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
Search by form
| Rank |
Probable prime |
Digits (> 50000) |
Who ? |
When ? |
| 3251 | 2^549049+2797607 | 165281 | Enzo Doria | 04/2016 |
| 3252 | (218*10^165258+7)/9 | 165260 | Robert Price | 06/2022 |
| 3253 | (7*10^165239+107)/3 | 165240 | Robert Price | 02/2018 |
| 3254 | 2^548880+23961 | 165230 | Enzo Doria | 10/2023 |
| 3255 | 5*2^548778+3 | 165200 | Jon Grantham | 07/2023 |
| 3256 | (44^100511-1)/43 | 165184 | Paul Bourdelais | 11/2017 |
| 3257 | (7*10^165134+107)/3 | 165135 | Robert Price | 02/2018 |
| 3258 | (301*10^165082+23)/9 | 165084 | Robert Price | 06/2021 |
| 3259 | (23*10^165060-83)/3 | 165061 | Robert Price | 08/2019 |
| 3260 | 7*10^165023-27 | 165024 | Robert Price | 11/2022 |
| 3261 | (76*10^164984+77)/9 | 164985 | Robert Price | 10/2019 |
| 3262 | 31058^36715-36715^31058 | 164931 | Frank Doornink | 01/2024 |
| 3263 | (4*10^164929-211)/9 | 164929 | Robert Price | 03/2022 |
| 3264 | 10^164878-500001 | 164878 | Robert Price | 03/2022 |
| 3265 | 9*10^164791-89 | 164792 | Robert Price | 04/2020 |
| 3266 | 2^547178-1856501 | 164717 | Enzo Doria | 10/2015 |
| 3267 | 11^158160-60 | 164707 | Enzo Doria | 07/2012 |
| 3268 | (26*10^164643-167)/3 | 164644 | Robert Price | 10/2019 |
| 3269 | (10^164643+83)/3 | 164643 | Robert Price | 08/2021 |
| 3270 | 2^546398-59201 | 164483 | Enzo Doria | 10/2015 |
| 3271 | 2^546332-114893 | 164463 | Enzo Doria | 05/2015 |
| 3272 | 36087^36087-36080^36080 | 164462 | Henri Lifchitz | 08/2024 |
| 3273 | 32003^36504-36504^32003 | 164458 | Frank Doornink | 01/2024 |
| 3274 | (65*10^164427+277)/9 | 164428 | Robert Price | 08/2021 |
| 3275 | 2^545958+1876189 | 164350 | Enzo Doria | 07/2016 |
| 3276 | 2^545878-49841 | 164326 | Enzo Doria | 10/2015 |
| 3277 | (10^164284+77)/3 | 164284 | Robert Price | 01/2018 |
| 3278 | 2^545668-4019 | 164263 | Yves Minet | 04/2017 |
| 3279 | 10^164216+780639 | 164217 | Patrick De Geest | 08/2021 |
| 3281 | 10^164216-50000000001 | 164216 | Robert Price | 12/2020 |
| 3280 | 10^164216-891051 | 164216 | Patrick De Geest | 08/2021 |
| 3282 | (13*53^238539*617^9)/10^247183 | 164151 | Hans Havermann | 07/2017 |
| 3283 | (16*10^164122+197)/3 | 164123 | Robert Price | 04/2019 |
| 3284 | 2^545185+76757 | 164118 | Enzo Doria | 05/2016 |
| 3285 | 2^545076-114329 | 164085 | Enzo Doria | 01/2015 |
| 3286 | (2*10^164043-143)/3 | 164043 | Robert Price | 03/2018 |
| 3287 | (33085^36481-1)/(33085^191-1) | 164018 | Ryan Propper | 11/2023 |
| 3288 | (29^112153+1)/30 | 164011 | Lelio R Paula | 03/2017 |
| 3289 | 2^544757+1874777 | 163989 | Enzo Doria | 06/2016 |
| 3290 | 2^544723+211193 | 163978 | Enzo Doria | 08/2023 |
