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 | 2^675235-195175 | 203266 | Stefano Morozzi | 06/2025 |
2252 | 2^675235-199855 | 203266 | Stefano Morozzi | 06/2025 |
2253 | 2^675229-71601 | 203265 | Stefano Morozzi | 06/2025 |
2254 | 2^675219-66709 | 203262 | Stefano Morozzi | 06/2025 |
2255 | 2^675220-98999 | 203262 | Stefano Morozzi | 06/2025 |
2256 | 2^675221-149589 | 203262 | Stefano Morozzi | 06/2025 |
2257 | 2^675211-198405 | 203259 | Stefano Morozzi | 04/2025 |
2258 | 2^675208-131505 | 203258 | Stefano Morozzi | 04/2025 |
2259 | 2^675202-14823 | 203257 | Stefano Morozzi | 04/2025 |
2260 | 2^675202-35967 | 203257 | Stefano Morozzi | 04/2025 |
2261 | 2^675202-54681 | 203257 | Stefano Morozzi | 04/2025 |
2262 | 2^675205-107845 | 203257 | Stefano Morozzi | 04/2025 |
2263 | 2^675199-131397 | 203256 | Stefano Morozzi | 04/2025 |
2264 | 2^675199-34219 | 203256 | Stefano Morozzi | 04/2025 |
2265 | 2^675199-56175 | 203256 | Stefano Morozzi | 04/2025 |
2266 | 2^675198-106925 | 203255 | Stefano Morozzi | 04/2025 |
2267 | 2^675192-192243 | 203254 | Stefano Morozzi | 04/2025 |
2268 | 2^675189-37383 | 203253 | Stefano Morozzi | 04/2025 |
2269 | 2^675190-68711 | 203253 | Stefano Morozzi | 04/2025 |
2270 | 2^675191-114549 | 203253 | Stefano Morozzi | 04/2025 |
2271 | 2^675191-29445 | 203253 | Stefano Morozzi | 04/2025 |
2272 | 2^675186-24563 | 203252 | Stefano Morozzi | 04/2025 |
2273 | 2^675187-185041 | 203252 | Stefano Morozzi | 04/2025 |
2274 | 2^675188-121613 | 203252 | Stefano Morozzi | 04/2025 |
2275 | 2^675183-43587 | 203251 | Stefano Morozzi | 04/2025 |
2276 | 2^675184-60563 | 203251 | Stefano Morozzi | 04/2025 |
2277 | 10247^50678-50678^10247 | 203250 | Norbert Schneider | 03/2022 |
2278 | 2^675177-30495 | 203249 | Stefano Morozzi | 04/2025 |
2279 | 2^675170-170651 | 203247 | Stefano Morozzi | 04/2025 |
2280 | 2^675171-21231 | 203247 | Stefano Morozzi | 04/2025 |
2281 | 2^675166-116351 | 203246 | Stefano Morozzi | 04/2025 |
2282 | 2^675166-63465 | 203246 | Stefano Morozzi | 04/2025 |
2283 | 2^675167-11047 | 203246 | Stefano Morozzi | 04/2025 |
2284 | 2^675168-197307 | 203246 | Stefano Morozzi | 04/2025 |
2285 | 2^675168-89379 | 203246 | Stefano Morozzi | 04/2025 |
2286 | 2^675162-24471 | 203245 | Stefano Morozzi | 04/2025 |
2287 | 2^675163-4971 | 203245 | Stefano Morozzi | 04/2025 |
2288 | 2^675163-69489 | 203245 | Stefano Morozzi | 04/2025 |
2289 | 2^675165-153541 | 203245 | Stefano Morozzi | 04/2025 |
2290 | 2^675159-107809 | 203244 | Stefano Morozzi | 04/2025 |
2291 | 2^675156-156785 | 203243 | Stefano Morozzi | 04/2025 |
2292 | 2^675157-177433 | 203243 | Stefano Morozzi | 04/2025 |
