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
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Rank |
Probable prime |
Digits (> 50000) |
Who ? |
When ? |
2251 | 2^527644-1856999 | 158837 | Enzo Doria | 10/2015 |
2252 | (37200^37199-37198^37199)/(2^37199) | 158822 | Henri Lifchitz | 06/2013 |
2253 | 2^527573-1863253 | 158816 | Enzo Doria | 12/2015 |
2254 | 2^527553-23401 | 158810 | Enzo Doria | 08/2013 |
2255 | (49*10^158783+437)/9 | 158784 | Robert Price | 09/2021 |
2256 | 10^158755+310207 | 158756 | Patrick De Geest | 08/2021 |
2257 | 10^158755-50001 | 158755 | Robert Price | 08/2020 |
2258 | (61*10^158748-619)/9 | 158749 | Robert Price | 03/2022 |
2259 | 11^152420-210 | 158730 | Enzo Doria | 09/2012 |
2260 | (13*10^158694+401)/9 | 158695 | Robert Price | 01/2018 |
2261 | 2^527052-69059 | 158659 | Enzo Doria | 11/2015 |
2262 | 2^526849-113233 | 158598 | Enzo Doria | 07/2014 |
2263 | (2^526763-lucasV(1,2,526763)+1)/2 | 158572 | Mike Oakes | 11/2016 |
2264 | (299*10^158544-17)/3 | 158546 | Robert Price | 04/2020 |
2265 | 2^526658-3551 | 158540 | Yves Minet | 03/2017 |
2266 | 7*10^158465-11 | 158466 | Robert Price | 06/2019 |
2267 | 2^526375-23115 | 158455 | Enzo Doria | 08/2013 |
2268 | (77*10^158407-293)/9 | 158408 | Robert Price | 09/2019 |
2269 | 2^526028-112793 | 158351 | Enzo Doria | 07/2014 |
2270 | (229*10^158339-1)/3 | 158341 | Robert Price | 07/2020 |
2271 | 2^525690-9221 | 158249 | Lelio R Paula | 01/2013 |
2272 | 2*10^158242-7 | 158243 | Robert Price | 10/2015 |
2273 | 2^525667-525667^2 | 158242 | Henri Lifchitz | 12/2017 |
2274 | (56*10^158230+187)/9 | 158231 | Robert Price | 10/2021 |
2275 | 10^158209-7000000001 | 158209 | Robert Price | 12/2021 |
2276 | 2^525186-1857431 | 158097 | Enzo Doria | 10/2015 |
2277 | 2^524515-23245 | 157895 | Enzo Doria | 08/2013 |
2278 | 2^524499-109087 | 157890 | Enzo Doria | 04/2014 |
2279 | 2^18067*(2^506221+1)-1 | 157827 | Makoto Morimoto | 05/2014 |
2280 | 2^524288+189093 | 157827 | Makoto Morimoto | 01/2016 |
2281 | 2^524288-164073 | 157827 | Matthias Baur | 03/2020 |
2282 | (2^(2^19)-9333)/(19*23*463*1213*31973) | 157814 | Makoto Morimoto | 09/2017 |
2283 | (10^157792+359)/9 | 157792 | Serge Batalov | 12/2014 |
2284 | 2^524154+25 | 157787 | Stefano Morozzi | 04/2021 |
2285 | 2^523924+1876591 | 157717 | Enzo Doria | 07/2016 |
2286 | (17*10^157705+67)/3 | 157706 | Robert Price | 01/2019 |
2287 | (46^94841+1)/47 | 157696 | Robert Price | 01/2014 |
2288 | 2^523774+77839 | 157672 | Enzo Doria | 05/2016 |
2289 | 2^523587+2799143 | 157616 | Enzo Doria | 04/2016 |
2290 | 2^523371+1872113 | 157551 | Enzo Doria | 05/2016 |
2291 | 8*10^157477+27 | 157478 | Robert Price | 09/2021 |
2292 | (8*10^157368+49)/3 | 157369 | Robert Price | 05/2020 |
2293 | (82*10^157319+449)/9 | 157320 | Robert Price | 11/2019 |
2294 | 2^522535-351457 | 157299 | Enzo Doria | 07/2015 |
2295 | 2^522226+2799079 | 157206 | Enzo Doria | 04/2016 |
2296 | (134*10^157191-11)/3 | 157193 | Robert Price | 01/2022 |
2297 | 2^522134-1849451 | 157178 | Enzo Doria | 08/2015 |
2298 | 9*10^157152+71 | 157153 | Robert Price | 08/2020 |