| 3291 | 2^544444-457199 | 163894 | Enzo Doria | 01/2015 |
| 3292 | (32804^36481-1)/(32804^191-1) | 163883 | Ryan Propper | 11/2023 |
| 3293 | 2^544264-343529 | 163840 | Enzo Doria | 07/2015 |
| 3294 | 7*10^163780+9 | 163781 | Robert Price | 09/2015 |
| 3295 | 2^543989+2793047 | 163758 | Enzo Doria | 02/2016 |
| 3296 | (28*10^163709+113)/3 | 163710 | Robert Price | 03/2020 |
| 3297 | (2013^49729-1)/(2013^223-1) | 163561 | Ryan Propper | 11/2023 |
| 3298 | (23*10^163523+301)/9 | 163524 | Robert Price | 06/2021 |
| 3299 | (68*10^163521-329)/9 | 163522 | Robert Price | 03/2021 |
| 3300 | 35820^35899+35899^35820 | 163489 | Norbert Schneider | 11/2021 |
| 3301 | 2^542870-69551 | 163421 | Enzo Doria | 12/2015 |
| 3302 | 2^542502+24799 | 163310 | Enzo Doria | 10/2023 |
| 3303 | 2^542395+72533 | 163278 | Enzo Doria | 04/2016 |
| 3304 | 2^542258+216949 | 163236 | Enzo Doria | 12/2023 |
| 3305 | 2^542072-3683 | 163180 | Yves Minet | 03/2017 |
| 3306 | fibonacci(780566)-4 | 163129 | Jon Grantham | 08/2023 |
| 3307 | (682*10^163106-7)/9 | 163108 | Robert Price | 08/2021 |
| 3308 | 2^541779-1867357 | 163092 | Enzo Doria | 04/2016 |
| 3309 | (29*10^163056+313)/9 | 163057 | Robert Price | 04/2021 |
| 3310 | 2^541476+214743 | 163001 | Enzo Doria | 11/2023 |
| 3311 | 13^142159+14^142159-2 | 162933 | Harsh Aggarwal | 05/2024 |
| 3312 | 8*10^162924+9 | 162925 | Robert Price | 12/2015 |
| 3313 | 2^540905+81557 | 162829 | Enzo Doria | 08/2016 |
| 3314 | 2^540628-2939 | 162746 | Yves Minet | 09/2014 |
| 3315 | 919^54919-918^54919 | 162743 | Jean-Louis Charton | 01/2013 |
| 3316 | (203*10^162689+1)/3 | 162691 | Robert Price | 03/2020 |
| 3317 | 3*10^162620-59 | 162621 | Robert Price | 09/2018 |
| 3318 | 2^540180+26791 | 162611 | Enzo Doria | 12/2023 |
| 3319 | 3^340694-112960 | 162553 | Enzo Doria | 07/2014 |
| 3320 | 2^539925+81 | 162534 | Henri Lifchitz | 11/2024 |
| 3321 | 2^539807-114081 | 162499 | Enzo Doria | 12/2014 |
| 3322 | 414^62093+62093^414 | 162498 | Norbert Schneider | 03/2022 |
| 3323 | 2^539654-114893 | 162453 | Enzo Doria | 05/2015 |
| 3324 | 9*10^162449-71 | 162450 | Robert Price | 11/2020 |
| 3325 | 2^539617-1851583 | 162441 | Enzo Doria | 08/2015 |
| 3326 | (509*10^162422+31)/9 | 162424 | Robert Price | 08/2022 |
| 3327 | (91*10^162410+11)/3 | 162412 | Robert Price | 02/2020 |
| 3328 | 2^539346+81049 | 162360 | Enzo Doria | 07/2016 |
| 3329 | 2^539220-115499 | 162322 | Enzo Doria | 07/2015 |
| 3330 | 2^539217-113713 | 162321 | Enzo Doria | 09/2014 |
| 3331 | 9^170099-8^170099 | 162316 | Jean-Louis Charton | 05/2005 |
| 3332 | 4*10^162263-39 | 162264 | Robert Price | 09/2020 |
