 2^675103+31599 | 203227 | Stefano Morozzi | 04/2025 |
| 2376 | 2^675103+124629 | 203227 | Stefano Morozzi | 06/2025 |
| 2377 | 2^675100-2775 | 203226 | Stefano Morozzi | 02/2025 |
| 2378 | 2^675098-170703 | 203225 | Stefano Morozzi | 02/2025 |
| 2379 | 2^675097+50651 | 203225 | Stefano Morozzi | 04/2025 |
| 2380 | 2^675093-162123 | 203224 | Stefano Morozzi | 02/2025 |
| 2381 | 2^675093-48955 | 203224 | Stefano Morozzi | 02/2025 |
| 2382 | 2^675095-73591 | 203224 | Stefano Morozzi | 02/2025 |
| 2383 | 2^675095-89937 | 203224 | Stefano Morozzi | 02/2025 |
| 2384 | 2^675093+87767 | 203224 | Stefano Morozzi | 04/2025 |
| 2385 | 2^675092-144539 | 203223 | Stefano Morozzi | 02/2025 |
| 2386 | 2^675090+92253 | 203223 | Stefano Morozzi | 04/2025 |
| 2387 | 2^675086-186387 | 203222 | Stefano Morozzi | 02/2025 |
| 2388 | 2^675088-68505 | 203222 | Stefano Morozzi | 02/2025 |
| 2389 | 2^675083-149199 | 203221 | Stefano Morozzi | 02/2025 |
| 2390 | 2^675081-91425 | 203220 | Stefano Morozzi | 02/2025 |
| 2391 | 2^675082-80213 | 203220 | Stefano Morozzi | 02/2025 |
| 2392 | 2^675080+112651 | 203220 | Stefano Morozzi | 04/2025 |
| 2393 | 2^675082+25435 | 203220 | Stefano Morozzi | 04/2025 |
| 2394 | 2^675082+180613 | 203220 | Stefano Morozzi | 04/2025 |
| 2395 | 2^675077-152683 | 203219 | Stefano Morozzi | 02/2025 |
| 2396 | 2^675077-79213 | 203219 | Stefano Morozzi | 02/2025 |
| 2397 | 2^675077+172221 | 203219 | Stefano Morozzi | 04/2025 |
| 2398 | 2^675073-149065 | 203218 | Stefano Morozzi | 02/2025 |
| 2399 | 2^675073-19663 | 203218 | Stefano Morozzi | 02/2025 |
| 2400 | 2^675074+25755 | 203218 | Stefano Morozzi | 04/2025 |
| 2401 | 2^675075+151203 | 203218 | Stefano Morozzi | 04/2025 |
| 2402 | 2^675069-147135 | 203217 | Stefano Morozzi | 02/2025 |
| 2403 | 2^675069-161461 | 203217 | Stefano Morozzi | 02/2025 |
| 2404 | 2^675071-175189 | 203217 | Stefano Morozzi | 02/2025 |
| 2405 | 2^675071+105575 | 203217 | Stefano Morozzi | 04/2025 |
| 2406 | 2^675071+162299 | 203217 | Stefano Morozzi | 04/2025 |
| 2407 | 2^675067+124541 | 203216 | Stefano Morozzi | 04/2025 |
| 2408 | 2^675068+163695 | 203216 | Stefano Morozzi | 04/2025 |
| 2409 | 2^675064+116445 | 203215 | Stefano Morozzi | 04/2025 |
| 2410 | 2^675065+26045 | 203215 | Stefano Morozzi | 04/2025 |
| 2411 | 2^675060+119983 | 203214 | Stefano Morozzi | 02/2025 |
| 2412 | 2^675060+161301 | 203214 | Stefano Morozzi | 02/2025 |
| 2413 | 2^675061-187773 | 203214 | Stefano Morozzi | 02/2025 |
| 2414 | 2^675062-92193 | 203214 | Stefano Morozzi | 02/2025 |
| 2415 | 2^675058-10403 | 203213 | Stefano Morozzi | 01/2025 |
| 2416 | 2^675058-40337 | 203213 | Stefano Morozzi | 01/2025 |