2293 | 2^675154-66563 | 203242 | Stefano Morozzi | 04/2025 |
2294 | 2^675148-71007 | 203240 | Stefano Morozzi | 04/2025 |
2295 | 2^675148-94815 | 203240 | Stefano Morozzi | 04/2025 |
2296 | 2^675146+28957 | 203240 | Stefano Morozzi | 06/2025 |
2297 | 2^675143+55865 | 203239 | Stefano Morozzi | 06/2025 |
2298 | 2^675143+100619 | 203239 | Stefano Morozzi | 06/2025 |
2299 | 2^675143+191895 | 203239 | Stefano Morozzi | 06/2025 |
2300 | 2^675144+34207 | 203239 | Stefano Morozzi | 06/2025 |
2301 | 2^675142+160903 | 203238 | Stefano Morozzi | 06/2025 |
2302 | 2^675138-52371 | 203237 | Stefano Morozzi | 04/2025 |
2303 | 2^675138+114979 | 203237 | Stefano Morozzi | 06/2025 |
2304 | 2^675133-7273 | 203236 | Stefano Morozzi | 04/2025 |
2305 | 2^675134-73473 | 203236 | Stefano Morozzi | 04/2025 |
2306 | 2^675129+146825 | 203235 | Stefano Morozzi | 06/2025 |
2307 | 2^675131+198275 | 203235 | Stefano Morozzi | 06/2025 |
2308 | 2^675132+156585 | 203235 | Stefano Morozzi | 06/2025 |
2309 | 2^675124-51675 | 203233 | Stefano Morozzi | 04/2025 |
2310 | 2^675124+3907 | 203233 | Stefano Morozzi | 06/2025 |
2311 | 2^675124+58711 | 203233 | Stefano Morozzi | 06/2025 |
2312 | 2^675124+115557 | 203233 | Stefano Morozzi | 06/2025 |
2313 | 2^675120-40809 | 203232 | Stefano Morozzi | 04/2025 |
2314 | 2^675120-50573 | 203232 | Stefano Morozzi | 04/2025 |
2315 | 2^675122+185715 | 203232 | Stefano Morozzi | 06/2025 |
2316 | 2^675116-109889 | 203231 | Stefano Morozzi | 04/2025 |
2317 | 2^675116+90607 | 203231 | Stefano Morozzi | 06/2025 |
2318 | 2^675113+69461 | 203230 | Stefano Morozzi | 06/2025 |
2319 | 2^675110+147825 | 203229 | Stefano Morozzi | 06/2025 |
2320 | 2^675110+179107 | 203229 | Stefano Morozzi | 06/2025 |
2321 | 2^675106-73241 | 203228 | Stefano Morozzi | 02/2025 |
2322 | 2^675103-188727 | 203227 | Stefano Morozzi | 02/2025 |
2323 | 2^675104-16199 | 203227 | Stefano Morozzi | 02/2025 |
2324 | 2^675104-195303 | 203227 | Stefano Morozzi | 02/2025 |
2325 | 2^675105-94521 | 203227 | Stefano Morozzi | 02/2025 |
2326 | 2^675103+31599 | 203227 | Stefano Morozzi | 04/2025 |
2327 | 2^675103+124629 | 203227 | Stefano Morozzi | 06/2025 |
2328 | 2^675100-2775 | 203226 | Stefano Morozzi | 02/2025 |
2329 | 2^675098-170703 | 203225 | Stefano Morozzi | 02/2025 |
2330 | 2^675097+50651 | 203225 | Stefano Morozzi | 04/2025 |
2331 | 2^675093-162123 | 203224 | Stefano Morozzi | 02/2025 |
2332 | 2^675093-48955 | 203224 | Stefano Morozzi | 02/2025 |
2333 | 2^675095-73591 | 203224 | Stefano Morozzi | 02/2025 |
2334 | 2^675095-89937 | 203224 | Stefano Morozzi | 02/2025 |
2335 | 2^675093+87767 | 203224 | Stefano Morozzi | 04/2025 |