| 3333 | 31243^36098-36098^31243 | 162252 | Frank Doornink | 01/2024 |
| 3334 | 31987^36000-36000^31987 | 162180 | Frank Doornink | 01/2024 |
| 3335 | (115*10^162153-1)/3 | 162155 | Serge Batalov | 12/2014 |
| 3336 | (10^162138+11)/3 | 162138 | Serge Batalov | 07/2015 |
| 3337 | (61*10^162100-403)/9 | 162101 | Robert Price | 10/2021 |
| 3338 | 2^538473-112723 | 162097 | Enzo Doria | 06/2014 |
| 3339 | 2^538157+79337 | 162002 | Enzo Doria | 06/2016 |
| 3340 | 2^538136-114749 | 161996 | Enzo Doria | 05/2015 |
| 3341 | 2^538104+1531 | 161986 | Lelio R Paula | 01/2013 |
| 3342 | (9*29^110727-1199)/14 | 161927 | Curtis Bright | 05/2015 |
| 3343 | ((2^179294-1)^3+2)/11 | 161918 | Serge Batalov | 03/2023 |
| 3344 | 31198^36027-36027^31198 | 161910 | Frank Doornink | 01/2024 |
| 3345 | 2^537815-22737 | 161899 | Enzo Doria | 07/2013 |
| 3346 | 2^537804-39839 | 161896 | Enzo Doria | 09/2015 |
| 3347 | (754*10^161816-7)/9 | 161818 | Robert Price | 05/2020 |
| 3348 | 2^537461+29867 | 161792 | Enzo Doria | 03/2024 |
| 3349 | 2^537458-59201 | 161791 | Enzo Doria | 10/2015 |
| 3350 | 2*10^161766+51 | 161767 | Robert Price | 05/2018 |
| 3351 | (7*10^161760+131)/3 | 161761 | Robert Price | 06/2020 |
| 3352 | 2^537209-49849 | 161717 | Enzo Doria | 10/2015 |
| 3353 | (58*10^161691+329)/9 | 161692 | Robert Price | 05/2019 |
| 3354 | 23*10^161668-3 | 161670 | Robert Price | 10/2021 |
| 3355 | 2^536937+1879397 | 161635 | Enzo Doria | 09/2016 |
| 3356 | 3*2^536868-5 | 161614 | Jon Grantham | 07/2023 |
| 3357 | 34*10^161593-9 | 161595 | Robert Price | 06/2020 |
| 3358 | (31*10^161582-1)/3 | 161584 | Robert Price | 02/2020 |
| 3359 | 24494^36813+36813^24494 | 161575 | Norbert Schneider | 11/2023 |
| 3360 | 2^536569-22881 | 161524 | Enzo Doria | 07/2013 |
| 3361 | (46*10^161505+593)/9 | 161506 | Robert Price | 04/2022 |
| 3362 | 10^161253+573493 | 161254 | Patrick De Geest | 07/2018 |
| 3363 | 10^161253-8001 | 161253 | Robert Price | 03/2018 |
| 3364 | 97*10^161247-3 | 161249 | Robert Price | 05/2020 |
| 3365 | 7*10^161192-9 | 161193 | Robert Price | 10/2015 |
| 3366 | 2^535415-19 | 161176 | Stefano Morozzi | 07/2022 |
| 3367 | 2^535269-113803 | 161133 | Enzo Doria | 09/2014 |
| 3368 | 2^535205-23295 | 161113 | Enzo Doria | 08/2013 |
| 3369 | (49*10^161105+437)/9 | 161106 | Robert Price | 09/2021 |
| 3370 | 2^534961+6561 | 161040 | Henri Lifchitz | 11/2024 |
| 3371 | (89^82609+1)/90 | 161036 | Paul Bourdelais | 10/2017 |
| 3372 | 35385^35385-17692^17692 | 160960 | Henri Lifchitz | 10/2024 |
| 3373 | 2^534429-19 | 160880 | Stefano Morozzi | 07/2022 |
| 3374 | 2^534359-23229 | 160859 | Enzo Doria | 08/2013 |
| 3375 | 10^160836-1001 | 160836 | Robert Price | 10/2022 |