| 2417 | 2^675057+123557 | 203213 | Stefano Morozzi | 02/2025 |
| 2418 | 2^675057+172475 | 203213 | Stefano Morozzi | 02/2025 |
| 2419 | 2^675053-4801 | 203212 | Stefano Morozzi | 01/2025 |
| 2420 | 2^675054-174341 | 203212 | Stefano Morozzi | 01/2025 |
| 2421 | 2^675054-53697 | 203212 | Stefano Morozzi | 01/2025 |
| 2422 | 2^675054+24825 | 203212 | Stefano Morozzi | 02/2025 |
| 2423 | 2^675055+160265 | 203212 | Stefano Morozzi | 02/2025 |
| 2424 | 2^675050-30015 | 203211 | Stefano Morozzi | 01/2025 |
| 2425 | 2^675051-85941 | 203211 | Stefano Morozzi | 01/2025 |
| 2426 | 2^675051+30885 | 203211 | Stefano Morozzi | 02/2025 |
| 2427 | 2^675052+12537 | 203211 | Stefano Morozzi | 02/2025 |
| 2428 | 2^675047-100299 | 203210 | Stefano Morozzi | 01/2025 |
| 2429 | 2^675048-97313 | 203210 | Stefano Morozzi | 01/2025 |
| 2430 | 2^675046+118119 | 203210 | Stefano Morozzi | 02/2025 |
| 2431 | 2^675048+128941 | 203210 | Stefano Morozzi | 02/2025 |
| 2432 | 2^675049+136359 | 203210 | Stefano Morozzi | 02/2025 |
| 2433 | 2^675044-81087 | 203209 | Stefano Morozzi | 01/2025 |
| 2434 | 2^675042-179811 | 203208 | Stefano Morozzi | 01/2025 |
| 2435 | 2^675036-192939 | 203207 | Stefano Morozzi | 01/2025 |
| 2436 | 2^675037-17853 | 203207 | Stefano Morozzi | 01/2025 |
| 2437 | 2^675036+47101 | 203207 | Stefano Morozzi | 02/2025 |
| 2438 | 2^675038+189589 | 203207 | Stefano Morozzi | 02/2025 |
| 2439 | 2^675034-169727 | 203206 | Stefano Morozzi | 01/2025 |
| 2440 | 2^675035-173055 | 203206 | Stefano Morozzi | 01/2025 |
| 2441 | 2^675035-73551 | 203206 | Stefano Morozzi | 01/2025 |
| 2442 | 2^675033+79109 | 203206 | Stefano Morozzi | 02/2025 |
| 2443 | 2^675034+154057 | 203206 | Stefano Morozzi | 02/2025 |
| 2444 | 2^675030+109245 | 203205 | Stefano Morozzi | 01/2025 |
| 2445 | 2^675030-160047 | 203205 | Stefano Morozzi | 01/2025 |
| 2446 | 2^675027+106733 | 203204 | Stefano Morozzi | 01/2025 |
| 2447 | 2^675026-67377 | 203204 | Stefano Morozzi | 01/2025 |
| 2448 | 2^675021+13335 | 203202 | Stefano Morozzi | 01/2025 |
| 2449 | 2^675020-180497 | 203202 | Stefano Morozzi | 01/2025 |
| 2450 | 2^675016+174777 | 203201 | Stefano Morozzi | 01/2025 |
| 2451 | 2^675017+128379 | 203201 | Stefano Morozzi | 01/2025 |
| 2452 | 2^675017+171249 | 203201 | Stefano Morozzi | 01/2025 |
| 2453 | 2^675018+86517 | 203201 | Stefano Morozzi | 01/2025 |
| 2454 | 2^675019+125891 | 203201 | Stefano Morozzi | 01/2025 |
| 2455 | 2^675019+163251 | 203201 | Stefano Morozzi | 01/2025 |
| 2456 | 2^675016-170847 | 203201 | Stefano Morozzi | 01/2025 |
| 2457 | 2^675019-44755 | 203201 | Stefano Morozzi | 01/2025 |
| 2458 | 2^675015+120225 | 203200 | Stefano Morozzi | 01/2025 |
