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 ? |
| 3251 | (3^388897+2^388897)/5 | 185551 | Jean-Louis Charton | 09/2011 |
| 3252 | 8*10^185529-67 | 185530 | Robert Price | 08/2019 |
| 3253 | (5*10^185520-11)/3 | 185521 | Tyler Busby | 02/2023 |
| 3254 | 5*2^616124+3 | 185473 | Jon Grantham | 07/2023 |
| 3255 | 2^615916+26791 | 185410 | Enzo Doria | 12/2023 |
| 3256 | 4*10^185355+9 | 185356 | Robert Price | 05/2015 |
| 3257 | (16*10^185347+89)/3 | 185348 | Robert Price | 03/2021 |
| 3258 | 40247^40247-56^56 | 185327 | Henri Lifchitz | 08/2024 |
| 3259 | 2^615622+76639 | 185321 | Enzo Doria | 05/2016 |
| 3260 | 2^615591+1879223 | 185312 | Enzo Doria | 08/2016 |
| 3261 | 2^615587+217013 | 185311 | Enzo Doria | 12/2023 |
| 3262 | 2^615503+1876643 | 185285 | Enzo Doria | 07/2016 |
| 3263 | 5^265007-4^265007 | 185232 | Jean-Louis Charton | 02/2013 |
| 3265 | (4*10^185221-91)/3 | 185222 | Robert Price | 03/2018 |
| 3264 | (7*10^185221+131)/3 | 185222 | Robert Price | 06/2020 |
| 3266 | (62*10^185216-413)/9 | 185217 | Robert Price | 09/2021 |
| 3267 | (232*10^185180+17)/3 | 185182 | Robert Price | 04/2021 |
| 3268 | 56*10^185139-3 | 185141 | Robert Price | 03/2020 |
| 3269 | (28*10^185105+47)/3 | 185106 | Robert Price | 02/2021 |
| 3270 | 2^614783-2790097 | 185069 | Enzo Doria | 12/2015 |
| 3271 | 2^614745-29323 | 185057 | Enzo Doria | 07/2015 |
| 3272 | (((((((((((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 |
| 3273 | (49*10^184993-67)/9 | 184994 | Robert Price | 03/2019 |
| 3274 | (5*10^184954-191)/3 | 184955 | Robert Price | 05/2021 |
| 3275 | (14*10^184950+211)/9 | 184951 | Robert Price | 04/2018 |
| 3276 | 2^614360+215221 | 184941 | Enzo Doria | 11/2023 |
| 3277 | 2^614315+81353 | 184928 | Enzo Doria | 08/2016 |
| 3278 | 2^614294-1849961 | 184921 | Enzo Doria | 08/2015 |
| 3279 | 2^614266+1877809 | 184913 | Enzo Doria | 08/2016 |
| 3280 | (185*10^184878-11)/3 | 184880 | Robert Price | 10/2020 |
| 3281 | 91*10^184867-9 | 184869 | Robert Price | 06/2021 |
| 3282 | (37^117841-1)/581320056003516 | 184784 | Paul Vanderveen | 06/2025 |
| 3283 | 39803^40170-40170^39803 | 184779 | Norbert Schneider | 05/2024 |
| 3284 | (14789^44521-1)/(14789^211-1) | 184770 | Ryan Propper | 11/2023 |
| 3285 | (85*10^184768+77)/9 | 184769 | Robert Price | 07/2022 |
| 3286 | 2^613715-1860727 | 184747 | Enzo Doria | 11/2015 |
| 3287 | (4*10^184730+89)/3 | 184731 | Robert Price | 08/2021 |
| 3288 | 2*10^184723+41 | 184724 | Robert Price | 05/2018 |
| 3289 | (49*10^184703+293)/9 | 184704 | Robert Price | 03/2021 |
| 3290 | 2^613487-349987 | 184678 | Enzo Doria | 07/2015 |
| 3291 | (95^93377+1)/96 | 184672 | Paul Bourdelais | 11/2017 |