| 3376 | 457^60454+60454^457 | 160803 | Norbert Schneider | 07/2021 |
| 3377 | 8*10^160782+53 | 160783 | Robert Price | 08/2020 |
| 3378 | 67^88037-66^88037 | 160763 | Robert Price | 10/2013 |
| 3379 | (88*10^160761-637)/9 | 160762 | Robert Price | 11/2020 |
| 3380 | 2^533981+81 | 160745 | Henri Lifchitz | 11/2024 |
| 3381 | 2^533948-1852559 | 160735 | Enzo Doria | 08/2015 |
| 3382 | 2^533665-23335 | 160650 | Enzo Doria | 08/2013 |
| 3383 | 2^533600+217981 | 160630 | Enzo Doria | 01/2024 |
| 3384 | (19*10^160619+77)/3 | 160620 | Robert Price | 05/2019 |
| 3385 | 2^533350-5 | 160555 | Stefano Morozzi | 07/2022 |
| 3386 | (38*10^160508+151)/9 | 160509 | Robert Price | 03/2022 |
| 3387 | 3^336353-2^336353 | 160482 | Mike Oakes | 10/2007 |
| 3388 | 26134^36315-36315^26134 | 160411 | Frank Doornink | 03/2024 |
| 3389 | 25821^36358-36358^25821 | 160411 | Frank Doornink | 03/2024 |
| 3390 | 2*10^160339-63 | 160340 | Robert Price | 01/2022 |
| 3391 | 24419^36532+36532^24419 | 160293 | Norbert Schneider | 10/2023 |
| 3392 | (91*10^160249+11)/3 | 160251 | Robert Price | 02/2020 |
| 3393 | (772*10^160239-7)/9 | 160241 | Robert Price | 06/2022 |
| 3394 | (2*10^160226+187)/9 | 160226 | Robert Price | 06/2022 |
| 3395 | 2^532253+1868417 | 160225 | Enzo Doria | 04/2016 |
| 3396 | 2^532108-291989 | 160181 | Enzo Doria | 07/2015 |
| 3397 | (28*10^160171-79)/3 | 160172 | Robert Price | 02/2021 |
| 3398 | (26*10^160166-131)/3 | 160167 | Robert Price | 10/2019 |
| 3399 | 55*10^160145+9 | 160147 | Robert Price | 03/2022 |
| 3400 | (17*10^160143+67)/3 | 160144 | Robert Price | 01/2019 |
| 3401 | (394^61637-1)/393 | 159977 | Jinyuan Wang | 04/2023 |
| 3402 | (19*10^159921-49)/3 | 159922 | Robert Price | 05/2019 |
| 3403 | 2^531110-1853771 | 159881 | Enzo Doria | 09/2015 |
| 3404 | (275^65536+53^65536)/2 | 159864 | Kellen Shenton | 11/2020 |
| 3405 | 2^530992-1845299 | 159845 | Enzo Doria | 07/2015 |
| 3406 | 2^530810+25 | 159790 | Stefano Morozzi | 04/2021 |
| 3407 | 25590^36241-36241^25590 | 159753 | Frank Doornink | 02/2024 |
| 3408 | (136*10^159736-1)/9 | 159738 | Serge Batalov | 12/2014 |
| 3409 | 2^530417-113833 | 159672 | Enzo Doria | 09/2014 |
| 3410 | 2^530406-69701 | 159669 | Enzo Doria | 02/2016 |
| 3411 | 5*10^159656+41 | 159657 | Robert Price | 03/2019 |
| 3412 | 8*10^159614+29 | 159615 | Robert Price | 11/2021 |
| 3413 | 7^188858-188858^7 | 159604 | Norbert Schneider | 05/2018 |
| 3414 | 28^110278+27 | 159590 | Alfred Reich | 02/2024 |
| 3415 | (45^96517-2^96517)/43 | 159562 | Robert Price | 11/2024 |
| 3416 | 7*10^159553-27 | 159554 | Robert Price | 11/2022 |
| 3417 | 3^334409-5*2^334409 | 159554 | Jon Grantham | 08/2023 |
