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 | (23*10^168608-83)/3 | 168609 | Robert Price | 08/2019 |
| 3252 | (94*10^168541+11)/3 | 168543 | Robert Price | 04/2020 |
| 3253 | 2^559686-350471 | 168483 | Enzo Doria | 06/2015 |
| 3254 | 2^559672-1855889 | 168479 | Enzo Doria | 09/2015 |
| 3255 | (5*10^168379-473)/9 | 168379 | Robert Price | 01/2018 |
| 3256 | 2024^50920+3 | 168353 | Martin Hopf | 01/2024 |
| 3257 | 2^559000-59939 | 168276 | Enzo Doria | 11/2015 |
| 3258 | 2^558830+25009 | 168225 | Enzo Doria | 11/2023 |
| 3259 | (16*10^168181+41)/3 | 168182 | Robert Price | 03/2019 |
| 3260 | (19*10^168173+77)/3 | 168174 | Robert Price | 05/2019 |
| 3261 | (74*10^168170+529)/9 | 168171 | Robert Price | 02/2022 |
| 3262 | 2^558640-114149 | 168168 | Enzo Doria | 12/2014 |
| 3263 | 2^558498-1849277 | 168125 | Enzo Doria | 08/2015 |
| 3264 | 2^558476-1850249 | 168119 | Enzo Doria | 08/2015 |
| 3265 | (7*10^168067+71)/3 | 168068 | Robert Price | 05/2018 |
| 3266 | 2^558150-1852211 | 168020 | Enzo Doria | 08/2015 |
| 3267 | 2^558125-113661 | 168013 | Enzo Doria | 09/2014 |
| 3268 | 393^64747-392^64747 | 167980 | Jean-Louis Charton | 08/2012 |
| 3269 | (8*10^167965-11)/3 | 167966 | Robert Price | 07/2023 |
| 3270 | 2^557916+216151 | 167950 | Enzo Doria | 12/2023 |
| 3271 | (13*10^167911+179)/3 | 167912 | Robert Price | 11/2018 |
| 3272 | (26*10^167861-167)/3 | 167862 | Robert Price | 10/2019 |
| 3273 | 36^107827-107827 | 167812 | Kellen Shenton | 06/2023 |
| 3274 | 32027^37242-37242^32027 | 167795 | Frank Doornink | 01/2024 |
| 3275 | 39^105456+2 | 167788 | Robert Price | 04/2015 |
| 3276 | 2^557322+217519 | 167771 | Enzo Doria | 01/2024 |
| 3277 | (28^115877-1)/27 | 167691 | Paul Bourdelais | 12/2017 |
| 3278 | 6*10^167662-13 | 167663 | Robert Price | 07/2022 |
| 3279 | 10^167639+121911 | 167640 | Patrick De Geest | 07/2018 |
| 3280 | 10^167639-8001 | 167639 | Robert Price | 03/2018 |
| 3281 | 2^556504-462059 | 167525 | Enzo Doria | 07/2015 |
| 3282 | (88*10^167522-637)/9 | 167523 | Robert Price | 11/2020 |
| 3283 | 5*10^167510+9 | 167511 | Robert Price | 08/2015 |
| 3284 | 7*10^167437-93 | 167438 | Robert Price | 08/2020 |
| 3285 | 25455^37978-37978^25455 | 167323 | Frank Doornink | 01/2024 |
| 3286 | 11^160663+6 | 167314 | Paul Bourdelais | 02/2021 |
| 3287 | (7*10^167308-493)/9 | 167308 | Robert Price | 04/2021 |
| 3288 | 2^555759+74333 | 167301 | Enzo Doria | 07/2023 |
| 3289 | 26084^37871-37871^26084 | 167253 | Frank Doornink | 03/2024 |
| 3290 | 2^555343+1874333 | 167175 | Enzo Doria | 06/2016 |
| 3291 | 2^555210-461261 | 167135 | Enzo Doria | 07/2015 |
| 3292 | 9*10^166996+59 | 166997 | Robert Price | 01/2020 |
| 3293 | (68*10^166976-329)/9 | 166977 | Robert Price | 03/2021 |
| 3294 | (64*10^166901+683)/9 | 166902 | Robert Price | 06/2022 |
| 3295 | 2^554372+1880527 | 166883 | Enzo Doria | 11/2016 |