| 3292 | 14^161089-161089^14 | 184629 | Serge Batalov | 05/2016 |
| 3293 | 40008^40109-40109^40008 | 184588 | Norbert Schneider | 05/2024 |
| 3294 | 2^613033-114621 | 184542 | Enzo Doria | 05/2015 |
| 3295 | 3*2^612759+5 | 184460 | Jon Grantham | 07/2023 |
| 3296 | 2^612587+213413 | 184408 | Enzo Doria | 09/2023 |
| 3298 | (9^193247+1)/10 | 184404 | Paul Bourdelais | 02/2010 |
| 3297 | Phi(193247,-9) | 184404 | Henri Lifchitz | 12/2025 |
| 3299 | 2^612424+212341 | 184358 | Enzo Doria | 08/2023 |
| 3300 | 2^612341-1604809 | 184334 | Enzo Doria | 05/2015 |
| 3301 | (11*10^184308-161)/3 | 184309 | Robert Price | 11/2021 |
| 3302 | 625^65919+624 | 184302 | Alfred Reich | 04/2026 |
| 3303 | (2^611999-1)/18464214225958267477777390354183 | 184199 | Dario Alpern | 06/2017 |
| 3304 | (14*10^184150+37)/3 | 184151 | Robert Price | 12/2018 |
| 3305 | 2^611731-4837 | 184150 | Yves Minet | 08/2018 |
| 3306 | 3*10^184124-7 | 184125 | Robert Price | 08/2015 |
| 3307 | 2^611644+29371 | 184124 | Enzo Doria | 02/2024 |
| 3308 | 9*10^184122-11 | 184123 | Mischa Rodermond | 04/2023 |
| 3309 | 2^611628-24537 | 184119 | Enzo Doria | 08/2013 |
| 3310 | 3*10^184110+13 | 184111 | Robert Price | 07/2018 |
| 3311 | (14280^44521-1)/(14280^211-1) | 184097 | Ryan Propper | 11/2023 |
| 3312 | (194*10^184093+1)/3 | 184095 | Robert Price | 01/2022 |
| 3313 | 2^611460+71881 | 184068 | Enzo Doria | 04/2016 |
| 3314 | 4*10^184004-63 | 184005 | Robert Price | 10/2018 |
| 3315 | 2^611111+84083 | 183963 | Boyan Hu | 05/2024 |
| 3316 | 2^610982-1867301 | 183924 | Enzo Doria | 03/2016 |
| 3317 | (10^183917+1)/11/9952852373 | 183906 | Alfred Reich | 02/2024 |
| 3318 | 3*10^183872-49 | 183873 | Robert Price | 07/2018 |
| 3319 | 2^610597+1178897 | 183809 | Enzo Doria | 05/2016 |
| 3320 | (8*10^183773-269)/9 | 183773 | Robert Price | 09/2021 |
| 3321 | (65*10^183768-29)/9 | 183769 | Robert Price | 01/2021 |
| 3322 | (17*10^183764+31)/3 | 183765 | Robert Price | 01/2019 |
| 3323 | (28*10^183760-1)/9 | 183761 | Serge Batalov | 10/2014 |
| 3324 | 2^610401+1277 | 183750 | Lelio R Paula | 07/2013 |
| 3325 | 2^610356-1849019 | 183736 | Enzo Doria | 08/2015 |
| 3326 | (63^102103+1)/64 | 183717 | Paul Bourdelais | 10/2017 |
| 3327 | 23*10^183710-7 | 183712 | Robert Price | 02/2020 |
| 3328 | (2^610289+1)/(3*528882550291) | 183704 | Gord Palameta | 08/2018 |
| 3329 | (4*10^183659+149)/9 | 183659 | Robert Price | 04/2018 |
| 3330 | (4*10^183657+41)/9 | 183657 | Serge Batalov | 11/2022 |
| 3331 | (11^176327-1)/31738870 | 183619 | Paul Vanderveen | 05/2025 |
| 3332 | 7*10^183596+39 | 183597 | Robert Price | 01/2023 |
