PRP Records

Probable Primes Top 10000

(295148 PRPs in the top)

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) !!!

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 1-250 251-500 501-750 751-1000 1001-1250 1251-1500 1501-1750 1751-2000 2001-2250 2251-2500 2501-2750 2751-3000 3001-3250 3251-3500 3501-3750 3751-4000 4001-4250 4251-4500 4501-4750 4751-5000 5001-5250 5251-5500 5501-5750 5751-6000 6001-6250 6251-6500 6501-6750 6751-7000 7001-7250 7251-7500 7501-7750 7751-8000 8001-8250 8251-8500 8501-8750 8751-9000 9001-9250 9251-9500 9501-9750 9751-10000

 Rank Probable prime Digits (> 50000) Who ? When ? 2251 (62*10^185216-413)/9 185217 Robert Price 09/2021 2252 (232*10^185180+17)/3 185182 Robert Price 04/2021 2253 56*10^185139-3 185141 Robert Price 03/2020 2254 (28*10^185105+47)/3 185106 Robert Price 02/2021 2255 2^614783-2790097 185069 Enzo Doria 12/2015 2256 2^614745-29323 185057 Enzo Doria 07/2015 2257 (((((((((((2^3+3)^3+30)^3+6)^3+80)^3+12)^3+450)^3+894)^3+3636)^3+70756)^3+97220)^3+66768)^3+300840 185052 Serge Batalov 07/2013 2258 (49*10^184993-67)/9 184994 Robert Price 03/2019 2259 (5*10^184954-191)/3 184955 Robert Price 05/2021 2260 (14*10^184950+211)/9 184951 Robert Price 04/2018 2261 2^614360+215221 184941 Enzo Doria 11/2023 2262 2^614315+81353 184928 Enzo Doria 08/2016 2263 2^614294-1849961 184921 Enzo Doria 08/2015 2264 2^614266+1877809 184913 Enzo Doria 08/2016 2265 (185*10^184878-11)/3 184880 Robert Price 10/2020 2266 91*10^184867-9 184869 Robert Price 06/2021 2267 39803^40170-40170^39803 184779 Norbert Schneider 05/2024 2268 (14789^44521-1)/(14789^211-1) 184770 Ryan Propper 11/2023 2269 (85*10^184768+77)/9 184769 Robert Price 07/2022 2270 2^613715-1860727 184747 Enzo Doria 11/2015 2271 (4*10^184730+89)/3 184731 Robert Price 08/2021 2272 2*10^184723+41 184724 Robert Price 05/2018 2273 (49*10^184703+293)/9 184704 Robert Price 03/2021 2274 2^613487-349987 184678 Enzo Doria 07/2015 2275 (95^93377+1)/96 184672 Paul Bourdelais 11/2017 2276 14^161089-161089^14 184629 Serge Batalov 05/2016 2277 40008^40109-40109^40008 184588 Norbert Schneider 05/2024 2278 2^613033-114621 184542 Enzo Doria 05/2015 2279 3*2^612759+5 184460 Jon Grantham 07/2023 2280 2^612587+213413 184408 Enzo Doria 09/2023 2281 (9^193247+1)/10 184404 Paul Bourdelais 02/2010 2282 2^612424+212341 184358 Enzo Doria 08/2023 2283 2^612341-1604809 184334 Enzo Doria 05/2015 2284 (11*10^184308-161)/3 184309 Robert Price 11/2021 2285 (2^611999-1)/18464214225958267477777390354183 184199 Dario Alpern 06/2017 2286 (14*10^184150+37)/3 184151 Robert Price 12/2018 2287 2^611731-4837 184150 Yves Minet 08/2018 2288 3*10^184124-7 184125 Robert Price 08/2015 2289 2^611644+29371 184124 Enzo Doria 02/2024 2290 9*10^184122-11 184123 Mischa Rodermond 04/2023 2291 2^611628-24537 184119 Enzo Doria 08/2013 2292 3*10^184110+13 184111 Robert Price 07/2018 2293 (14280^44521-1)/(14280^211-1) 184097 Ryan Propper 11/2023 2294 (194*10^184093+1)/3 184095 Robert Price 01/2022 2295 2^611460+71881 184068 Enzo Doria 04/2016 2296 4*10^184004-63 184005 Robert Price 10/2018 2297 2^611111+84083 183963 Boyan Hu 05/2024 2298 2^610982-1867301 183924 Enzo Doria 03/2016 2299 (10^183917+1)/11/9952852373 183906 Alfred Reich 02/2024 2300 3*10^183872-49 183873 Robert Price 07/2018 2301 2^610597+1178897 183809 Enzo Doria 05/2016 2302 (8*10^183773-269)/9 183773 Robert Price 09/2021 2303 (65*10^183768-29)/9 183769 Robert Price 