| 3296 | 2^554299+72173 | 166861 | Enzo Doria | 04/2016 |
| 3297 | (185*10^166837+7)/3 | 166839 | Robert Price | 03/2020 |
| 3298 | (14*10^166813+139)/9 | 166814 | Robert Price | 11/2021 |
| 3299 | 26084^37767-37767^26084 | 166794 | Frank Doornink | 03/2024 |
| 3300 | 2^554037-2797063 | 166782 | Enzo Doria | 03/2016 |
| 3301 | 31861^37028-37028^31861 | 166747 | Frank Doornink | 01/2024 |
| 3302 | (49*10^166721-139)/9 | 166722 | Robert Price | 03/2019 |
| 3303 | 2*10^166646+69 | 166647 | Robert Price | 06/2020 |
| 3304 | 2^553484-29819 | 166616 | Enzo Doria | 08/2015 |
| 3305 | (188*10^166611+7)/3 | 166613 | Robert Price | 03/2020 |
| 3306 | 2^553383-2784217 | 166585 | Enzo Doria | 10/2015 |
| 3307 | 2^553069+76427 | 166491 | Enzo Doria | 05/2016 |
| 3308 | 25218^37819-37819^25218 | 166469 | Frank Doornink | 12/2023 |
| 3309 | 2*10^166458+51 | 166459 | Robert Price | 05/2018 |
| 3310 | 589^60089-588^60089 | 166454 | Jean-Louis Charton | 09/2012 |
| 3311 | 25214^37799-37799^25214 | 166378 | Frank Doornink | 11/2023 |
| 3312 | 11^159756-2424 | 166369 | Mike Oakes | 06/2010 |
| 3313 | 2^552649-361275 | 166364 | Enzo Doria | 05/2014 |
| 3314 | 2^552628-113669 | 166358 | Enzo Doria | 09/2014 |
| 3315 | (19*10^166325+137)/3 | 166326 | Robert Price | 03/2022 |
| 3316 | 10^166324+550603 | 166325 | Patrick De Geest | 07/2018 |
| 3317 | 10^166324-801 | 166324 | Robert Price | 02/2018 |
| 3318 | (85*10^166297-1)/3 | 166299 | Robert Price | 02/2020 |
| 3319 | (19*10^166280-7)/3 | 166281 | Robert Price | 12/2023 |
| 3320 | 25533^37726-37726^25533 | 166263 | Frank Doornink | 02/2024 |
| 3321 | 8*10^166227+87 | 166228 | Robert Price | 10/2019 |
| 3322 | 2^552137+1879397 | 166210 | Enzo Doria | 09/2016 |
| 3323 | 262273205671539190984629()252475512364409752762433 | 166141 | Anonymous | 01/2025 |
| 3324 | 490079063773165613318095()218182139934160868002603 | 166141 | Anonymous | 01/2025 |
| 3325 | 140717254840416411192803()712689271538459396766869 | 166140 | Anonymous | 01/2025 |
| 3326 | 122398296040696255481419()271117913237372866926417 | 166140 | Anonymous | 01/2025 |
| 3327 | (103*10^166126+11)/3 | 166128 | Robert Price | 01/2021 |
| 3328 | (22*10^166077+179)/3 | 166078 | Robert Price | 02/2022 |
| 3329 | (23^121949-1)/22 | 166061 | Paul Bourdelais | 10/2017 |
| 3330 | 2^551576+236221 | 166041 | Enzo Doria | 05/2025 |
| 3331 | 2^551542+19249 | 166031 | Payam Samidoost | 08/2002 |
| 3332 | 2^551535-23821 | 166029 | Enzo Doria | 08/2013 |
| 3333 | 2^551507-23557 | 166021 | Enzo Doria | 08/2013 |
| 3334 | 32030^36841-36841^32030 | 165990 | Frank Doornink | 01/2024 |
| 3335 | 10^165947-7000000001 | 165947 | Robert Price | 12/2021 |
| 3336 | 4*10^165938-47 | 165939 | Robert Price | 10/2021 |
| 3337 | 7*10^165916-3 | 165917 | Robert Price | 08/2015 |
| 3338 | (29*10^165796+67)/3 | 165797 | Robert Price | 12/2019 |