2299 | 4*10^157150+93 | 157151 | Robert Price | 08/2018 |
2300 | 2^521401-29593 | 156958 | Enzo Doria | 08/2015 |
2301 | 7*10^156956+87 | 156957 | Robert Price | 07/2019 |
2302 | 2^521348-23397 | 156942 | Enzo Doria | 08/2013 |
2303 | 10^156902+34509 | 156903 | Patrick De Geest | 08/2021 |
2305 | 10^156902-80000001 | 156902 | Robert Price | 04/2021 |
2304 | 10^156902-69789 | 156902 | Patrick De Geest | 08/2021 |
2306 | (98^78797+1)/99 | 156901 | Paul Bourdelais | 12/2017 |
2307 | 65^86522+64 | 156857 | Lelio R Paula | 04/2016 |
2308 | 8^173687-7^173687 | 156855 | Jean-Louis Charton | 09/2004 |
2309 | 2^520977-1858183 | 156830 | Enzo Doria | 10/2015 |
2310 | (8*10^156718-101)/3 | 156719 | Robert Price | 08/2018 |
2311 | (10^156640+7)/53 | 156639 | Alfred Reich | 07/2021 |
2312 | 2^520314-1849481 | 156631 | Enzo Doria | 08/2015 |
2313 | (16*10^156563-637)/9 | 156564 | Robert Price | 09/2022 |
2314 | (13*10^156522+89)/3 | 156523 | Robert Price | 09/2018 |
2315 | (2^(6*86654+1)-5)/3 | 156513 | Kevin Acres | 12/2013 |
2316 | (2^519925-5)/3 | 156513 | Stefano Morozzi | 08/2022 |
2317 | (4*10^156501+119)/3 | 156502 | Robert Price | 12/2021 |
2318 | (83*10^156476-101)/9 | 156477 | Robert Price | 08/2021 |
2319 | 3*10^156435-97 | 156436 | Robert Price | 07/2018 |
2320 | (8*10^156371-77)/3 | 156372 | Robert Price | 07/2018 |
2321 | 53^90679-52^90679 | 156356 | Robert Price | 01/2013 |
2322 | (418*10^156309-31)/9 | 156311 | Robert Price | 05/2022 |
2323 | 2^519106-59141 | 156267 | Enzo Doria | 10/2015 |
2324 | 2^519053+6077 | 156251 | Enzo Doria | 02/2016 |
2325 | 2^518968-1860989 | 156225 | Enzo Doria | 11/2015 |
2326 | (25*10^156221-7)/9 | 156222 | Robert Price | 05/2018 |
2327 | 2^518931-2782297 | 156214 | Enzo Doria | 09/2015 |
2328 | 2^518608-2939 | 156117 | Yves Minet | 09/2014 |
2329 | 10*27^109005+697 | 156027 | Curtis Bright | 05/2015 |
2330 | (49*10^155933-319)/9 | 155934 | Robert Price | 10/2021 |
2331 | 2^517967-113485 | 155924 | Enzo Doria | 08/2014 |
2332 | (103*10^155904+17)/3 | 155906 | Robert Price | 08/2020 |
2333 | (8*10^155887-719)/9 | 155887 | Robert Price | 03/2021 |
2334 | 4*10^155853-39 | 155854 | Robert Price | 09/2020 |
2335 | 2^517698+4429 | 155843 | Lelio R Paula | 01/2013 |
2336 | 2^517543-113257 | 155796 | Enzo Doria | 07/2014 |
2337 | (14*10^155740-143)/3 | 155741 | Robert Price | 11/2018 |
2338 | 31^104309-30^104309 | 155563 | Henri Lifchitz | 08/2013 |
2339 | 2^516742-39851 | 155555 | Enzo Doria | 09/2015 |
2340 | (22*10^155543+47)/3 | 155544 | Robert Price | 06/2021 |
2341 | (19*10^155504+131)/3 | 155505 | Robert Price | 06/2020 |
2342 | 7*10^155496+61 | 155497 | Robert Price | 08/2019 |
2343 | 2^516440+1878421 | 155464 | Enzo Doria | 08/2016 |
2344 | 2^515863-1867237 | 155291 | Enzo Doria | 03/2016 |
2345 | 2^515786-461861 | 155268 | Enzo Doria | 07/2015 |
2346 | 2^515644-113247 | 155225 | Enzo Doria | 07/2014 |
2347 | (7*10^155203+107)/3 | 155204 | Robert Price | 02/2018 |
2348 | 10^155163+206871 | 155164 | Patrick De Geest | 05/2021 |
2349 | 10^155163-40001 | 155163 | Robert Price | 01/2021 |