| 3418 | (24^115597-1)/23 | 159547 | Paul Bourdelais | 09/2017 |
| 3419 | 25472^36209-36209^25472 | 159540 | Frank Doornink | 01/2024 |
| 3420 | (17*10^159438-377)/9 | 159439 | Robert Price | 03/2018 |
| 3421 | (203*10^159381+1)/3 | 159383 | Robert Price | 03/2020 |
| 3422 | 32282^35343-35343^32282 | 159361 | Frank Doornink | 02/2024 |
| 3423 | 2^529215+219383 | 159310 | Enzo Doria | 02/2024 |
| 3424 | 89*10^159258-9 | 159260 | Robert Price | 05/2020 |
| 3425 | 2^528944-461315 | 159229 | Enzo Doria | 07/2015 |
| 3426 | (13*10^159147+161)/3 | 159148 | Robert Price | 11/2018 |
| 3427 | 2^528620-113879 | 159131 | Enzo Doria | 10/2014 |
| 3428 | 32125^35306-35306^32125 | 159119 | Frank Doornink | 02/2024 |
| 3429 | (47*10^159083+259)/9 | 159084 | Robert Price | 03/2022 |
| 3430 | (861^54181-1)/860 | 159019 | Jinyuan Wang | 11/2023 |
| 3431 | 2^528000-23307 | 158944 | Enzo Doria | 08/2013 |
| 3432 | (29*10^158909+61)/9 | 158910 | Robert Price | 08/2018 |
| 3433 | 2^527817+1876817 | 158889 | Enzo Doria | 07/2016 |
| 3434 | 2^527774-49451 | 158876 | Enzo Doria | 10/2015 |
| 3435 | 2^527745-291553 | 158868 | Enzo Doria | 07/2015 |
| 3436 | (91*10^158862+11)/3 | 158864 | Robert Price | 02/2020 |
| 3437 | 2^527644-1856999 | 158837 | Enzo Doria | 10/2015 |
| 3438 | (37200^37199-37198^37199)/(2^37199) | 158822 | Henri Lifchitz | 06/2013 |
| 3439 | (17*10^158819+7)/3 | 158820 | Robert Price | 06/2023 |
| 3440 | 2^527573-1863253 | 158816 | Enzo Doria | 12/2015 |
| 3441 | 2^527553-23401 | 158810 | Enzo Doria | 08/2013 |
| 3442 | (49*10^158783+437)/9 | 158784 | Robert Price | 09/2021 |
| 3443 | 10^158755+310207 | 158756 | Patrick De Geest | 08/2021 |
| 3444 | 10^158755-50001 | 158755 | Robert Price | 08/2020 |
| 3445 | (61*10^158748-619)/9 | 158749 | Robert Price | 03/2022 |
| 3446 | 11^152420-210 | 158730 | Enzo Doria | 09/2012 |
| 3447 | (13*10^158694+401)/9 | 158695 | Robert Price | 01/2018 |
| 3448 | 2^527052-69059 | 158659 | Enzo Doria | 11/2015 |
| 3449 | 2^526849-113233 | 158598 | Enzo Doria | 07/2014 |
| 3450 | 24286^36161+36161^24286 | 158579 | Norbert Schneider | 08/2023 |
| 3451 | (2^526763-lucasV(1,2,526763)+1)/2 | 158572 | Mike Oakes | 11/2016 |
| 3452 | (299*10^158544-17)/3 | 158546 | Robert Price | 04/2020 |
| 3453 | 2^526658-3551 | 158540 | Yves Minet | 03/2017 |
| 3454 | 7*10^158465-11 | 158466 | Robert Price | 06/2019 |
| 3455 | (7^187507-3^187507)/4 | 158462 | Jon Grantham | 08/2023 |
| 3456 | 2^526375-23115 | 158455 | Enzo Doria | 08/2013 |
| 3457 | (77*10^158407-293)/9 | 158408 | Robert Price | 09/2019 |
| 3458 | 31209^35242-35242^31209 | 158388 | Frank Doornink | 01/2024 |