01/2021 2304 (17*10^183764+31)/3 183765 Robert Price 01/2019 2305 (28*10^183760-1)/9 183761 Serge Batalov 10/2014 2306 2^610401+1277 183750 Lelio R Paula 07/2013 2307 2^610356-1849019 183736 Enzo Doria 08/2015 2308 (63^102103+1)/64 183717 Paul Bourdelais 10/2017 2309 23*10^183710-7 183712 Robert Price 02/2020 2310 (2^610289+1)/(3*528882550291) 183704 Gord Palameta 08/2018 2311 (4*10^183659+149)/9 183659 Robert Price 04/2018 2312 (4*10^183657+41)/9 183657 Serge Batalov 11/2022 2313 7*10^183596+39 183597 Robert Price 01/2023 2314 2^609846-1834251 183582 Enzo Doria 07/2015 2315 10^183546+1547323 183547 Patrick De Geest 02/2021 2317 10^183546-800000001 183546 Robert Price 09/2020 2316 10^183546-584297 183546 Patrick De Geest 02/2021 2318 7*10^183511+39 183512 Robert Price 01/2023 2319 (23*10^183477-71)/3 183478 Robert Price 07/2020 2320 11^176176-240 183469 Enzo Doria 11/2012 2321 (41^113749+1)/42 183451 Paul Bourdelais 11/2017 2322 6*10^183429+53 183430 Robert Price 05/2020 2323 (28*10^183403+191)/3 183404 Robert Price 02/2020 2324 (101^91463+1)/102 183320 Paul Bourdelais 11/2017 2325 2^608965-113989 183317 Enzo Doria 10/2014 2326 A005165(43592) 183312 Serge Batalov 07/2017 2327 (61*10^183294+119)/9 183295 Robert Price 05/2019 2328 2^608814-461261 183272 Enzo Doria 06/2015 2329 (163*10^183227-1)/9 183229 Serge Batalov 12/2014 2330 2^608541-608541^2 183190 Henri Lifchitz 02/2018 2331 2^608293+143807 183115 Enzo Doria 10/2016 2332 2^608164-462419 183076 Enzo Doria 08/2015 2333 2^607950-1862303 183012 Enzo Doria 12/2015 2334 5*3^383376+2^383376 182918 Jon Grantham 08/2023 2335 (46*10^182896+683)/9 182897 Robert Price 03/2019 2336 (2*10^182787+73)/3 182787 Robert Price 09/2020 2337 2^607101+1871987 182756 Enzo Doria 05/2016 2338 2^606869-69175 182686 Enzo Doria 11/2015 2339 8*10^182671+71 182672 Robert Price 05/2022 2340 (23*10^182666-71)/3 182667 Robert Price 07/2020 2341 3*10^182614-11 182615 Robert Price 07/2018 2342 2^606560-357 182593 Enzo Doria 05/2014 2343 66*10^182420+7 182422 Robert Price 07/2020 2344 2^605687+1866983 182330 Enzo Doria 03/2016 2345 2^605655-114445 182321 Enzo Doria 02/2015 2346 94*10^182291-3 182293 Robert Price 05/2020 2347 (20^140053+1)/21 182212 Paul Bourdelais 04/2010 2348 (14*10^182177-221)/9 182178 Robert Price 04/2018 2349 2^605174-112751 182176 Enzo Doria 06/2014 2350 (905^61609-1)/904 182154 Anonymous 05/2024 2351 2^604761+1874507 182052 Enzo Doria 06/2016 2352 2^604705+1871957 182035 Enzo Doria 05/2016 2353 (14*10^182000+229)/9 182001 Robert Price 03/2018 2354 (10^181996+41)/3 181996 Robert Price 12/2017 2355 (17*10^181979+91)/9 181980 Robert Price 02/2022 2356 (5*10^181950-101)/3 181951 Robert Price 04/2018 2357 2^603915+75233 181797 Enzo Doria 04/2016 2358 39470^39537+39537^39470 181723 Norbert Schneider 12/2022 2359 (10^181710+7)/563747/2019847 181698 Alfred Reich 08/2021 2360 7*10^181594-57 181595 Robert Price 06/2020 2361 8*10^181580+29 181581 Robert Price 11/2021 2362 (83*10^181544+61)/9 181545 Serge Batalov 01/2023 2363 (2*10^181457+7)/9 181457 Rytis Slatkevicius 01/2023 2364 3*10^181445+23 181446 Robert Price 03/2022 2365 (194*10^181369-11)/3 181371 Robert Price 09/2020 2366 11^174145-360 181354 Enzo Doria 10/2012 2367 2^602351-396765 181326 Enzo Doria 08/2013 2368 6*10^181306+17 181307 Robert Price 04/2019 2369 (353^71143-1)/352 181254 Anonymous 04/2024 2370 (286*10^181220-1)/3 181222 Robert Price 11/2020 2371 