2350 | (17*10^155133-89)/9 | 155134 | Robert Price | 07/2018 |
2351 | 2^515227-114997 | 155099 | Enzo Doria | 06/2015 |
2353 | EPrime(155025) | 155025 | Eric W. Weisstein | 10/2010 |
2352 | (14*10^155024-221)/9 | 155025 | Robert Price | 04/2018 |
2354 | (4*10^155022+173)/3 | 155023 | Robert Price | 02/2018 |
2355 | (266*10^154897+1)/3 | 154899 | Robert Price | 04/2020 |
2356 | (115*10^154869-1)/3 | 154871 | Serge Batalov | 12/2014 |
2357 | (86*10^154853-221)/9 | 154854 | Robert Price | 09/2019 |
2358 | 2^514361+78167 | 154839 | Enzo Doria | 05/2016 |
2359 | 2^514281-115033 | 154815 | Enzo Doria | 06/2015 |
2360 | 2^514194-3311 | 154788 | Yves Minet | 12/2014 |
2361 | (14*10^154773+37)/3 | 154774 | Robert Price | 12/2018 |
2362 | (16*10^154748+131)/3 | 154749 | Robert Price | 03/2022 |
2363 | 6*10^154742-31 | 154743 | Robert Price | 07/2020 |
2364 | (14*10^154645+139)/9 | 154646 | Robert Price | 11/2021 |
2365 | 5*10^154618-79 | 154619 | Robert Price | 03/2021 |
2366 | (167*10^154595+1)/3 | 154597 | Robert Price | 04/2021 |
2367 | 2^513437+1879337 | 154560 | Enzo Doria | 09/2016 |
2368 | 2^513306-113201 | 154521 | Enzo Doria | 07/2014 |
2369 | (10^154494-13)/3 | 154494 | Robert Price | 12/2017 |
2370 | 2^513042-113787 | 154442 | Enzo Doria | 09/2014 |
2371 | (151*10^154434-7)/9 | 154436 | Robert Price | 01/2020 |
2372 | (118*10^154428+11)/3 | 154430 | Robert Price | 03/2022 |
2373 | (14*10^154413+139)/9 | 154414 | Robert Price | 11/2021 |
2374 | (77*10^154389-149)/9 | 154390 | Robert Price | 03/2022 |
2375 | 2^512628-114053 | 154317 | Enzo Doria | 11/2014 |
2376 | 2^512529-49783 | 154287 | Enzo Doria | 10/2015 |
2377 | (355573#+6991)/(6991*2031599) | 154285 | Makoto Morimoto | 06/2019 |
2378 | 2^512315-115297 | 154223 | Enzo Doria | 06/2015 |
2379 | (47*10^154221+241)/9 | 154222 | Robert Price | 06/2022 |
2380 | (7*10^154211+173)/9 | 154211 | Robert Price | 01/2022 |
2381 | 2^512168+79561 | 154178 | Enzo Doria | 06/2016 |
2382 | (77*10^154175+67)/9 | 154176 | Robert Price | 12/2021 |
2383 | (5*10^154158-311)/9 | 154158 | Robert Price | 12/2021 |
2384 | (89*10^154103-737)/9 | 154104 | Robert Price | 01/2022 |
2385 | 4*10^154078-57 | 154079 | Robert Price | 10/2018 |
2386 | (355049#+1859)/(11*13*10148891*62587751) | 154051 | Makoto Morimoto | 06/2019 |
2387 | 7*10^154038-57 | 154039 | Robert Price | 06/2020 |
2388 | 2^511658-114371 | 154025 | Enzo Doria | 02/2015 |
2389 | (57^87719+1)/58 | 154022 | Paul Bourdelais | 11/2017 |
2390 | 2^511580-1846679 | 154001 | Enzo Doria | 07/2015 |
2391 | (259*10^153998-1)/3 | 154000 | Robert Price | 12/2020 |
2392 | 2^511541-113713 | 153990 | Enzo Doria | 09/2014 |
2393 | 49958^32768+49957^32768 | 153965 | Kellen Shenton | 11/2020 |
2394 | 10^153935+970801 | 153936 | Patrick De Geest | 05/2021 |
2395 | 10^153935-1000001 | 153935 | Robert Price | 08/2020 |
2396 | (16*10^153868-73)/3 | 153869 | Robert Price | 07/2020 |
2397 | 9*10^153851-67 | 153852 | Robert Price | 11/2020 |
2398 | 2^511077-112723 | 153850 | Enzo Doria | 06/2014 |
2399 | 69^83653-68^83653 | 153826 | Robert Price | 12/2013 |