| 3459 | 32071^35144-35144^32071 | 158363 | Frank Doornink | 01/2024 |
| 3460 | 2^526028-112793 | 158351 | Enzo Doria | 07/2014 |
| 3461 | (229*10^158339-1)/3 | 158341 | Robert Price | 07/2020 |
| 3462 | 32042^35123-35123^32042 | 158255 | Frank Doornink | 01/2024 |
| 3463 | 2^525690-9221 | 158249 | Lelio R Paula | 01/2013 |
| 3464 | 2*10^158242-7 | 158243 | Robert Price | 10/2015 |
| 3465 | 2^525667-525667^2 | 158242 | Henri Lifchitz | 12/2017 |
| 3466 | (56*10^158230+187)/9 | 158231 | Robert Price | 10/2021 |
| 3467 | 10^158209-7000000001 | 158209 | Robert Price | 12/2021 |
| 3468 | 31050^35207-35207^31050 | 158153 | Frank Doornink | 01/2024 |
| 3469 | 2^525186-1857431 | 158097 | Enzo Doria | 10/2015 |
| 3470 | 31527^35108-35108^31527 | 157940 | Frank Doornink | 01/2024 |
| 3471 | 2^524515-23245 | 157895 | Enzo Doria | 08/2013 |
| 3472 | 2^524499-109087 | 157890 | Enzo Doria | 04/2014 |
| 3473 | 2^524384-219533 | 157856 | Enzo Doria | 03/2024 |
| 3475 | 2^18067*(2^506221+1)-1 | 157827 | Makoto Morimoto | 05/2014 |
| 3476 | 2^524288+189093 | 157827 | Makoto Morimoto | 01/2016 |
| 3474 | 2^524288-164073 | 157827 | Matthias Baur | 03/2020 |
| 3477 | (2^(2^19)-9333)/(19*23*463*1213*31973) | 157814 | Makoto Morimoto | 09/2017 |
| 3478 | (10^157792+359)/9 | 157792 | Serge Batalov | 12/2014 |
| 3479 | 2^524154+25 | 157787 | Stefano Morozzi | 04/2021 |
| 3480 | 2^523924+1876591 | 157717 | Enzo Doria | 07/2016 |
| 3481 | (17*10^157705+67)/3 | 157706 | Robert Price | 01/2019 |
| 3482 | (46^94841+1)/47 | 157696 | Robert Price | 01/2014 |
| 3483 | 2^523774+77839 | 157672 | Enzo Doria | 05/2016 |
| 3484 | 2^523587+2799143 | 157616 | Enzo Doria | 04/2016 |
| 3485 | 2^523496+220141 | 157588 | Enzo Doria | 03/2024 |
| 3486 | 2^523371+1872113 | 157551 | Enzo Doria | 05/2016 |
| 3487 | 8*10^157477+27 | 157478 | Robert Price | 09/2021 |
| 3488 | p(30987)#-p(30987+1) | 157417 | Henri Lifchitz | 11/2024 |
| 3489 | 32268^34909-34909^32268 | 157397 | Frank Doornink | 02/2024 |
| 3490 | (8*10^157368+49)/3 | 157369 | Robert Price | 05/2020 |
| 3491 | (82*10^157319+449)/9 | 157320 | Robert Price | 11/2019 |
| 3492 | 2^522535-351457 | 157299 | Enzo Doria | 07/2015 |
| 3493 | 25401^35704-35704^25401 | 157271 | Frank Doornink | 01/2024 |
| 3494 | 2^522226+2799079 | 157206 | Enzo Doria | 04/2016 |
| 3495 | (134*10^157191-11)/3 | 157193 | Robert Price | 01/2022 |
| 3496 | 2^522134-1849451 | 157178 | Enzo Doria | 08/2015 |
| 3497 | 9*10^157152+71 | 157153 | Robert Price | 08/2020 |
| 3498 | 4*10^157150+93 | 157151 | Robert Price | 08/2018 |
| 3499 | 31227^34952-34952^31227 | 157093 | Frank Doornink | 01/2024 |
| 3500 | (32^104347+5^104347)/37 | 157057 | Anonymous | 12/2023 |