2336 | 2^675092-144539 | 203223 | Stefano Morozzi | 02/2025 |
2337 | 2^675090+92253 | 203223 | Stefano Morozzi | 04/2025 |
2338 | 2^675086-186387 | 203222 | Stefano Morozzi | 02/2025 |
2339 | 2^675088-68505 | 203222 | Stefano Morozzi | 02/2025 |
2340 | 2^675083-149199 | 203221 | Stefano Morozzi | 02/2025 |
2341 | 2^675081-91425 | 203220 | Stefano Morozzi | 02/2025 |
2342 | 2^675082-80213 | 203220 | Stefano Morozzi | 02/2025 |
2343 | 2^675080+112651 | 203220 | Stefano Morozzi | 04/2025 |
2344 | 2^675082+25435 | 203220 | Stefano Morozzi | 04/2025 |
2345 | 2^675082+180613 | 203220 | Stefano Morozzi | 04/2025 |
2346 | 2^675077-152683 | 203219 | Stefano Morozzi | 02/2025 |
2347 | 2^675077-79213 | 203219 | Stefano Morozzi | 02/2025 |
2348 | 2^675077+172221 | 203219 | Stefano Morozzi | 04/2025 |
2349 | 2^675073-149065 | 203218 | Stefano Morozzi | 02/2025 |
2350 | 2^675073-19663 | 203218 | Stefano Morozzi | 02/2025 |
2351 | 2^675074+25755 | 203218 | Stefano Morozzi | 04/2025 |
2352 | 2^675075+151203 | 203218 | Stefano Morozzi | 04/2025 |
2353 | 2^675069-147135 | 203217 | Stefano Morozzi | 02/2025 |
2354 | 2^675069-161461 | 203217 | Stefano Morozzi | 02/2025 |
2355 | 2^675071-175189 | 203217 | Stefano Morozzi | 02/2025 |
2356 | 2^675071+105575 | 203217 | Stefano Morozzi | 04/2025 |
2357 | 2^675071+162299 | 203217 | Stefano Morozzi | 04/2025 |
2358 | 2^675067+124541 | 203216 | Stefano Morozzi | 04/2025 |
2359 | 2^675068+163695 | 203216 | Stefano Morozzi | 04/2025 |
2360 | 2^675064+116445 | 203215 | Stefano Morozzi | 04/2025 |
2361 | 2^675065+26045 | 203215 | Stefano Morozzi | 04/2025 |
2362 | 2^675060+119983 | 203214 | Stefano Morozzi | 02/2025 |
2363 | 2^675060+161301 | 203214 | Stefano Morozzi | 02/2025 |
2364 | 2^675061-187773 | 203214 | Stefano Morozzi | 02/2025 |
2365 | 2^675062-92193 | 203214 | Stefano Morozzi | 02/2025 |
2366 | 2^675058-10403 | 203213 | Stefano Morozzi | 01/2025 |
2367 | 2^675058-40337 | 203213 | Stefano Morozzi | 01/2025 |
2368 | 2^675057+123557 | 203213 | Stefano Morozzi | 02/2025 |
2369 | 2^675057+172475 | 203213 | Stefano Morozzi | 02/2025 |
2370 | 2^675053-4801 | 203212 | Stefano Morozzi | 01/2025 |
2371 | 2^675054-174341 | 203212 | Stefano Morozzi | 01/2025 |
2372 | 2^675054-53697 | 203212 | Stefano Morozzi | 01/2025 |
2373 | 2^675054+24825 | 203212 | Stefano Morozzi | 02/2025 |
2374 | 2^675055+160265 | 203212 | Stefano Morozzi | 02/2025 |
2375 | 2^675050-30015 | 203211 | Stefano Morozzi | 01/2025 |
2376 | 2^675051-85941 | 203211 | Stefano Morozzi | 01/2025 |
2377 | 2^675051+30885 | 203211 | Stefano Morozzi | 02/2025 |
2378 | 2^675052+12537 | 203211 | Stefano Morozzi | 02/2025 |