| 3333 | 2^609846-1834251 | 183582 | Enzo Doria | 07/2015 |
| 3334 | 10^183546+1547323 | 183547 | Patrick De Geest | 02/2021 |
| 3336 | 10^183546-800000001 | 183546 | Robert Price | 09/2020 |
| 3335 | 10^183546-584297 | 183546 | Patrick De Geest | 02/2021 |
| 3337 | 7*10^183511+39 | 183512 | Robert Price | 01/2023 |
| 3338 | (23*10^183477-71)/3 | 183478 | Robert Price | 07/2020 |
| 3339 | 11^176176-240 | 183469 | Enzo Doria | 11/2012 |
| 3340 | (41^113749+1)/42 | 183451 | Paul Bourdelais | 11/2017 |
| 3341 | 6*10^183429+53 | 183430 | Robert Price | 05/2020 |
| 3342 | (28*10^183403+191)/3 | 183404 | Robert Price | 02/2020 |
| 3343 | U(1096855) | 183383 | Serge Batalov | 07/2024 |
| 3344 | (5^262337-1)/363486427756606700767551233751524443601036 | 183325 | Paul Vanderveen | 05/2025 |
| 3345 | (101^91463+1)/102 | 183320 | Paul Bourdelais | 11/2017 |
| 3346 | 2^608965-113989 | 183317 | Enzo Doria | 10/2014 |
| 3347 | A005165(43592) | 183312 | Serge Batalov | 07/2017 |
| 3348 | (61*10^183294+119)/9 | 183295 | Robert Price | 05/2019 |
| 3349 | 2^608814-461261 | 183272 | Enzo Doria | 06/2015 |
| 3350 | (163*10^183227-1)/9 | 183229 | Serge Batalov | 12/2014 |
| 3351 | 2^608541-608541^2 | 183190 | Henri Lifchitz | 02/2018 |
| 3352 | 2^608293+143807 | 183115 | Enzo Doria | 10/2016 |
| 3353 | Phi(612539,-2) | 183111 | Henri Lifchitz | 02/2026 |
| 3354 | 2^608164-462419 | 183076 | Enzo Doria | 08/2015 |
| 3355 | 2^607950-1862303 | 183012 | Enzo Doria | 12/2015 |
| 3356 | 5*3^383376+2^383376 | 182918 | Jon Grantham | 08/2023 |
| 3357 | (46*10^182896+683)/9 | 182897 | Robert Price | 03/2019 |
| 3358 | (2*10^182787+73)/3 | 182787 | Robert Price | 09/2020 |
| 3359 | 2^607101+1871987 | 182756 | Enzo Doria | 05/2016 |
| 3360 | 2^606869-69175 | 182686 | Enzo Doria | 11/2015 |
| 3361 | 8*10^182671+71 | 182672 | Robert Price | 05/2022 |
| 3362 | (23*10^182666-71)/3 | 182667 | Robert Price | 07/2020 |
| 3363 | 3*10^182614-11 | 182615 | Robert Price | 07/2018 |
| 3364 | 2^606560-357 | 182593 | Enzo Doria | 05/2014 |
| 3365 | 66*10^182420+7 | 182422 | Robert Price | 07/2020 |
| 3366 | 2^605687+1866983 | 182330 | Enzo Doria | 03/2016 |
| 3367 | 2^605655-114445 | 182321 | Enzo Doria | 02/2015 |
| 3368 | 94*10^182291-3 | 182293 | Robert Price | 05/2020 |
| 3369 | (20^140053+1)/21 | 182212 | Paul Bourdelais | 04/2010 |
| 3370 | (14*10^182177-221)/9 | 182178 | Robert Price | 04/2018 |
| 3371 | 2^605174-112751 | 182176 | Enzo Doria | 06/2014 |
| 3372 | (905^61609-1)/904 | 182154 | Anonymous | 05/2024 |
| 3373 | 2^604761+1874507 | 182052 | Enzo Doria | 06/2016 |
| 3374 | 2^604705+1871957 | 182035 | Enzo Doria | 05/2016 |