| 3339 | 81^86837-80^86837 | 165728 | Robert Price | 01/2015 |
| 3340 | (71*10^165716-17)/9 | 165717 | Serge Batalov | 01/2023 |
| 3341 | fibonacci(792909)+3 | 165708 | Jon Grantham | 08/2023 |
| 3342 | (71*10^165663-539)/9 | 165664 | Robert Price | 07/2019 |
| 3343 | 25682^37567-37567^25682 | 165657 | Frank Doornink | 02/2024 |
| 3344 | 2^550270-69551 | 165648 | Enzo Doria | 12/2015 |
| 3345 | 2^550250+29329 | 165642 | Enzo Doria | 03/2024 |
| 3346 | (202*10^165569-13)/9 | 165571 | Robert Price | 01/2020 |
| 3347 | 2^550000-23625 | 165567 | Enzo Doria | 08/2013 |
| 3348 | 31688^36783-36783^31688 | 165557 | Frank Doornink | 01/2024 |
| 3349 | 2^549675-1852057 | 165469 | Enzo Doria | 08/2015 |
| 3350 | 2^549663+212543 | 165466 | Enzo Doria | 08/2023 |
| 3351 | (529*10^165394-7)/9 | 165396 | Robert Price | 08/2021 |
| 3352 | 26253^37424-37424^26253 | 165384 | Frank Doornink | 03/2024 |
| 3353 | -tau(103^14938) | 165374 | Nik Lygeros / Olivier Rozier | 10/2013 |
| 3354 | (28*10^165358-1)/9 | 165359 | Serge Batalov | 10/2014 |
| 3355 | 2^549278+1879669 | 165350 | Enzo Doria | 09/2016 |
| 3356 | (7*10^165350-439)/9 | 165350 | Robert Price | 02/2018 |
| 3357 | 2^549252-351269 | 165342 | Enzo Doria | 06/2015 |
| 3358 | 2^549221+335931 | 165332 | Enzo Doria | 09/2024 |
| 3359 | 67*10^165327-9 | 165329 | Robert Price | 03/2021 |
| 3360 | (14*10^165282+73)/3 | 165283 | Robert Price | 12/2018 |
| 3361 | (8*10^165283-629)/9 | 165283 | Robert Price | 01/2022 |
| 3362 | 2^549049+2797607 | 165281 | Enzo Doria | 04/2016 |
| 3363 | (218*10^165258+7)/9 | 165260 | Robert Price | 06/2022 |
| 3364 | (7*10^165239+107)/3 | 165240 | Robert Price | 02/2018 |
| 3365 | 2^548880+23961 | 165230 | Enzo Doria | 10/2023 |
| 3366 | 5*2^548778+3 | 165200 | Jon Grantham | 07/2023 |
| 3367 | (44^100511-1)/43 | 165184 | Paul Bourdelais | 11/2017 |
| 3368 | (7*10^165134+107)/3 | 165135 | Robert Price | 02/2018 |
| 3369 | (301*10^165082+23)/9 | 165084 | Robert Price | 06/2021 |
| 3370 | (23*10^165060-83)/3 | 165061 | Robert Price | 08/2019 |
| 3371 | 7*10^165023-27 | 165024 | Robert Price | 11/2022 |
| 3372 | (76*10^164984+77)/9 | 164985 | Robert Price | 10/2019 |
| 3373 | 31058^36715-36715^31058 | 164931 | Frank Doornink | 01/2024 |
| 3374 | (4*10^164929-211)/9 | 164929 | Robert Price | 03/2022 |
| 3375 | 10^164878-500001 | 164878 | Robert Price | 03/2022 |
| 3376 | 9*10^164791-89 | 164792 | Robert Price | 04/2020 |
| 3377 | 2^547178-1856501 | 164717 | Enzo Doria | 10/2015 |
| 3378 | 11^158160-60 | 164707 | Enzo Doria | 07/2012 |
| 3379 | (26*10^164643-167)/3 | 164644 | Robert Price | 10/2019 |
| 3380 | (10^164643+83)/3 | 164643 | Robert Price | 08/2021 |
| 3381 | 2^546398-59201 | 164483 | Enzo Doria | 10/2015 |
| 3382 | 2^546332-114893 | 164463 | Enzo Doria | 05/2015 |
| 3383 | 36087^36087-36080^36080 | 164462 | Henri Lifchitz | 08/2024 |
