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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See the Latest PRPs
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| Rank |
Probable prime |
Digits (> 50000) |
Who ? |
When ? |
| 3251 | (10^183917+1)/11/9952852373 | 183906 | Alfred Reich | 02/2024 |
| 3252 | 3*10^183872-49 | 183873 | Robert Price | 07/2018 |
| 3253 | 2^610597+1178897 | 183809 | Enzo Doria | 05/2016 |
| 3254 | (8*10^183773-269)/9 | 183773 | Robert Price | 09/2021 |
| 3255 | (65*10^183768-29)/9 | 183769 | Robert Price | 01/2021 |
| 3256 | (17*10^183764+31)/3 | 183765 | Robert Price | 01/2019 |
| 3257 | (28*10^183760-1)/9 | 183761 | Serge Batalov | 10/2014 |
| 3258 | 2^610401+1277 | 183750 | Lelio R Paula | 07/2013 |
| 3259 | 2^610356-1849019 | 183736 | Enzo Doria | 08/2015 |
| 3260 | (63^102103+1)/64 | 183717 | Paul Bourdelais | 10/2017 |
| 3261 | 23*10^183710-7 | 183712 | Robert Price | 02/2020 |
| 3262 | (2^610289+1)/(3*528882550291) | 183704 | Gord Palameta | 08/2018 |
| 3263 | (4*10^183659+149)/9 | 183659 | Robert Price | 04/2018 |
| 3264 | (4*10^183657+41)/9 | 183657 | Serge Batalov | 11/2022 |
| 3265 | (11^176327-1)/31738870 | 183619 | Paul Vanderveen | 05/2025 |
| 3266 | 7*10^183596+39 | 183597 | Robert Price | 01/2023 |
| 3267 | 2^609846-1834251 | 183582 | Enzo Doria | 07/2015 |
| 3268 | 10^183546+1547323 | 183547 | Patrick De Geest | 02/2021 |
| 3270 | 10^183546-800000001 | 183546 | Robert Price | 09/2020 |
| 3269 | 10^183546-584297 | 183546 | Patrick De Geest | 02/2021 |
| 3271 | 7*10^183511+39 | 183512 | Robert Price | 01/2023 |
| 3272 | (23*10^183477-71)/3 | 183478 | Robert Price | 07/2020 |
| 3273 | 11^176176-240 | 183469 | Enzo Doria | 11/2012 |
| 3274 | (41^113749+1)/42 | 183451 | Paul Bourdelais | 11/2017 |
| 3275 | 6*10^183429+53 | 183430 | Robert Price | 05/2020 |
| 3276 | (28*10^183403+191)/3 | 183404 | Robert Price | 02/2020 |
| 3277 | U(1096855) | 183383 | Serge Batalov | 07/2024 |
| 3278 | (5^262337-1)/363486427756606700767551233751524443601036 | 183325 | Paul Vanderveen | 05/2025 |
| 3279 | (101^91463+1)/102 | 183320 | Paul Bourdelais | 11/2017 |
| 3280 | 2^608965-113989 | 183317 | Enzo Doria | 10/2014 |
| 3281 | A005165(43592) | 183312 | Serge Batalov | 07/2017 |
| 3282 | (61*10^183294+119)/9 | 183295 | Robert Price | 05/2019 |
| 3283 | 2^608814-461261 | 183272 | Enzo Doria | 06/2015 |
| 3284 | (163*10^183227-1)/9 | 183229 | Serge Batalov | 12/2014 |
| 3285 | 2^608541-608541^2 | 183190 | Henri Lifchitz | 02/2018 |
| 3286 | 2^608293+143807 | 183115 | Enzo Doria | 10/2016 |
| 3287 | Phi(612539,-2) | 183111 | Henri Lifchitz | 02/2026 |
| 3288 | 2^608164-462419 | 183076 | Enzo Doria | 08/2015 |