| 3375 | (14*10^182000+229)/9 | 182001 | Robert Price | 03/2018 |
| 3376 | (10^181996+41)/3 | 181996 | Robert Price | 12/2017 |
| 3377 | (17*10^181979+91)/9 | 181980 | Robert Price | 02/2022 |
| 3378 | (10^181960+3)/7 | 181960 | Jinyuan Wang | 11/2024 |
| 3379 | (5*10^181950-101)/3 | 181951 | Robert Price | 04/2018 |
| 3380 | 2^603915+75233 | 181797 | Enzo Doria | 04/2016 |
| 3381 | 39470^39537+39537^39470 | 181723 | Norbert Schneider | 12/2022 |
| 3382 | (10^181710+7)/563747/2019847 | 181698 | Alfred Reich | 08/2021 |
| 3383 | 7*10^181594-57 | 181595 | Robert Price | 06/2020 |
| 3384 | 8*10^181580+29 | 181581 | Robert Price | 11/2021 |
| 3385 | (83*10^181544+61)/9 | 181545 | Serge Batalov | 01/2023 |
| 3386 | (2*10^181457+7)/9 | 181457 | Rytis Slatkevicius | 01/2023 |
| 3387 | 3*10^181445+23 | 181446 | Robert Price | 03/2022 |
| 3388 | Phi(306341,-5) | 181375 | Henri Lifchitz | 02/2026 |
| 3389 | (194*10^181369-11)/3 | 181371 | Robert Price | 09/2020 |
| 3390 | 11^174145-360 | 181354 | Enzo Doria | 10/2012 |
| 3391 | 2^602351-396765 | 181326 | Enzo Doria | 08/2013 |
| 3392 | 6*10^181306+17 | 181307 | Robert Price | 04/2019 |
| 3393 | (353^71143-1)/352 | 181254 | Anonymous | 04/2024 |
| 3394 | (286*10^181220-1)/3 | 181222 | Robert Price | 11/2020 |
| 3395 | 2^601957-113833 | 181208 | Enzo Doria | 09/2014 |
| 3396 | 66^99581-65^99581 | 181193 | Robert Price | 09/2013 |
| 3397 | 10^181182+383973 | 181183 | Patrick De Geest | 04/2016 |
| 3398 | 10^181182-21 | 181182 | Serge Batalov | 12/2014 |
| 3399 | (797*10^181171-41)/9 | 181173 | Robert Price | 04/2022 |
| 3400 | 33385^40046-40046^33385 | 181151 | Norbert Schneider | 02/2026 |
| 3401 | 2^601722+74209 | 181137 | Enzo Doria | 08/2023 |
| 3402 | (5*10^181127-29)/3 | 181128 | Robert Price | 03/2018 |
| 3403 | 2^601521-29143 | 181076 | Enzo Doria | 07/2015 |
| 3404 | 2^601442-2797811 | 181053 | Enzo Doria | 04/2016 |
| 3405 | 44*10^181029+3 | 181031 | Robert Price | 04/2020 |
| 3406 | 5*10^180992-9 | 180993 | Robert Price | 05/2015 |
| 3407 | 10^180979+79477 | 180980 | Patrick De Geest | 04/2016 |
| 3408 | 10^180979+107739 | 180980 | Patrick De Geest | 04/2016 |
| 3409 | 10^180979-11 | 180979 | Serge Batalov | 12/2014 |
| 3410 | 2^601023-113851 | 180926 | Enzo Doria | 10/2014 |
| 3411 | (23*10^180862-143)/3 | 180863 | Robert Price | 12/2019 |
| 3412 | 3*10^180852+29 | 180853 | Robert Price | 05/2018 |
| 3413 | (277*10^180782-7)/9 | 180784 | Robert Price | 02/2022 |
| 3414 | 2^600412+29851 | 180743 | Enzo Doria | 03/2024 |
| 3415 | (8*10^180725-629)/9 | 180725 | Robert Price | 01/2022 |
| 3416 | (79*10^180710-1)/3 | 180712 | Robert Price | 02/2020 |