2^601957-113833 181208 Enzo Doria 09/2014 2372 66^99581-65^99581 181193 Robert Price 09/2013 2373 10^181182+383973 181183 Patrick De Geest 04/2016 2374 10^181182-21 181182 Serge Batalov 12/2014 2375 (797*10^181171-41)/9 181173 Robert Price 04/2022 2376 2^601722+74209 181137 Enzo Doria 08/2023 2377 (5*10^181127-29)/3 181128 Robert Price 03/2018 2378 2^601521-29143 181076 Enzo Doria 07/2015 2379 2^601442-2797811 181053 Enzo Doria 04/2016 2380 44*10^181029+3 181031 Robert Price 04/2020 2381 5*10^180992-9 180993 Robert Price 05/2015 2382 10^180979+79477 180980 Patrick De Geest 04/2016 2383 10^180979+107739 180980 Patrick De Geest 04/2016 2384 10^180979-11 180979 Serge Batalov 12/2014 2385 2^601023-113851 180926 Enzo Doria 10/2014 2386 (23*10^180862-143)/3 180863 Robert Price 12/2019 2387 3*10^180852+29 180853 Robert Price 05/2018 2388 (277*10^180782-7)/9 180784 Robert Price 02/2022 2389 2^600412+29851 180743 Enzo Doria 03/2024 2390 (8*10^180725-629)/9 180725 Robert Price 01/2022 2391 (79*10^180710-1)/3 180712 Robert Price 02/2020 2392 2^600300-1852559 180709 Enzo Doria 08/2015 2393 (2*10^180706-77)/3 180706 Robert Price 02/2021 2394 (10^180689+71)/9 180689 Serge Batalov 07/2015 2395 2^600209+76487 180681 Enzo Doria 05/2016 2396 2^599999+378461 180618 Norman Luhn 09/2023 2397 (8*10^180536-269)/9 180536 Robert Price 09/2021 2398 2^599702-369885 180529 Enzo Doria 11/2013 2399 Tau(643^11688) 180524 Nik Lygeros / Olivier Rozier 05/2015 2400 (2951*29^123418-3)/4 180490 Curtis Bright 05/2015 2401 (29*10^180432-17)/3 180433 Robert Price 09/2019 2402 4*10^180360+93 180361 Robert Price 08/2018 2403 2^599035+219323 180328 Enzo Doria 03/2024 2404 2^598942+80779 180300 Enzo Doria 07/2016 2405 (38*10^180296+403)/9 180297 Robert Price 10/2018 2406 (85*10^180241+77)/9 180242 Robert Price 07/2022 2407 2^598591-1844797 180194 Enzo Doria 06/2015 2408 (100^90089+1)/101 180176 Paul Bourdelais 08/2017 2409 2^598301+28517 180107 Enzo Doria 01/2024 2410 (29*10^180072+691)/9 180073 Robert Price 08/2021 2411 (59*10^180038+157)/9 180039 Robert Price 12/2021 2412 95*10^180019-9 180021 Robert Price 01/2022 2413 6*10^179970+91 179971 Robert Price 05/2019 2414 (4*10^179963-79)/3 179964 Robert Price 02/2018 2415 (403*10^179944-43)/9 179946 Robert Price 06/2021 2416 Gamma-Prime(179849) 179849 Eric W. Weisstein 06/2011 2417 2^597424-1859729 179843 Enzo Doria 11/2015 2418 Phi(180683,10) 179760 Maksym Voznyy 09/2015 2419 (10^180683-1)*9/(10^643-1)/(10^281-1) 179760 Robert Price 07/2016 2420 (3^376657-2^376657)/22301107657 179701 Mike Oakes 04/2017 2421 (29*10^179697+223)/9 179698 Robert Price 09/2018 2422 2^596884+73 179680 Stefano Morozzi 04/2021 2423 (11*10^179679+13)/3 179680 Robert Price 03/2022 2424 (68*10^179656+7)/3 179658 Robert Price 01/2020 2425 (10^179643+173)/3 179643 Robert Price 05/2021 2426 2^596690-461261 179622 Enzo Doria 07/2015 2427 2^596684-113939 179620 Enzo Doria 10/2014 2428 2^596642+39 179608 Jon Grantham 08/2023 2429 2*10^179602+63 179603 Robert Price 05/2018 2430 32262^39815-39815^32262 179514 Frank Doornink 02/2024 2431 (25*10^179488-403)/9 179489 Robert Price 01/2021 2432 7*10^179460+99 179461 Robert Price 05/2021 2433 2^596127+74333 179453 Enzo Doria 07/2023 2434 3^375887-112696 179344 Enzo Doria 07/2014 2435 4*10^179265-71 179266 Robert Price 12/2018 2436 2*10^179193+83 179194 Robert Price 12/2021 2437 2^595144-1850429 179157 Enzo Doria 08/2015 2438 2^595122-5 179150 