## PRP Records

### Probable Primes Top 10000

#### (295158 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 (16*10^185347+89)/3 185348 Robert Price 03/2021 2252 2^615622+76639 185321 Enzo Doria 05/2016 2253 2^615591+1879223 185312 Enzo Doria 08/2016 2254 2^615587+217013 185311 Enzo Doria 12/2023 2255 2^615503+1876643 185285 Enzo Doria 07/2016 2256 5^265007-4^265007 185232 Jean-Louis Charton 02/2013 2258 (4*10^185221-91)/3 185222 Robert Price 03/2018 2257 (7*10^185221+131)/3 185222 Robert Price 06/2020 2259 (62*10^185216-413)/9 185217 Robert Price 09/2021 2260 (232*10^185180+17)/3 185182 Robert Price 04/2021 2261 56*10^185139-3 185141 Robert Price 03/2020 2262 (28*10^185105+47)/3 185106 Robert Price 02/2021 2263 2^614783-2790097 185069 Enzo Doria 12/2015 2264 2^614745-29323 185057 Enzo Doria 07/2015 2265 (((((((((((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 2266 (49*10^184993-67)/9 184994 Robert Price 03/2019 2267 (5*10^184954-191)/3 184955 Robert Price 05/2021 2268 (14*10^184950+211)/9 184951 Robert Price 04/2018 2269 2^614360+215221 184941 Enzo Doria 11/2023 2270 2^614315+81353 184928 Enzo Doria 08/2016 2271 2^614294-1849961 184921 Enzo Doria 08/2015 2272 2^614266+1877809 184913 Enzo Doria 08/2016 2273 (185*10^184878-11)/3 184880 Robert Price 10/2020 2274 91*10^184867-9 184869 Robert Price 06/2021 2275 39803^40170-40170^39803 184779 Norbert Schneider 05/2024 2276 (14789^44521-1)/(14789^211-1) 184770 Ryan Propper 11/2023 2277 (85*10^184768+77)/9 184769 Robert Price 07/2022 2278 2^613715-1860727 184747 Enzo Doria 11/2015 2279 (4*10^184730+89)/3 184731 Robert Price 08/2021 2280 2*10^184723+41 184724 Robert Price 05/2018 2281 (49*10^184703+293)/9 184704 Robert Price 03/2021 2282 2^613487-349987 184678 Enzo Doria 07/2015 2283 (95^93377+1)/96 184672 Paul Bourdelais 11/2017 2284 14^161089-161089^14 184629 Serge Batalov 05/2016 2285 40008^40109-40109^40008 184588 Norbert Schneider 05/2024 2286 2^613033-114621 184542 Enzo Doria 05/2015 2287 3*2^612759+5 184460 Jon Grantham 07/2023 2288 2^612587+213413 184408 Enzo Doria 09/2023 2289 (9^193247+1)/10 184404 Paul Bourdelais 02/2010 2290 2^612424+212341 184358 Enzo Doria 08/2023 2291 2^612341-1604809 184334 Enzo Doria 05/2015 2292 (11*10^184308-161)/3 184309 Robert Price 11/2021 2293 (2^611999-1)/18464214225958267477777390354183 184199 Dario Alpern 06/2017 2294 (14*10^184150+37)/3 184151 Robert Price 12/2018 2295 2^611731-4837 184150 Yves Minet 08/2018 2296 3*10^184124-7 184125 Robert Price 08/2015 2297 2^611644+29371 184124 Enzo Doria 02/2024 2298 9*10^184122-11 184123 Mischa Rodermond 04/2023 2299 2^611628-24537 184119 Enzo Doria 08/2013 2300 3*10^184110+13 184111 Robert Price 07/2018 2301 (14280^44521-1)/(14280^211-1) 184097 Ryan Propper 11/2023 2302 (194*10^184093+1)/3 184095 Robert Price 01/2022 2303 2^611460+71881 184068 Enzo Doria 04/2016 2304 4*10^184004-63 184005 Robert Price 10/2018 2305 2^611111+84083 183963 Boyan Hu 05/2024 2306 2^610982-1867301 183924 Enzo Doria 03/2016 2307 (10^183917+1)/11/9952852373 183906 Alfred Reich 02/2024 2308 3*10^183872-49 183873 Robert Price 07/2018 2309 2^610597+1178897 183809 Enzo Doria 05/2016 2310 (8*10^183773-269)/9 183773 Robert Price 09/2021 2311 (65*10^183768-29)/9 183769 Robert Price 01/2021 2312 (17*10^183764+31)/3 