| 3384 | 32003^36504-36504^32003 | 164458 | Frank Doornink | 01/2024 |
| 3385 | (65*10^164427+277)/9 | 164428 | Robert Price | 08/2021 |
| 3386 | 2^545958+1876189 | 164350 | Enzo Doria | 07/2016 |
| 3387 | 2^545878-49841 | 164326 | Enzo Doria | 10/2015 |
| 3388 | (10^164284+77)/3 | 164284 | Robert Price | 01/2018 |
| 3389 | 2^545668-4019 | 164263 | Yves Minet | 04/2017 |
| 3390 | 10^164216+780639 | 164217 | Patrick De Geest | 08/2021 |
| 3392 | 10^164216-50000000001 | 164216 | Robert Price | 12/2020 |
| 3391 | 10^164216-891051 | 164216 | Patrick De Geest | 08/2021 |
| 3393 | (13*53^238539*617^9)/10^247183 | 164151 | Hans Havermann | 07/2017 |
| 3394 | (16*10^164122+197)/3 | 164123 | Robert Price | 04/2019 |
| 3395 | 2^545185+76757 | 164118 | Enzo Doria | 05/2016 |
| 3396 | 2^545076-114329 | 164085 | Enzo Doria | 01/2015 |
| 3397 | (2*10^164043-143)/3 | 164043 | Robert Price | 03/2018 |
| 3398 | (33085^36481-1)/(33085^191-1) | 164018 | Ryan Propper | 11/2023 |
| 3399 | (29^112153+1)/30 | 164011 | Lelio R Paula | 03/2017 |
| 3400 | 2^544757+1874777 | 163989 | Enzo Doria | 06/2016 |
| 3401 | 2^544723+211193 | 163978 | Enzo Doria | 08/2023 |
| 3402 | 2^544444-457199 | 163894 | Enzo Doria | 01/2015 |
| 3403 | (32804^36481-1)/(32804^191-1) | 163883 | Ryan Propper | 11/2023 |
| 3404 | 2^544264-343529 | 163840 | Enzo Doria | 07/2015 |
| 3405 | 7*10^163780+9 | 163781 | Robert Price | 09/2015 |
| 3406 | 2^543989+2793047 | 163758 | Enzo Doria | 02/2016 |
| 3407 | (28*10^163709+113)/3 | 163710 | Robert Price | 03/2020 |
| 3408 | (2^543398)/(543398^2) | 163568 | Henri Lifchitz | 05/2025 |
| 3409 | (2013^49729-1)/(2013^223-1) | 163561 | Ryan Propper | 11/2023 |
| 3410 | (23*10^163523+301)/9 | 163524 | Robert Price | 06/2021 |
| 3411 | (68*10^163521-329)/9 | 163522 | Robert Price | 03/2021 |
| 3412 | 35820^35899+35899^35820 | 163489 | Norbert Schneider | 11/2021 |
| 3413 | 2^542870-69551 | 163421 | Enzo Doria | 12/2015 |
| 3414 | 2^542502+24799 | 163310 | Enzo Doria | 10/2023 |
| 3415 | 2^542395+72533 | 163278 | Enzo Doria | 04/2016 |
| 3416 | 2^542258+216949 | 163236 | Enzo Doria | 12/2023 |
| 3417 | 2^542072-3683 | 163180 | Yves Minet | 03/2017 |
| 3418 | fibonacci(780566)-4 | 163129 | Jon Grantham | 08/2023 |
| 3419 | (682*10^163106-7)/9 | 163108 | Robert Price | 08/2021 |
| 3420 | 2^541779-1867357 | 163092 | Enzo Doria | 04/2016 |
| 3421 | (29*10^163056+313)/9 | 163057 | Robert Price | 04/2021 |
| 3422 | 2^541476+214743 | 163001 | Enzo Doria | 11/2023 |
| 3423 | 13^142159+14^142159-2 | 162933 | Harsh Aggarwal | 05/2024 |
| 3424 | 8*10^162924+9 | 162925 | Robert Price | 12/2015 |
| 3425 | 2^540905+81557 | 162829 | Enzo Doria | 08/2016 |
| 3426 | 2^540628-2939 | 162746 | Yves Minet | 09/2014 |
| 3427 | 919^54919-918^54919 | 162743 | Jean-Louis Charton | 01/2013 |
| 3428 | (203*10^162689+1)/3 | 162691 | Robert Price | 03/2020 |