| 3289 | 2^607950-1862303 | 183012 | Enzo Doria | 12/2015 |
| 3290 | 5*3^383376+2^383376 | 182918 | Jon Grantham | 08/2023 |
| 3291 | (46*10^182896+683)/9 | 182897 | Robert Price | 03/2019 |
| 3292 | (2*10^182787+73)/3 | 182787 | Robert Price | 09/2020 |
| 3293 | 2^607101+1871987 | 182756 | Enzo Doria | 05/2016 |
| 3294 | 2^606869-69175 | 182686 | Enzo Doria | 11/2015 |
| 3295 | 8*10^182671+71 | 182672 | Robert Price | 05/2022 |
| 3296 | (23*10^182666-71)/3 | 182667 | Robert Price | 07/2020 |
| 3297 | 3*10^182614-11 | 182615 | Robert Price | 07/2018 |
| 3298 | 2^606560-357 | 182593 | Enzo Doria | 05/2014 |
| 3299 | 66*10^182420+7 | 182422 | Robert Price | 07/2020 |
| 3300 | 2^605687+1866983 | 182330 | Enzo Doria | 03/2016 |
| 3301 | 2^605655-114445 | 182321 | Enzo Doria | 02/2015 |
| 3302 | 94*10^182291-3 | 182293 | Robert Price | 05/2020 |
| 3303 | (20^140053+1)/21 | 182212 | Paul Bourdelais | 04/2010 |
| 3304 | (14*10^182177-221)/9 | 182178 | Robert Price | 04/2018 |
| 3305 | 2^605174-112751 | 182176 | Enzo Doria | 06/2014 |
| 3306 | (905^61609-1)/904 | 182154 | Anonymous | 05/2024 |
| 3307 | 2^604761+1874507 | 182052 | Enzo Doria | 06/2016 |
| 3308 | 2^604705+1871957 | 182035 | Enzo Doria | 05/2016 |
| 3309 | (14*10^182000+229)/9 | 182001 | Robert Price | 03/2018 |
| 3310 | (10^181996+41)/3 | 181996 | Robert Price | 12/2017 |
| 3311 | (17*10^181979+91)/9 | 181980 | Robert Price | 02/2022 |
| 3312 | (10^181960+3)/7 | 181960 | Jinyuan Wang | 11/2024 |
| 3313 | (5*10^181950-101)/3 | 181951 | Robert Price | 04/2018 |
| 3314 | 2^603915+75233 | 181797 | Enzo Doria | 04/2016 |
| 3315 | 39470^39537+39537^39470 | 181723 | Norbert Schneider | 12/2022 |
| 3316 | (10^181710+7)/563747/2019847 | 181698 | Alfred Reich | 08/2021 |
| 3317 | 7*10^181594-57 | 181595 | Robert Price | 06/2020 |
| 3318 | 8*10^181580+29 | 181581 | Robert Price | 11/2021 |
| 3319 | (83*10^181544+61)/9 | 181545 | Serge Batalov | 01/2023 |
| 3320 | (2*10^181457+7)/9 | 181457 | Rytis Slatkevicius | 01/2023 |
| 3321 | 3*10^181445+23 | 181446 | Robert Price | 03/2022 |
| 3322 | Phi(306341,-5) | 181375 | Henri Lifchitz | 02/2026 |
| 3323 | (194*10^181369-11)/3 | 181371 | Robert Price | 09/2020 |
| 3324 | 11^174145-360 | 181354 | Enzo Doria | 10/2012 |
| 3325 | 2^602351-396765 | 181326 | Enzo Doria | 08/2013 |
| 3326 | 6*10^181306+17 | 181307 | Robert Price | 04/2019 |
| 3327 | (353^71143-1)/352 | 181254 | Anonymous | 04/2024 |
| 3328 | (286*10^181220-1)/3 | 181222 | Robert Price | 11/2020 |
| 3329 | 2^601957-113833 | 181208 | Enzo Doria | 09/2014 |
| 3330 | 66^99581-65^99581 | 181193 | Robert Price | 09/2013 |
| 3331 | 10^181182+383973 | 181183 | Patrick De Geest | 04/2016 |