Stefano Morozzi 07/2022 2439 3*10^179138+89 179139 Robert Price 10/2018 2440 (52*10^179062-133)/9 179063 Robert Price 09/2021 2441 2^594531+82253 178972 Enzo Doria 09/2016 2442 (664*10^178939-61)/9 178941 Robert Price 09/2021 2443 2^594260-2787899 178891 Enzo Doria 11/2015 2444 (14*10^178822+67)/9 178823 Robert Price 05/2022 2445 (29*10^178732-119)/9 178733 Robert Price 12/2021 2446 2^593631+101381 178701 Jorge Menendez 04/2018 2447 10^178695+136719 178696 Patrick De Geest 05/2016 2448 10^178695-71 178695 Serge Batalov 12/2014 2449 (2*10^178649-161)/3 178649 Robert Price 12/2020 2450 (691^62903-1)/690 178609 Michael Stocker 05/2020 2451 (2^148330+1)^4-2 178608 Cletus Emmanuel 12/2003 2452 2^593242+28309 178584 Enzo Doria 01/2024 2453 2^593222-14145 178578 Jorge Menendez 10/2017 2454 7*10^178566+33 178567 Robert Price 06/2020 2455 2^593178+1867219 178565 Enzo Doria 03/2016 2456 2^593152+22441 178557 Enzo Doria 09/2023 2457 (38*10^178456+151)/9 178457 Robert Price 03/2022 2458 (302*10^178369+13)/9 178371 Robert Price 02/2020 2459 (26*10^178296-113)/3 178297 Robert Price 06/2020 2460 (18^142031-1)/17 178287 Paul Bourdelais 03/2010 2461 (13*10^178233+137)/3 178234 Robert Price 06/2021 2462 (5*10^178206+91)/3 178207 Robert Price 04/2018 2463 2^591872-291929 178172 Enzo Doria 07/2015 2464 2^591682-286871 178115 Enzo Doria 07/2015 2465 (7^210761-5^210761)/2 178114 Jon Grantham 08/2023 2466 4*10^178091+9 178092 Robert Price 05/2015 2467 410747#+478483 178007 Makoto Morimoto 02/2016 2468 3*10^177872+73 177873 Robert Price 08/2018 2469 2^590762-396765 177838 Enzo Doria 08/2013 2470 (136*10^177754-1)/9 177756 Serge Batalov 12/2014 2471 ReverseConsecutiveIntegerPrime(37765) 177719 Eric W. Weisstein 04/2010 2472 Smr(37765) 177719 Eric W. Weisstein 12/2021 2473 (266*10^177577-11)/3 177579 Robert Price 04/2020 2474 (11*10^177466-113)/3 177467 Robert Price 10/2018 2475 3*10^177373-97 177374 Robert Price 07/2018 2476 2^589204+1881151 177369 Enzo Doria 11/2016 2477 2^589132-69479 177347 Enzo Doria 01/2016 2478 (101*10^177302-17)/3 177304 Robert Price 02/2020 2479 2^588912-113519 177281 Enzo Doria 08/2014 2480 (682*10^177266-7)/9 177268 Robert Price 08/2021 2481 15^150706+2 177245 Robert Price 06/2015 2482 (31208^39601-1)/(31208^199-1) 177084 Ryan Propper 11/2023 2483 2^588194-1861001 177065 Enzo Doria 11/2015 2484 5*10^177016-37 177017 Robert Price 11/2021 2485 fibonacci(846926)-4 176997 Jon Grantham 08/2023 2486 (23*10^176964-47)/3 176965 Robert Price 09/2019 2487 20530^41031+41031^20530 176942 Norbert Schneider 07/2022 2488 (19*10^176932+521)/9 176933 Robert Price 05/2018 2489 (8*10^176908+43)/3 176909 Robert Price 06/2018 2490 (85*10^176900+203)/9 176901 Robert Price 09/2020 2491 2^587560-113699 176874 Enzo Doria 09/2014 2492 20596^40995+40995^20596 176844 Norbert Schneider 07/2022 2493 (101*10^176815-17)/3 176817 Robert Price 02/2020 2494 (25*10^176715-37)/3 176716 Robert Price 10/2019 2495 5^252763-12862 176674 Enzo Doria 05/2014 2496 38442^38531+38531^38442 176658 Norbert Schneider 09/2022 2497 2^586829+23961 176654 Enzo Doria 10/2023 2498 2^586804+81721 176646 Enzo Doria 08/2016 2499 (10^176584+77)/3 176584 Robert Price 01/2018 2500 2^586570+1874419 176576 Enzo Doria 06/2016

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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: May, 20 2024 09:22 (Time in France)

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