2379 | 2^675047-100299 | 203210 | Stefano Morozzi | 01/2025 |
2380 | 2^675048-97313 | 203210 | Stefano Morozzi | 01/2025 |
2381 | 2^675046+118119 | 203210 | Stefano Morozzi | 02/2025 |
2382 | 2^675048+128941 | 203210 | Stefano Morozzi | 02/2025 |
2383 | 2^675049+136359 | 203210 | Stefano Morozzi | 02/2025 |
2384 | 2^675044-81087 | 203209 | Stefano Morozzi | 01/2025 |
2385 | 2^675042-179811 | 203208 | Stefano Morozzi | 01/2025 |
2386 | 2^675036-192939 | 203207 | Stefano Morozzi | 01/2025 |
2387 | 2^675037-17853 | 203207 | Stefano Morozzi | 01/2025 |
2388 | 2^675036+47101 | 203207 | Stefano Morozzi | 02/2025 |
2389 | 2^675038+189589 | 203207 | Stefano Morozzi | 02/2025 |
2390 | 2^675034-169727 | 203206 | Stefano Morozzi | 01/2025 |
2391 | 2^675035-173055 | 203206 | Stefano Morozzi | 01/2025 |
2392 | 2^675035-73551 | 203206 | Stefano Morozzi | 01/2025 |
2393 | 2^675033+79109 | 203206 | Stefano Morozzi | 02/2025 |
2394 | 2^675034+154057 | 203206 | Stefano Morozzi | 02/2025 |
2395 | 2^675030+109245 | 203205 | Stefano Morozzi | 01/2025 |
2396 | 2^675030-160047 | 203205 | Stefano Morozzi | 01/2025 |
2397 | 2^675027+106733 | 203204 | Stefano Morozzi | 01/2025 |
2398 | 2^675026-67377 | 203204 | Stefano Morozzi | 01/2025 |
2399 | 2^675021+13335 | 203202 | Stefano Morozzi | 01/2025 |
2400 | 2^675020-180497 | 203202 | Stefano Morozzi | 01/2025 |
2401 | 2^675016+174777 | 203201 | Stefano Morozzi | 01/2025 |
2402 | 2^675017+128379 | 203201 | Stefano Morozzi | 01/2025 |
2403 | 2^675017+171249 | 203201 | Stefano Morozzi | 01/2025 |
2404 | 2^675018+86517 | 203201 | Stefano Morozzi | 01/2025 |
2405 | 2^675019+125891 | 203201 | Stefano Morozzi | 01/2025 |
2406 | 2^675019+163251 | 203201 | Stefano Morozzi | 01/2025 |
2407 | 2^675016-170847 | 203201 | Stefano Morozzi | 01/2025 |
2408 | 2^675019-44755 | 203201 | Stefano Morozzi | 01/2025 |
2409 | 2^675015+120225 | 203200 | Stefano Morozzi | 01/2025 |
2410 | 2^675013-69831 | 203200 | Stefano Morozzi | 01/2025 |
2411 | 2^675014-3897 | 203200 | Stefano Morozzi | 01/2025 |
2412 | 2^675006+75357 | 203198 | Stefano Morozzi | 01/2025 |
2413 | 2^675008+112231 | 203198 | Stefano Morozzi | 01/2025 |
2414 | 2^675007-123309 | 203198 | Stefano Morozzi | 01/2025 |
2415 | 2^675003+52529 | 203197 | Stefano Morozzi | 01/2025 |
2416 | 2^675002+50595 | 203196 | Stefano Morozzi | 01/2025 |
2417 | 2^674627-25161 | 203083 | Enzo Doria | 09/2013 |
2418 | 2^674603-69337 | 203076 | Enzo Doria | 12/2015 |
2419 | (182*10^203048+1)/3 | 203050 | Robert Price | 09/2023 |
2420 | 2^674459+74213 | 203033 | Enzo Doria | 04/2016 |
2421 | 2^674116-458879 | 202930 | Enzo Doria | 04/2015 |