| 3332 | 10^181182-21 | 181182 | Serge Batalov | 12/2014 |
| 3333 | (797*10^181171-41)/9 | 181173 | Robert Price | 04/2022 |
| 3334 | 33385^40046-40046^33385 | 181151 | Norbert Schneider | 02/2026 |
| 3335 | 2^601722+74209 | 181137 | Enzo Doria | 08/2023 |
| 3336 | (5*10^181127-29)/3 | 181128 | Robert Price | 03/2018 |
| 3337 | 2^601521-29143 | 181076 | Enzo Doria | 07/2015 |
| 3338 | 2^601442-2797811 | 181053 | Enzo Doria | 04/2016 |
| 3339 | 44*10^181029+3 | 181031 | Robert Price | 04/2020 |
| 3340 | 5*10^180992-9 | 180993 | Robert Price | 05/2015 |
| 3341 | 10^180979+79477 | 180980 | Patrick De Geest | 04/2016 |
| 3342 | 10^180979+107739 | 180980 | Patrick De Geest | 04/2016 |
| 3343 | 10^180979-11 | 180979 | Serge Batalov | 12/2014 |
| 3344 | 2^601023-113851 | 180926 | Enzo Doria | 10/2014 |
| 3345 | (23*10^180862-143)/3 | 180863 | Robert Price | 12/2019 |
| 3346 | 3*10^180852+29 | 180853 | Robert Price | 05/2018 |
| 3347 | (277*10^180782-7)/9 | 180784 | Robert Price | 02/2022 |
| 3348 | 2^600412+29851 | 180743 | Enzo Doria | 03/2024 |
| 3349 | (8*10^180725-629)/9 | 180725 | Robert Price | 01/2022 |
| 3350 | (79*10^180710-1)/3 | 180712 | Robert Price | 02/2020 |
| 3351 | 2^600300-1852559 | 180709 | Enzo Doria | 08/2015 |
| 3352 | (2*10^180706-77)/3 | 180706 | Robert Price | 02/2021 |
| 3353 | (156^82393-1)/155 | 180696 | Anonymous | 06/2024 |
| 3354 | (10^180689+71)/9 | 180689 | Serge Batalov | 07/2015 |
| 3355 | 2^600209+76487 | 180681 | Enzo Doria | 05/2016 |
| 3356 | 2^599999+378461 | 180618 | Norman Luhn | 09/2023 |
| 3357 | (8*10^180536-269)/9 | 180536 | Robert Price | 09/2021 |
| 3358 | 2^599702-369885 | 180529 | Enzo Doria | 11/2013 |
| 3359 | Tau(643^11688) | 180524 | Nik Lygeros / Olivier Rozier | 05/2015 |
| 3360 | (2951*29^123418-3)/4 | 180490 | Curtis Bright | 05/2015 |
| 3361 | (29*10^180432-17)/3 | 180433 | Robert Price | 09/2019 |
| 3362 | 4*10^180360+93 | 180361 | Robert Price | 08/2018 |
| 3363 | 2^599035+219323 | 180328 | Enzo Doria | 03/2024 |
| 3364 | 2^598942+80779 | 180300 | Enzo Doria | 07/2016 |
| 3365 | (38*10^180296+403)/9 | 180297 | Robert Price | 10/2018 |
| 3366 | (85*10^180241+77)/9 | 180242 | Robert Price | 07/2022 |
| 3367 | 2^598591-1844797 | 180194 | Enzo Doria | 06/2015 |
| 3368 | (100^90089+1)/101 | 180176 | Paul Bourdelais | 08/2017 |
| 3369 | Phi(90089,-100) | 180176 | Henri Lifchitz | 12/2025 |
| 3370 | 2^598301+28517 | 180107 | Enzo Doria | 01/2024 |
| 3371 | (29*10^180072+691)/9 | 180073 | Robert Price | 08/2021 |
| 3372 | (59*10^180038+157)/9 | 180039 | Robert Price | 12/2021 |
| 3373 | 95*10^180019-9 | 180021 | Robert Price | 01/2022 |
| 3374 | 6*10^179970+91 | 179971 | Robert Price | 05/2019 |