183765 Robert Price 01/2019 2313 (28*10^183760-1)/9 183761 Serge Batalov 10/2014 2314 2^610401+1277 183750 Lelio R Paula 07/2013 2315 2^610356-1849019 183736 Enzo Doria 08/2015 2316 (63^102103+1)/64 183717 Paul Bourdelais 10/2017 2317 23*10^183710-7 183712 Robert Price 02/2020 2318 (2^610289+1)/(3*528882550291) 183704 Gord Palameta 08/2018 2319 (4*10^183659+149)/9 183659 Robert Price 04/2018 2320 (4*10^183657+41)/9 183657 Serge Batalov 11/2022 2321 7*10^183596+39 183597 Robert Price 01/2023 2322 2^609846-1834251 183582 Enzo Doria 07/2015 2323 10^183546+1547323 183547 Patrick De Geest 02/2021 2325 10^183546-800000001 183546 Robert Price 09/2020 2324 10^183546-584297 183546 Patrick De Geest 02/2021 2326 7*10^183511+39 183512 Robert Price 01/2023 2327 (23*10^183477-71)/3 183478 Robert Price 07/2020 2328 11^176176-240 183469 Enzo Doria 11/2012 2329 (41^113749+1)/42 183451 Paul Bourdelais 11/2017 2330 6*10^183429+53 183430 Robert Price 05/2020 2331 (28*10^183403+191)/3 183404 Robert Price 02/2020 2332 (101^91463+1)/102 183320 Paul Bourdelais 11/2017 2333 2^608965-113989 183317 Enzo Doria 10/2014 2334 A005165(43592) 183312 Serge Batalov 07/2017 2335 (61*10^183294+119)/9 183295 Robert Price 05/2019 2336 2^608814-461261 183272 Enzo Doria 06/2015 2337 (163*10^183227-1)/9 183229 Serge Batalov 12/2014 2338 2^608541-608541^2 183190 Henri Lifchitz 02/2018 2339 2^608293+143807 183115 Enzo Doria 10/2016 2340 2^608164-462419 183076 Enzo Doria 08/2015 2341 2^607950-1862303 183012 Enzo Doria 12/2015 2342 5*3^383376+2^383376 182918 Jon Grantham 08/2023 2343 (46*10^182896+683)/9 182897 Robert Price 03/2019 2344 (2*10^182787+73)/3 182787 Robert Price 09/2020 2345 2^607101+1871987 182756 Enzo Doria 05/2016 2346 2^606869-69175 182686 Enzo Doria 11/2015 2347 8*10^182671+71 182672 Robert Price 05/2022 2348 (23*10^182666-71)/3 182667 Robert Price 07/2020 2349 3*10^182614-11 182615 Robert Price 07/2018 2350 2^606560-357 182593 Enzo Doria 05/2014 2351 66*10^182420+7 182422 Robert Price 07/2020 2352 2^605687+1866983 182330 Enzo Doria 03/2016 2353 2^605655-114445 182321 Enzo Doria 02/2015 2354 94*10^182291-3 182293 Robert Price 05/2020 2355 (20^140053+1)/21 182212 Paul Bourdelais 04/2010 2356 (14*10^182177-221)/9 182178 Robert Price 04/2018 2357 2^605174-112751 182176 Enzo Doria 06/2014 2358 (905^61609-1)/904 182154 Anonymous 05/2024 2359 2^604761+1874507 182052 Enzo Doria 06/2016 2360 2^604705+1871957 182035 Enzo Doria 05/2016 2361 (14*10^182000+229)/9 182001 Robert Price 03/2018 2362 (10^181996+41)/3 181996 Robert Price 12/2017 2363 (17*10^181979+91)/9 181980 Robert Price 02/2022 2364 (5*10^181950-101)/3 181951 Robert Price 04/2018 2365 2^603915+75233 181797 Enzo Doria 04/2016 2366 39470^39537+39537^39470 181723 Norbert Schneider 12/2022 2367 (10^181710+7)/563747/2019847 181698 Alfred Reich 08/2021 2368 7*10^181594-57 181595 Robert Price 06/2020 2369 8*10^181580+29 181581 Robert Price 11/2021 2370 (83*10^181544+61)/9 181545 Serge Batalov 01/2023 2371 (2*10^181457+7)/9 181457 Rytis Slatkevicius 01/2023 2372 3*10^181445+23 181446 Robert Price 03/2022 2373 (194*10^181369-11)/3 181371 Robert Price 09/2020 2374 11^174145-360 181354 Enzo Doria 10/2012 2375 2^602351-396765 181326 Enzo Doria 08/2013 2376 6*10^181306+17 181307 Robert Price 04/2019 