2422 | 2^674076-114755 | 202918 | Enzo Doria | 04/2015 |
2423 | 5^289937-4^289937 | 202658 | Jean-Louis Charton | 03/2013 |
2424 | 5^289926-289926^5 | 202650 | Henri Lifchitz | 07/2024 |
2425 | (2^673184-7)/3 | 202649 | Stefano Morozzi | 08/2022 |
2426 | (467617#+14534)/(2^2*13*43) | 202603 | Makoto Morimoto | 06/2019 |
2427 | (155^92479-1)/154 | 202558 | Anonymous | 06/2024 |
2428 | 2^672773+219407 | 202525 | Enzo Doria | 03/2024 |
2429 | 1374^64531-64531^1374 | 202498 | Henri Lifchitz | 10/2024 |
2430 | 2^672556-1835519 | 202460 | Enzo Doria | 04/2015 |
2431 | (7*10^202267+179)/3 | 202268 | Robert Price | 02/2023 |
2432 | 2^671446-351401 | 202126 | Enzo Doria | 07/2015 |
2433 | 2^671373+77747 | 202104 | Enzo Doria | 05/2016 |
2434 | (2*10^202059+7)/9 | 202059 | Rytis Slatkevicius | 01/2023 |
2435 | 98*10^202021-9 | 202023 | Robert Price | 05/2023 |
2436 | 2^670726-114845 | 201909 | Enzo Doria | 05/2015 |
2437 | 2^670539-25045 | 201853 | Enzo Doria | 09/2013 |
2438 | 10^201801-93 | 201801 | Robert Price | 02/2023 |
2439 | 43284^43519-43519^43284 | 201769 | Norbert Schneider | 08/2018 |
2440 | 2^670213+282317 | 201755 | Enzo Doria | 09/2016 |
2441 | 2^670133+89 | 201731 | Stefano Morozzi | 05/2021 |
2442 | 2^669854-113501 | 201647 | Enzo Doria | 08/2014 |
2443 | 2^669718+81619 | 201606 | Enzo Doria | 08/2016 |
2444 | (299*10^201547-17)/3 | 201549 | Robert Price | 02/2023 |
2445 | (145*10^201504-1)/9 | 201506 | Serge Batalov | 12/2014 |
2446 | 2^668938-1839821 | 201371 | Enzo Doria | 06/2015 |
2447 | (198^87623-1)/197 | 201239 | Anonymous | 06/2024 |
2448 | 2^668492+1879303 | 201237 | Enzo Doria | 08/2016 |
2449 | 7*10^201140-87 | 201141 | Robert Price | 03/2023 |
2450 | 6^258413-5^258413 | 201085 | Jean-Louis Charton | 03/2013 |
2451 | 10194^50161-50161^10194 | 201063 | Norbert Schneider | 09/2020 |
2452 | 2^667894+1875589 | 201057 | Enzo Doria | 06/2016 |
2453 | 2^667569-1836559 | 200959 | Enzo Doria | 05/2015 |
2454 | (172*10^200746-1)/9 | 200748 | Serge Batalov | 12/2014 |
2455 | (166^90407-1)/165 | 200712 | Anonymous | 06/2024 |
2456 | 2^666430+782569 | 200616 | Enzo Doria | 10/2016 |
2457 | (13*10^200610-43)/3 | 200611 | Robert Price | 08/2023 |
2458 | (8*10^200408-11)/3 | 200409 | Robert Price | 07/2023 |
2459 | p(38635)#-p(38635+1) | 200356 | Henri Lifchitz | 11/2024 |
2460 | (19*10^200260+101)/3 | 200261 | Robert Price | 06/2023 |
2461 | 43183^43183+4^4 | 200167 | Serge Batalov | 04/2024 |
2462 | (86^103471+1)/87 | 200163 | Paul Bourdelais | 05/2018 |
2463 | (10^(2*100072+1)+36*10^100072-1)/9 | 200145 | Robert Price | 09/2023 |
2464 | 2^664778+34789 | 200119 | Enzo Doria | 07/2024 |