| 3375 | (4*10^179963-79)/3 | 179964 | Robert Price | 02/2018 |
| 3376 | (403*10^179944-43)/9 | 179946 | Robert Price | 06/2021 |
| 3377 | Gamma-Prime(179849) | 179849 | Eric W. Weisstein | 06/2011 |
| 3378 | 2^597424-1859729 | 179843 | Enzo Doria | 11/2015 |
| 3379 | Phi(180683,10) | 179760 | Maksym Voznyy | 09/2015 |
| 3380 | (10^180683-1)*9/(10^643-1)/(10^281-1) | 179760 | Robert Price | 07/2016 |
| 3381 | (3^376657-2^376657)/22301107657 | 179701 | Mike Oakes | 04/2017 |
| 3382 | (29*10^179697+223)/9 | 179698 | Robert Price | 09/2018 |
| 3383 | U(1289697) | 179687 | Serge Batalov | 07/2024 |
| 3385 | 2^596884+73 | 179680 | Stefano Morozzi | 04/2021 |
| 3384 | (11*10^179679+13)/3 | 179680 | Robert Price | 03/2022 |
| 3386 | (68*10^179656+7)/3 | 179658 | Robert Price | 01/2020 |
| 3387 | 26952^40547-40547^26952 | 179648 | Norbert Schneider | 01/2026 |
| 3388 | (10^179643+173)/3 | 179643 | Robert Price | 05/2021 |
| 3389 | 2^596690-461261 | 179622 | Enzo Doria | 07/2015 |
| 3390 | 2^596684-113939 | 179620 | Enzo Doria | 10/2014 |
| 3391 | 2^596642+39 | 179608 | Jon Grantham | 08/2023 |
| 3392 | 2*10^179602+63 | 179603 | Robert Price | 05/2018 |
| 3393 | 32262^39815-39815^32262 | 179514 | Frank Doornink | 02/2024 |
| 3394 | (25*10^179488-403)/9 | 179489 | Robert Price | 01/2021 |
| 3395 | 7*10^179460+99 | 179461 | Robert Price | 05/2021 |
| 3396 | 2^596127+74333 | 179453 | Enzo Doria | 07/2023 |
| 3397 | 3^375887-112696 | 179344 | Enzo Doria | 07/2014 |
| 3398 | 4*10^179265-71 | 179266 | Robert Price | 12/2018 |
| 3399 | 2*10^179193+83 | 179194 | Robert Price | 12/2021 |
| 3400 | 2^595144-1850429 | 179157 | Enzo Doria | 08/2015 |
| 3401 | 2^595122-5 | 179150 | Stefano Morozzi | 07/2022 |
| 3402 | 3*10^179138+89 | 179139 | Robert Price | 10/2018 |
| 3403 | (52*10^179062-133)/9 | 179063 | Robert Price | 09/2021 |
| 3404 | 2^594531+82253 | 178972 | Enzo Doria | 09/2016 |
| 3405 | (664*10^178939-61)/9 | 178941 | Robert Price | 09/2021 |
| 3406 | 2^594260-2787899 | 178891 | Enzo Doria | 11/2015 |
| 3407 | (14*10^178822+67)/9 | 178823 | Robert Price | 05/2022 |
| 3408 | (29*10^178732-119)/9 | 178733 | Robert Price | 12/2021 |
| 3409 | 2^593631+101381 | 178701 | Jorge Menendez | 04/2018 |
| 3410 | 10^178695+136719 | 178696 | Patrick De Geest | 05/2016 |
| 3411 | 10^178695-71 | 178695 | Serge Batalov | 12/2014 |
| 3412 | (2*10^178649-161)/3 | 178649 | Robert Price | 12/2020 |
| 3413 | (691^62903-1)/690 | 178609 | Michael Stocker | 05/2020 |
| 3414 | (2^148330+1)^4-2 | 178608 | Cletus Emmanuel | 12/2003 |
| 3415 | 2^593242+28309 | 178584 | Enzo Doria | 01/2024 |
| 3416 | 2^593222-14145 | 178578 | Jorge Menendez | 10/2017 |