2377 (353^71143-1)/352 181254 Anonymous 04/2024 2378 (286*10^181220-1)/3 181222 Robert Price 11/2020 2379 2^601957-113833 181208 Enzo Doria 09/2014 2380 66^99581-65^99581 181193 Robert Price 09/2013 2381 10^181182+383973 181183 Patrick De Geest 04/2016 2382 10^181182-21 181182 Serge Batalov 12/2014 2383 (797*10^181171-41)/9 181173 Robert Price 04/2022 2384 2^601722+74209 181137 Enzo Doria 08/2023 2385 (5*10^181127-29)/3 181128 Robert Price 03/2018 2386 2^601521-29143 181076 Enzo Doria 07/2015 2387 2^601442-2797811 181053 Enzo Doria 04/2016 2388 44*10^181029+3 181031 Robert Price 04/2020 2389 5*10^180992-9 180993 Robert Price 05/2015 2390 10^180979+79477 180980 Patrick De Geest 04/2016 2391 10^180979+107739 180980 Patrick De Geest 04/2016 2392 10^180979-11 180979 Serge Batalov 12/2014 2393 2^601023-113851 180926 Enzo Doria 10/2014 2394 (23*10^180862-143)/3 180863 Robert Price 12/2019 2395 3*10^180852+29 180853 Robert Price 05/2018 2396 (277*10^180782-7)/9 180784 Robert Price 02/2022 2397 2^600412+29851 180743 Enzo Doria 03/2024 2398 (8*10^180725-629)/9 180725 Robert Price 01/2022 2399 (79*10^180710-1)/3 180712 Robert Price 02/2020 2400 2^600300-1852559 180709 Enzo Doria 08/2015 2401 (2*10^180706-77)/3 180706 Robert Price 02/2021 2402 (10^180689+71)/9 180689 Serge Batalov 07/2015 2403 2^600209+76487 180681 Enzo Doria 05/2016 2404 2^599999+378461 180618 Norman Luhn 09/2023 2405 (8*10^180536-269)/9 180536 Robert Price 09/2021 2406 2^599702-369885 180529 Enzo Doria 11/2013 2407 Tau(643^11688) 180524 Nik Lygeros / Olivier Rozier 05/2015 2408 (2951*29^123418-3)/4 180490 Curtis Bright 05/2015 2409 (29*10^180432-17)/3 180433 Robert Price 09/2019 2410 4*10^180360+93 180361 Robert Price 08/2018 2411 2^599035+219323 180328 Enzo Doria 03/2024 2412 2^598942+80779 180300 Enzo Doria 07/2016 2413 (38*10^180296+403)/9 180297 Robert Price 10/2018 2414 (85*10^180241+77)/9 180242 Robert Price 07/2022 2415 2^598591-1844797 180194 Enzo Doria 06/2015 2416 (100^90089+1)/101 180176 Paul Bourdelais 08/2017 2417 2^598301+28517 180107 Enzo Doria 01/2024 2418 (29*10^180072+691)/9 180073 Robert Price 08/2021 2419 (59*10^180038+157)/9 180039 Robert Price 12/2021 2420 95*10^180019-9 180021 Robert Price 01/2022 2421 6*10^179970+91 179971 Robert Price 05/2019 2422 (4*10^179963-79)/3 179964 Robert Price 02/2018 2423 (403*10^179944-43)/9 179946 Robert Price 06/2021 2424 Gamma-Prime(179849) 179849 Eric W. Weisstein 06/2011 2425 2^597424-1859729 179843 Enzo Doria 11/2015 2426 Phi(180683,10) 179760 Maksym Voznyy 09/2015 2427 (10^180683-1)*9/(10^643-1)/(10^281-1) 179760 Robert Price 07/2016 2428 (3^376657-2^376657)/22301107657 179701 Mike Oakes 04/2017 2429 (29*10^179697+223)/9 179698 Robert Price 09/2018 2430 2^596884+73 179680 Stefano Morozzi 04/2021 2431 (11*10^179679+13)/3 179680 Robert Price 03/2022 2432 (68*10^179656+7)/3 179658 Robert Price 01/2020 2433 (10^179643+173)/3 179643 Robert Price 05/2021 2434 2^596690-461261 179622 Enzo Doria 07/2015 2435 2^596684-113939 179620 Enzo Doria 10/2014 2436 2^596642+39 179608 Jon Grantham 08/2023 2437 2*10^179602+63 179603 Robert Price 05/2018 2438 32262^39815-39815^32262 179514 Frank Doornink 02/2024 2439 (25*10^179488-403)/9 179489 Robert Price 01/2021 2440 7*10^179460+99 179461 Robert Price 05/2021 2441 