| 3417 | 2^600300-1852559 | 180709 | Enzo Doria | 08/2015 |
| 3418 | (2*10^180706-77)/3 | 180706 | Robert Price | 02/2021 |
| 3419 | (156^82393-1)/155 | 180696 | Anonymous | 06/2024 |
| 3420 | (10^180689+71)/9 | 180689 | Serge Batalov | 07/2015 |
| 3421 | 2^600209+76487 | 180681 | Enzo Doria | 05/2016 |
| 3422 | 2^599999+378461 | 180618 | Norman Luhn | 09/2023 |
| 3423 | (8*10^180536-269)/9 | 180536 | Robert Price | 09/2021 |
| 3424 | 2^599702-369885 | 180529 | Enzo Doria | 11/2013 |
| 3425 | Tau(643^11688) | 180524 | Nik Lygeros / Olivier Rozier | 05/2015 |
| 3426 | (2951*29^123418-3)/4 | 180490 | Curtis Bright | 05/2015 |
| 3427 | (29*10^180432-17)/3 | 180433 | Robert Price | 09/2019 |
| 3428 | 4*10^180360+93 | 180361 | Robert Price | 08/2018 |
| 3429 | 2^599035+219323 | 180328 | Enzo Doria | 03/2024 |
| 3430 | 2^598942+80779 | 180300 | Enzo Doria | 07/2016 |
| 3431 | (38*10^180296+403)/9 | 180297 | Robert Price | 10/2018 |
| 3432 | (85*10^180241+77)/9 | 180242 | Robert Price | 07/2022 |
| 3433 | 2^598591-1844797 | 180194 | Enzo Doria | 06/2015 |
| 3434 | (100^90089+1)/101 | 180176 | Paul Bourdelais | 08/2017 |
| 3435 | Phi(90089,-100) | 180176 | Henri Lifchitz | 12/2025 |
| 3436 | 2^598301+28517 | 180107 | Enzo Doria | 01/2024 |
| 3437 | (29*10^180072+691)/9 | 180073 | Robert Price | 08/2021 |
| 3438 | (59*10^180038+157)/9 | 180039 | Robert Price | 12/2021 |
| 3439 | 95*10^180019-9 | 180021 | Robert Price | 01/2022 |
| 3440 | 6*10^179970+91 | 179971 | Robert Price | 05/2019 |
| 3441 | (4*10^179963-79)/3 | 179964 | Robert Price | 02/2018 |
| 3442 | (403*10^179944-43)/9 | 179946 | Robert Price | 06/2021 |
| 3443 | Gamma-Prime(179849) | 179849 | Eric W. Weisstein | 06/2011 |
| 3444 | 2^597424-1859729 | 179843 | Enzo Doria | 11/2015 |
| 3445 | Phi(180683,10) | 179760 | Maksym Voznyy | 09/2015 |
| 3446 | (10^180683-1)*9/(10^643-1)/(10^281-1) | 179760 | Robert Price | 07/2016 |
| 3447 | (3^376657-2^376657)/22301107657 | 179701 | Mike Oakes | 04/2017 |
| 3448 | (29*10^179697+223)/9 | 179698 | Robert Price | 09/2018 |
| 3449 | U(1289697) | 179687 | Serge Batalov | 07/2024 |
| 3451 | 2^596884+73 | 179680 | Stefano Morozzi | 04/2021 |
| 3450 | (11*10^179679+13)/3 | 179680 | Robert Price | 03/2022 |
| 3452 | (68*10^179656+7)/3 | 179658 | Robert Price | 01/2020 |
| 3453 | 26952^40547-40547^26952 | 179648 | Norbert Schneider | 01/2026 |
| 3454 | (10^179643+173)/3 | 179643 | Robert Price | 05/2021 |
| 3455 | 2^596690-461261 | 179622 | Enzo Doria | 07/2015 |
| 3456 | 2^596684-113939 | 179620 | Enzo Doria | 10/2014 |
| 3457 | 2^596642+39 | 179608 | Jon Grantham | 08/2023 |
| 3458 | 2*10^179602+63 | 179603 | Robert Price | 05/2018 |