2400 | 2^510963-113707 | 153816 | Enzo Doria | 09/2014 |
2401 | (154*10^153810-1)/9 | 153812 | Serge Batalov | 12/2014 |
2402 | (181*25^109991-75077)/8 | 153763 | Curtis Bright | 05/2015 |
2403 | 2*10^153746-3 | 153747 | Robert Price | 07/2015 |
2404 | 2^510626+1179379 | 153714 | Enzo Doria | 05/2016 |
2405 | (7*10^153664+113)/3 | 153665 | Robert Price | 02/2018 |
2406 | 2^510420+81121 | 153652 | Enzo Doria | 07/2016 |
2407 | (197*7^181761-1)/2 | 153608 | Karsten Bonath | 05/2017 |
2408 | 2^509894-459161 | 153494 | Enzo Doria | 05/2015 |
2409 | (74*10^153489+673)/9 | 153490 | Robert Price | 02/2022 |
2410 | (49*10^153484-211)/9 | 153485 | Robert Price | 06/2022 |
2411 | 2^509841+71657 | 153478 | Enzo Doria | 04/2016 |
2412 | 9*10^153446+41 | 153447 | Robert Price | 08/2020 |
2413 | 2^509533-1846723 | 153385 | Enzo Doria | 07/2015 |
2414 | 2^509468-39989 | 153366 | Enzo Doria | 09/2015 |
2415 | 70^83117-69^83117 | 153360 | Robert Price | 01/2014 |
2416 | (7*10^153116-1)/3 | 153117 | Robert Price | 08/2022 |
2417 | (112*10^153025-1)/3 | 153027 | Serge Batalov | 12/2014 |
2418 | (19*10^153010+131)/3 | 153011 | Robert Price | 06/2020 |
2419 | 2^508174-1855151 | 152976 | Enzo Doria | 09/2015 |
2420 | 181^67757-2 | 152974 | Lelio R Paula | 12/2017 |
2421 | 2^508160-1864829 | 152972 | Enzo Doria | 01/2016 |
2422 | 10^152960+412563 | 152961 | Patrick De Geest | 05/2021 |
2423 | 10^152960-50000000001 | 152960 | Robert Price | 12/2020 |
2424 | 10^152960-423749 | 152960 | Patrick De Geest | 05/2021 |
2425 | (71*10^152933-143)/9 | 152934 | Robert Price | 10/2021 |
2426 | 2^507857-1848199 | 152881 | Enzo Doria | 07/2015 |
2427 | 2^507638-115361 | 152815 | Enzo Doria | 07/2015 |
2428 | 2^507551-114025 | 152789 | Enzo Doria | 11/2014 |
2429 | (6^196337+1)/7 | 152780 | Paul Bourdelais | 02/2010 |
2430 | (22*10^152670-13)/9 | 152671 | Robert Price | 06/2018 |
2431 | 2^506451-22339 | 152457 | Enzo Doria | 07/2013 |
2432 | 2^505995-113185 | 152320 | Enzo Doria | 07/2014 |
2433 | (8*10^152260-17)/9 | 152260 | Serge Batalov | 11/2022 |
2434 | (4*10^152253+149)/9 | 152253 | Robert Price | 04/2018 |
2435 | 578^55117-577^55117 | 152230 | Jean-Louis Charton | 08/2012 |
2436 | 2^505431-505431 | 152150 | Henri Lifchitz | 04/2005 |
2437 | (203*10^152143+1)/3 | 152145 | Robert Price | 03/2020 |
2438 | 2^505053+73097 | 152037 | Enzo Doria | 04/2016 |
2439 | 22*10^151998+3 | 152000 | Robert Price | 01/2020 |
2440 | (238*10^151979-1)/3 | 151981 | Robert Price | 04/2020 |
2441 | (2^504793-7)/46765 | 151954 | Lelio R Paula | 12/2017 |
2442 | 350377#+797581 | 151937 | Nicolas PALAU | 08/2017 |
2443 | (79*10^151906-529)/9 | 151907 | Robert Price | 01/2022 |
2444 | 2^504618-343991 | 151906 | Enzo Doria | 07/2015 |
2445 | 2^504212-461939 | 151783 | Enzo Doria | 07/2015 |
2446 | 7*10^151772-41 | 151773 | Robert Price | 08/2021 |
2447 | 2^504054-2231 | 151736 | Yves Minet | 10/2011 |
2448 | (28*10^151682+191)/3 | 151683 | Robert Price | 02/2020 |
2449 | 2^503475-933075 | 151562 | Paul Bourdelais | 06/2021 |
2450 | 2^503361-39883 | 151527 | Enzo Doria | 09/2015 |