2^596127+74333 179453 Enzo Doria 07/2023 2442 3^375887-112696 179344 Enzo Doria 07/2014 2443 4*10^179265-71 179266 Robert Price 12/2018 2444 2*10^179193+83 179194 Robert Price 12/2021 2445 2^595144-1850429 179157 Enzo Doria 08/2015 2446 2^595122-5 179150 Stefano Morozzi 07/2022 2447 3*10^179138+89 179139 Robert Price 10/2018 2448 (52*10^179062-133)/9 179063 Robert Price 09/2021 2449 2^594531+82253 178972 Enzo Doria 09/2016 2450 (664*10^178939-61)/9 178941 Robert Price 09/2021 2451 2^594260-2787899 178891 Enzo Doria 11/2015 2452 (14*10^178822+67)/9 178823 Robert Price 05/2022 2453 (29*10^178732-119)/9 178733 Robert Price 12/2021 2454 2^593631+101381 178701 Jorge Menendez 04/2018 2455 10^178695+136719 178696 Patrick De Geest 05/2016 2456 10^178695-71 178695 Serge Batalov 12/2014 2457 (2*10^178649-161)/3 178649 Robert Price 12/2020 2458 (691^62903-1)/690 178609 Michael Stocker 05/2020 2459 (2^148330+1)^4-2 178608 Cletus Emmanuel 12/2003 2460 2^593242+28309 178584 Enzo Doria 01/2024 2461 2^593222-14145 178578 Jorge Menendez 10/2017 2462 7*10^178566+33 178567 Robert Price 06/2020 2463 2^593178+1867219 178565 Enzo Doria 03/2016 2464 2^593152+22441 178557 Enzo Doria 09/2023 2465 (38*10^178456+151)/9 178457 Robert Price 03/2022 2466 (302*10^178369+13)/9 178371 Robert Price 02/2020 2467 (26*10^178296-113)/3 178297 Robert Price 06/2020 2468 (18^142031-1)/17 178287 Paul Bourdelais 03/2010 2469 (13*10^178233+137)/3 178234 Robert Price 06/2021 2470 (5*10^178206+91)/3 178207 Robert Price 04/2018 2471 2^591872-291929 178172 Enzo Doria 07/2015 2472 2^591682-286871 178115 Enzo Doria 07/2015 2473 (7^210761-5^210761)/2 178114 Jon Grantham 08/2023 2474 4*10^178091+9 178092 Robert Price 05/2015 2475 410747#+478483 178007 Makoto Morimoto 02/2016 2476 3*10^177872+73 177873 Robert Price 08/2018 2477 2^590762-396765 177838 Enzo Doria 08/2013 2478 (136*10^177754-1)/9 177756 Serge Batalov 12/2014 2479 ReverseConsecutiveIntegerPrime(37765) 177719 Eric W. Weisstein 04/2010 2480 Smr(37765) 177719 Eric W. Weisstein 12/2021 2481 (266*10^177577-11)/3 177579 Robert Price 04/2020 2482 (11*10^177466-113)/3 177467 Robert Price 10/2018 2483 3*10^177373-97 177374 Robert Price 07/2018 2484 2^589204+1881151 177369 Enzo Doria 11/2016 2485 2^589132-69479 177347 Enzo Doria 01/2016 2486 (101*10^177302-17)/3 177304 Robert Price 02/2020 2487 2^588912-113519 177281 Enzo Doria 08/2014 2488 (682*10^177266-7)/9 177268 Robert Price 08/2021 2489 15^150706+2 177245 Robert Price 06/2015 2490 (31208^39601-1)/(31208^199-1) 177084 Ryan Propper 11/2023 2491 2^588194-1861001 177065 Enzo Doria 11/2015 2492 5*10^177016-37 177017 Robert Price 11/2021 2493 fibonacci(846926)-4 176997 Jon Grantham 08/2023 2494 (23*10^176964-47)/3 176965 Robert Price 09/2019 2495 20530^41031+41031^20530 176942 Norbert Schneider 07/2022 2496 (19*10^176932+521)/9 176933 Robert Price 05/2018 2497 (8*10^176908+43)/3 176909 Robert Price 06/2018 2498 (85*10^176900+203)/9 176901 Robert Price 09/2020 2499 2^587560-113699 176874 Enzo Doria 09/2014 2500 20596^40995+40995^20596 176844 Norbert Schneider 07/2022

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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: May, 27 2024 13:30 (Time in France)

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