| 3459 | 3^376380+531440 | 179579 | Alfred Reich | 03/2026 |
| 3460 | 32262^39815-39815^32262 | 179514 | Frank Doornink | 02/2024 |
| 3461 | (25*10^179488-403)/9 | 179489 | Robert Price | 01/2021 |
| 3462 | 7*10^179460+99 | 179461 | Robert Price | 05/2021 |
| 3463 | 2^596127+74333 | 179453 | Enzo Doria | 07/2023 |
| 3464 | 3^375887-112696 | 179344 | Enzo Doria | 07/2014 |
| 3465 | 4*10^179265-71 | 179266 | Robert Price | 12/2018 |
| 3466 | 2*10^179193+83 | 179194 | Robert Price | 12/2021 |
| 3467 | 2^595144-1850429 | 179157 | Enzo Doria | 08/2015 |
| 3468 | 2^595122-5 | 179150 | Stefano Morozzi | 07/2022 |
| 3469 | 3*10^179138+89 | 179139 | Robert Price | 10/2018 |
| 3470 | (52*10^179062-133)/9 | 179063 | Robert Price | 09/2021 |
| 3471 | 2^594531+82253 | 178972 | Enzo Doria | 09/2016 |
| 3472 | (664*10^178939-61)/9 | 178941 | Robert Price | 09/2021 |
| 3473 | 2^594260-2787899 | 178891 | Enzo Doria | 11/2015 |
| 3474 | (14*10^178822+67)/9 | 178823 | Robert Price | 05/2022 |
| 3475 | (29*10^178732-119)/9 | 178733 | Robert Price | 12/2021 |
| 3476 | 2^593631+101381 | 178701 | Jorge Menendez | 04/2018 |
| 3477 | 10^178695+136719 | 178696 | Patrick De Geest | 05/2016 |
| 3478 | 10^178695-71 | 178695 | Serge Batalov | 12/2014 |
| 3479 | (2*10^178649-161)/3 | 178649 | Robert Price | 12/2020 |
| 3480 | (691^62903-1)/690 | 178609 | Michael Stocker | 05/2020 |
| 3481 | (2^148330+1)^4-2 | 178608 | Cletus Emmanuel | 12/2003 |
| 3482 | 2^593242+28309 | 178584 | Enzo Doria | 01/2024 |
| 3483 | 2^593222-14145 | 178578 | Jorge Menendez | 10/2017 |
| 3484 | 7*10^178566+33 | 178567 | Robert Price | 06/2020 |
| 3485 | 2^593178+1867219 | 178565 | Enzo Doria | 03/2016 |
| 3486 | 2^593152+22441 | 178557 | Enzo Doria | 09/2023 |
| 3487 | (38*10^178456+151)/9 | 178457 | Robert Price | 03/2022 |
| 3488 | (302*10^178369+13)/9 | 178371 | Robert Price | 02/2020 |
| 3489 | (26*10^178296-113)/3 | 178297 | Robert Price | 06/2020 |
| 3490 | (18^142031-1)/17 | 178287 | Paul Bourdelais | 03/2010 |
| 3491 | (13*10^178233+137)/3 | 178234 | Robert Price | 06/2021 |
| 3492 | (5*10^178206+91)/3 | 178207 | Robert Price | 04/2018 |
| 3493 | 2^591872-291929 | 178172 | Enzo Doria | 07/2015 |
| 3494 | 2^591682-286871 | 178115 | Enzo Doria | 07/2015 |
| 3495 | (7^210761-5^210761)/2 | 178114 | Jon Grantham | 08/2023 |
| 3496 | 4*10^178091+9 | 178092 | Robert Price | 05/2015 |
| 3497 | 2^591435+335931 | 178040 | Enzo Doria | 09/2024 |
| 3498 | Phi(148280,2^11) | 178018 | Henri Lifchitz | 12/2025 |
| 3499 | 410747#+478483 | 178007 | Makoto Morimoto | 02/2016 |
| 3500 | 3*10^177872+73 | 177873 | Robert Price | 08/2018 |