| 3417 | 7*10^178566+33 | 178567 | Robert Price | 06/2020 |
| 3418 | 2^593178+1867219 | 178565 | Enzo Doria | 03/2016 |
| 3419 | 2^593152+22441 | 178557 | Enzo Doria | 09/2023 |
| 3420 | (38*10^178456+151)/9 | 178457 | Robert Price | 03/2022 |
| 3421 | (302*10^178369+13)/9 | 178371 | Robert Price | 02/2020 |
| 3422 | (26*10^178296-113)/3 | 178297 | Robert Price | 06/2020 |
| 3423 | (18^142031-1)/17 | 178287 | Paul Bourdelais | 03/2010 |
| 3424 | (13*10^178233+137)/3 | 178234 | Robert Price | 06/2021 |
| 3425 | (5*10^178206+91)/3 | 178207 | Robert Price | 04/2018 |
| 3426 | 2^591872-291929 | 178172 | Enzo Doria | 07/2015 |
| 3427 | 2^591682-286871 | 178115 | Enzo Doria | 07/2015 |
| 3428 | (7^210761-5^210761)/2 | 178114 | Jon Grantham | 08/2023 |
| 3429 | 4*10^178091+9 | 178092 | Robert Price | 05/2015 |
| 3430 | 2^591435+335931 | 178040 | Enzo Doria | 09/2024 |
| 3431 | Phi(148280,2^11) | 178018 | Henri Lifchitz | 12/2025 |
| 3432 | 410747#+478483 | 178007 | Makoto Morimoto | 02/2016 |
| 3433 | 3*10^177872+73 | 177873 | Robert Price | 08/2018 |
| 3434 | 2^590762-396765 | 177838 | Enzo Doria | 08/2013 |
| 3435 | (136*10^177754-1)/9 | 177756 | Serge Batalov | 12/2014 |
| 3436 | ReverseConsecutiveIntegerPrime(37765) | 177719 | Eric W. Weisstein | 04/2010 |
| 3437 | Smr(37765) | 177719 | Eric W. Weisstein | 12/2021 |
| 3438 | 598^128^209+209^128^598 | 177594 | Henri Lifchitz | 03/2025 |
| 3439 | (266*10^177577-11)/3 | 177579 | Robert Price | 04/2020 |
| 3440 | Phi(100093,2^7) | 177512 | Henri Lifchitz | 10/2025 |
| 3441 | (11*10^177466-113)/3 | 177467 | Robert Price | 10/2018 |
| 3442 | 3*10^177373-97 | 177374 | Robert Price | 07/2018 |
| 3443 | 2^589204+1881151 | 177369 | Enzo Doria | 11/2016 |
| 3444 | 2^589132-69479 | 177347 | Enzo Doria | 01/2016 |
| 3445 | (3^371666)/(371666^3) | 177314 | Henri Lifchitz | 05/2025 |
| 3446 | (101*10^177302-17)/3 | 177304 | Robert Price | 02/2020 |
| 3447 | 2^588912-113519 | 177281 | Enzo Doria | 08/2014 |
| 3448 | (682*10^177266-7)/9 | 177268 | Robert Price | 08/2021 |
| 3449 | 15^150706+2 | 177245 | Robert Price | 06/2015 |
| 3450 | 2^588403+335931 | 177127 | Enzo Doria | 09/2024 |
| 3451 | (31208^39601-1)/(31208^199-1) | 177084 | Ryan Propper | 11/2023 |
| 3452 | 2^588194-1861001 | 177065 | Enzo Doria | 11/2015 |
| 3453 | 5*10^177016-37 | 177017 | Robert Price | 11/2021 |
| 3454 | fibonacci(846926)-4 | 176997 | Jon Grantham | 08/2023 |
| 3455 | (23*10^176964-47)/3 | 176965 | Robert Price | 09/2019 |
| 3456 | 20530^41031+41031^20530 | 176942 | Norbert Schneider | 07/2022 |
| 3457 | (19*10^176932+521)/9 | 176933 | Robert Price | 05/2018 |
| 3458 | (8*10^176908+43)/3 | 176909 | Robert Price | 06/2018 |