2465 | 103*(10^100000+20110)^2-4707*(10^100000+20110)+50383 | 200003 | Robert Price | 05/2017 |
2466 | 103*(10^100000+33798)^2-4707*(10^100000+33798)+50383 | 200003 | Robert Price | 01/2018 |
2467 | numbpart(32235776596) | 200002 | Serge Batalov | 04/2017 |
2468 | (10^200001+149)/3 | 200001 | Serge Batalov | 12/2014 |
2469 | 10^200000+571791 | 200001 | Patrick De Geest | 08/2019 |
2470 | (3^419180-621444)/3 | 200000 | Stefano Morozzi | 06/2019 |
2471 | (3^419180-1941384)/3 | 200000 | Stefano Morozzi | 08/2019 |
2472 | 10^200000-45557 | 200000 | Patrick De Geest | 08/2019 |
2474 | (10^200000-1)/9-10^58838 | 200000 | Akihiko Yoshida | 04/2020 |
2473 | 2593604092947240127723272^8192+2593604092947240127722755^8192 | 200000 | Youcef Lemsafer | 01/2023 |
2475 | (2593604092947240127723019^8192+2593604092947240127723011^8192)/2 | 199999 | Youcef Lemsafer | 01/2023 |
2476 | (2593604092947240127723087^8192+2593604092947240127722984^8192)/147457 | 199994 | Youcef Lemsafer | 01/2023 |
2477 | (2593604092947240127723229^8192+2593604092947240127723171^8192)/15032745986 | 199989 | Youcef Lemsafer | 01/2023 |
2478 | (2593604092947240127723215^8192+2593604092947240127722938^8192)/12728329863169 | 199986 | Youcef Lemsafer | 01/2023 |
2479 | 92*10^199980-9 | 199982 | Robert Price | 12/2021 |
2480 | (2593604092947240127723216^8192+2593604092947240127723163^8192)/20172788859482903707649 | 199977 | Youcef Lemsafer | 01/2023 |
2481 | (85*10^199951-139)/9 | 199952 | Robert Price | 08/2021 |
2482 | (10^199926+7)/29/373/2339 | 199919 | Alfred Reich | 08/2021 |
2483 | 2^663838+25819 | 199836 | Enzo Doria | 11/2023 |
2484 | 23*10^199833-9 | 199835 | Robert Price | 10/2021 |
2485 | fibonacci(956176)-4 | 199829 | Jon Grantham | 08/2023 |
2486 | (299*10^199801-17)/3 | 199803 | Robert Price | 04/2020 |
2487 | 6*10^199788+77 | 199789 | Robert Price | 06/2020 |
2488 | (2^663604+1)/270750449 | 199757 | Anonymous | 10/2024 |
2489 | (23*10^199615+37)/3 | 199616 | Robert Price | 02/2022 |
2490 | (17*10^199607-167)/3 | 199608 | Robert Price | 05/2022 |
2491 | 2^663020-933075 | 199589 | Paul Bourdelais | 06/2021 |
2492 | 2^663007+29963 | 199585 | Enzo Doria | 03/2024 |
2493 | 3*2^662703-5 | 199494 | Jon Grantham | 07/2023 |
2494 | (14*10^199447+73)/3 | 199448 | Robert Price | 12/2018 |
2495 | (2^662424-15)/7 | 199409 | Stefano Morozzi | 08/2022 |
2496 | 2^662194+22189 | 199341 | Enzo Doria | 09/2023 |
2497 | 2^662103-29287 | 199313 | Enzo Doria | 08/2015 |
2498 | (2*10^199283+457)/9 | 199283 | Robert Price | 01/2018 |
2499 | (10^199248-19)/9 | 199248 | Robert Price | 01/2018 |
2500 | (83*10^199213+529)/9 | 199214 | Robert Price | 12/2021 |