| 2459 | 2^675013-69831 | 203200 | Stefano Morozzi | 01/2025 |
| 2460 | 2^675014-3897 | 203200 | Stefano Morozzi | 01/2025 |
| 2461 | 2^675006+75357 | 203198 | Stefano Morozzi | 01/2025 |
| 2462 | 2^675008+112231 | 203198 | Stefano Morozzi | 01/2025 |
| 2463 | 2^675007-123309 | 203198 | Stefano Morozzi | 01/2025 |
| 2464 | 2^675003+52529 | 203197 | Stefano Morozzi | 01/2025 |
| 2465 | 2^675002+50595 | 203196 | Stefano Morozzi | 01/2025 |
| 2466 | 2^674627-25161 | 203083 | Enzo Doria | 09/2013 |
| 2467 | 2^674603-69337 | 203076 | Enzo Doria | 12/2015 |
| 2468 | (182*10^203048+1)/3 | 203050 | Robert Price | 09/2023 |
| 2469 | 2^674459+74213 | 203033 | Enzo Doria | 04/2016 |
| 2470 | 2^674116-458879 | 202930 | Enzo Doria | 04/2015 |
| 2471 | 2^674076-114755 | 202918 | Enzo Doria | 04/2015 |
| 2472 | 5^289937-4^289937 | 202658 | Jean-Louis Charton | 03/2013 |
| 2473 | 5^289926-289926^5 | 202650 | Henri Lifchitz | 07/2024 |
| 2474 | (2^673184-7)/3 | 202649 | Stefano Morozzi | 08/2022 |
| 2475 | (467617#+14534)/(2^2*13*43) | 202603 | Makoto Morimoto | 06/2019 |
| 2476 | (155^92479-1)/154 | 202558 | Anonymous | 06/2024 |
| 2477 | 2^672773+219407 | 202525 | Enzo Doria | 03/2024 |
| 2478 | 1374^64531-64531^1374 | 202498 | Henri Lifchitz | 10/2024 |
| 2479 | 2^672556-1835519 | 202460 | Enzo Doria | 04/2015 |
| 2480 | (7*10^202267+179)/3 | 202268 | Robert Price | 02/2023 |
| 2481 | 2^671446-351401 | 202126 | Enzo Doria | 07/2015 |
| 2482 | 2^671373+77747 | 202104 | Enzo Doria | 05/2016 |
| 2483 | (2*10^202059+7)/9 | 202059 | Rytis Slatkevicius | 01/2023 |
| 2484 | 98*10^202021-9 | 202023 | Robert Price | 05/2023 |
| 2485 | 2^670726-114845 | 201909 | Enzo Doria | 05/2015 |
| 2486 | 2^670539-25045 | 201853 | Enzo Doria | 09/2013 |
| 2487 | 10^201801-93 | 201801 | Robert Price | 02/2023 |
| 2488 | 43284^43519-43519^43284 | 201769 | Norbert Schneider | 08/2018 |
| 2489 | 2^670213+282317 | 201755 | Enzo Doria | 09/2016 |
| 2490 | 2^670133+89 | 201731 | Stefano Morozzi | 05/2021 |
| 2491 | 2^669854-113501 | 201647 | Enzo Doria | 08/2014 |
| 2492 | 2^669718+81619 | 201606 | Enzo Doria | 08/2016 |
| 2493 | (299*10^201547-17)/3 | 201549 | Robert Price | 02/2023 |
| 2494 | (145*10^201504-1)/9 | 201506 | Serge Batalov | 12/2014 |
| 2495 | 2^668938-1839821 | 201371 | Enzo Doria | 06/2015 |
| 2496 | (198^87623-1)/197 | 201239 | Anonymous | 06/2024 |
| 2497 | 2^668492+1879303 | 201237 | Enzo Doria | 08/2016 |
| 2498 | 7*10^201140-87 | 201141 | Robert Price | 03/2023 |
| 2499 | 6^258413-5^258413 | 201085 | Jean-Louis Charton | 03/2013 |
| 2500 | 10194^50161-50161^10194 | 201063 | Norbert Schneider | 09/2020 |