2451 | 2^503225+382667 | 151486 | Enzo Doria | 10/2016 |
2452 | (206*10^151483-11)/3 | 151485 | Robert Price | 02/2022 |
2453 | (844*10^151396-7)/9 | 151398 | Robert Price | 05/2021 |
2454 | (26*10^151391-503)/9 | 151392 | Robert Price | 07/2018 |
2455 | 2^502769+1877567 | 151349 | Enzo Doria | 08/2016 |
2456 | 2^502576-4019 | 151291 | Yves Minet | 10/2011 |
2457 | 5*10^151257+41 | 151258 | Robert Price | 03/2019 |
2458 | 2^502290-2792501 | 151205 | Enzo Doria | 02/2016 |
2459 | 2^502181+1868417 | 151172 | Enzo Doria | 04/2016 |
2460 | 6*10^151063-77 | 151064 | Robert Price | 09/2021 |
2461 | 2^501781-1850503 | 151052 | Enzo Doria | 08/2015 |
2462 | (5*10^151007+37)/3 | 151008 | Robert Price | 03/2018 |
2463 | 2^501627-991 | 151005 | Yves Minet | 02/2014 |
2464 | 2^501577-115333 | 150990 | Enzo Doria | 07/2015 |
2465 | 8*10^150975+3 | 150976 | Robert Price | 08/2015 |
2466 | 2^501512-113669 | 150971 | Enzo Doria | 09/2014 |
2467 | (83*10^150908+493)/9 | 150909 | Robert Price | 12/2021 |
2468 | 2*10^150818+83 | 150819 | Robert Price | 12/2021 |
2469 | (12^139739+1)/13 | 150803 | Paul Bourdelais | 09/2011 |
2470 | (31^101111-1)/30 | 150792 | Alexander Zhirkov | 11/2010 |
2471 | 2^500899-500899 | 150786 | Henri Lifchitz | 04/2005 |
2472 | 2^500832+1876801 | 150766 | Enzo Doria | 07/2016 |
2473 | (23*10^150763-59)/9 | 150764 | Robert Price | 05/2018 |
2474 | 2^500699+1884953 | 150726 | Enzo Doria | 02/2017 |
2475 | (13*10^150675-37)/3 | 150676 | Robert Price | 01/2019 |
2476 | (2^500527+lucasV(1,2,500527)+1)/4 | 150674 | Mike Oakes | 11/2016 |
2477 | 2^500337-71101 | 150617 | Enzo Doria | 04/2016 |
2478 | (74*10^150616+133)/9 | 150617 | Robert Price | 06/2019 |
2479 | (2*10^150612-17)/3 | 150612 | Serge Batalov | 11/2022 |
2480 | 4*10^150577+91 | 150578 | Robert Price | 08/2018 |
2481 | 2^500160+80071 | 150564 | Enzo Doria | 06/2016 |
2482 | (2^500120+5)/9 | 150551 | Lelio R Paula | 12/2017 |
2483 | (43*10^150515-421)/9 | 150516 | Robert Price | 01/2019 |
2484 | (10^150551-1)/9/385207015049/57498437921/7808738631274081 | 150512 | Maksym Voznyy | 08/2014 |
2485 | (10^150551-1)/1556587827131683185788921941743157225041 | 150512 | Robert Price | 07/2016 |
2486 | 2^499861-29503 | 150474 | Enzo Doria | 08/2015 |
2487 | 2^499653-113533 | 150411 | Enzo Doria | 08/2014 |
2488 | (14*10^150391-191)/3 | 150392 | Robert Price | 10/2020 |
2489 | 2^499534-221 | 150375 | Yves Minet | 06/2012 |
2490 | (28*10^150294+41)/3 | 150295 | Robert Price | 07/2021 |
2491 | 2^499225+49727 | 150282 | Enzo Doria | 09/2016 |
2492 | (695*10^150274+7)/9 | 150276 | Robert Price | 12/2021 |
2493 | 2^499054-29261 | 150231 | Enzo Doria | 07/2015 |
2494 | (844*10^150196-7)/9 | 150198 | Robert Price | 05/2021 |
2495 | 2^498907-933075 | 150186 | Paul Bourdelais | 06/2021 |
2496 | (2^498898-7)/9 | 150183 | Lelio R Paula | 10/2015 |
2497 | 3*10^150182+17 | 150183 | Robert Price | 07/2018 |
2498 | 5*10^150175+63 | 150176 | Robert Price | 09/2020 |
2499 | 32363^33292+33292^32363 | 150149 | Norbert Schneider | 07/2022 |
2500 | (77*10^150128+67)/9 | 150129 | Robert Price | 12/2021 |