| 3459 | Phi(146979,2^7) | 176905 | Henri Lifchitz | 10/2025 |
| 3460 | Phi(342951,2^3) | 176905 | Henri Lifchitz | 12/2025 |
| 3461 | (85*10^176900+203)/9 | 176901 | Robert Price | 09/2020 |
| 3462 | 2^587560-113699 | 176874 | Enzo Doria | 09/2014 |
| 3463 | 20596^40995+40995^20596 | 176844 | Norbert Schneider | 07/2022 |
| 3464 | (101*10^176815-17)/3 | 176817 | Robert Price | 02/2020 |
| 3465 | (25*10^176715-37)/3 | 176716 | Robert Price | 10/2019 |
| 3466 | 5^252763-12862 | 176674 | Enzo Doria | 05/2014 |
| 3467 | 38442^38531+38531^38442 | 176658 | Norbert Schneider | 09/2022 |
| 3468 | 2^586829+23961 | 176654 | Enzo Doria | 10/2023 |
| 3469 | 2^586804+81721 | 176646 | Enzo Doria | 08/2016 |
| 3470 | (10^176584+77)/3 | 176584 | Robert Price | 01/2018 |
| 3471 | 2^586570+1874419 | 176576 | Enzo Doria | 06/2016 |
| 3472 | (157*10^176482-1)/3 | 176484 | Robert Price | 01/2022 |
| 3473 | 5*2^586202+3 | 176466 | Jon Grantham | 07/2023 |
| 3474 | 27122^39799-39799^27122 | 176442 | Frank Doornink | 01/2024 |
| 3475 | 2^585994-3311 | 176402 | Yves Minet | 12/2014 |
| 3476 | 8*10^176383-81 | 176384 | Robert Price | 02/2021 |
| 3477 | (23*10^176357+61)/3 | 176358 | Robert Price | 01/2022 |
| 3478 | 2^585832-112799 | 176354 | Enzo Doria | 07/2014 |
| 3479 | fibonacci(843383)+4 | 176257 | Jon Grantham | 08/2023 |
| 3480 | (29*10^176240+49)/3 | 176241 | Robert Price | 09/2021 |
| 3481 | (2^585387-11)/3 | 176219 | Stefano Morozzi | 08/2022 |
| 3482 | 2^585336-461039 | 176204 | Enzo Doria | 06/2015 |
| 3483 | (25*10^176164+143)/3 | 176165 | Robert Price | 08/2020 |
| 3484 | 2^585095-1848127 | 176132 | Enzo Doria | 08/2015 |
| 3485 | (5*10^176101-311)/9 | 176101 | Robert Price | 12/2021 |
| 3486 | 6*10^176092+77 | 176093 | Robert Price | 06/2020 |
| 3487 | 2^584950-115451 | 176088 | Enzo Doria | 07/2015 |
| 3488 | (646*10^176044+11)/9 | 176046 | Robert Price | 10/2021 |
| 3489 | (7^208283-5^208283)/2 | 176020 | Jon Grantham | 08/2023 |
| 3490 | 2^584671-3697 | 176004 | Yves Minet | 03/2017 |
| 3491 | (13*10^175965-37)/3 | 175966 | Robert Price | 01/2019 |
| 3492 | 31728^39089-39089^31728 | 175957 | Frank Doornink | 01/2024 |
| 3493 | 2*10^175860-87 | 175861 | Robert Price | 04/2018 |
| 3494 | 27009^39670-39670^27009 | 175798 | Frank Doornink | 01/2024 |
| 3495 | (86*10^175774-221)/9 | 175775 | Robert Price | 09/2019 |
| 3496 | 2^583614+216037 | 175686 | Enzo Doria | 11/2023 |
| 3497 | 9*10^175654+47 | 175655 | Robert Price | 01/2022 |
| 3498 | 25430^39869-39869^25430 | 175637 | Frank Doornink | 01/2024 |
| 3499 | 10^175608+2971 | 175609 | Mike Oakes | 05/2010 |
| 3500 | 10^175608-55829 | 175608 | Patrick De Geest | 09/2013 |