| 3429 | 3*10^162620-59 | 162621 | Robert Price | 09/2018 |
| 3430 | 2^540180+26791 | 162611 | Enzo Doria | 12/2023 |
| 3431 | 3^340694-112960 | 162553 | Enzo Doria | 07/2014 |
| 3432 | 2^539925+81 | 162534 | Henri Lifchitz | 11/2024 |
| 3433 | 2^539807-114081 | 162499 | Enzo Doria | 12/2014 |
| 3434 | 414^62093+62093^414 | 162498 | Norbert Schneider | 03/2022 |
| 3435 | 2^539654-114893 | 162453 | Enzo Doria | 05/2015 |
| 3436 | 9*10^162449-71 | 162450 | Robert Price | 11/2020 |
| 3437 | 2^539617-1851583 | 162441 | Enzo Doria | 08/2015 |
| 3438 | (509*10^162422+31)/9 | 162424 | Robert Price | 08/2022 |
| 3439 | (91*10^162410+11)/3 | 162412 | Robert Price | 02/2020 |
| 3440 | 2^539346+81049 | 162360 | Enzo Doria | 07/2016 |
| 3441 | 2^539220-115499 | 162322 | Enzo Doria | 07/2015 |
| 3442 | 2^539217-113713 | 162321 | Enzo Doria | 09/2014 |
| 3443 | 9^170099-8^170099 | 162316 | Jean-Louis Charton | 05/2005 |
| 3444 | 4*10^162263-39 | 162264 | Robert Price | 09/2020 |
| 3445 | 31243^36098-36098^31243 | 162252 | Frank Doornink | 01/2024 |
| 3446 | 31987^36000-36000^31987 | 162180 | Frank Doornink | 01/2024 |
| 3447 | (115*10^162153-1)/3 | 162155 | Serge Batalov | 12/2014 |
| 3448 | (10^162138+11)/3 | 162138 | Serge Batalov | 07/2015 |
| 3449 | (61*10^162100-403)/9 | 162101 | Robert Price | 10/2021 |
| 3450 | 2^538473-112723 | 162097 | Enzo Doria | 06/2014 |
| 3451 | 2^538157+79337 | 162002 | Enzo Doria | 06/2016 |
| 3452 | 2^538136-114749 | 161996 | Enzo Doria | 05/2015 |
| 3453 | 2^538104+1531 | 161986 | Lelio R Paula | 01/2013 |
| 3454 | (9*29^110727-1199)/14 | 161927 | Curtis Bright | 05/2015 |
| 3455 | ((2^179294-1)^3+2)/11 | 161918 | Serge Batalov | 03/2023 |
| 3456 | 31198^36027-36027^31198 | 161910 | Frank Doornink | 01/2024 |
| 3457 | 2^537815-22737 | 161899 | Enzo Doria | 07/2013 |
| 3458 | 2^537804-39839 | 161896 | Enzo Doria | 09/2015 |
| 3459 | (754*10^161816-7)/9 | 161818 | Robert Price | 05/2020 |
| 3460 | 2^537461+29867 | 161792 | Enzo Doria | 03/2024 |
| 3461 | 2^537458-59201 | 161791 | Enzo Doria | 10/2015 |
| 3462 | 2*10^161766+51 | 161767 | Robert Price | 05/2018 |
| 3463 | (7*10^161760+131)/3 | 161761 | Robert Price | 06/2020 |
| 3464 | 2^537209-49849 | 161717 | Enzo Doria | 10/2015 |
| 3465 | (58*10^161691+329)/9 | 161692 | Robert Price | 05/2019 |
| 3466 | 23*10^161668-3 | 161670 | Robert Price | 10/2021 |
| 3467 | 2^536937+1879397 | 161635 | Enzo Doria | 09/2016 |
| 3468 | 3*2^536868-5 | 161614 | Jon Grantham | 07/2023 |
| 3469 | 34*10^161593-9 | 161595 | Robert Price | 06/2020 |
| 3470 | (31*10^161582-1)/3 | 161584 | Robert Price | 02/2020 |
| 3471 | 24494^36813+36813^24494 | 161575 | Norbert Schneider | 11/2023 |
| 3472 | 2^536569-22881 | 161524 | Enzo Doria | 07/2013 |
| 3473 | (46*10^161505+593)/9 | 161506 | Robert Price | 04/2022 |
| 3474 | 10^161253+573493 | 161254 | Patrick De Geest | 07/2018 |
| 3475 | 10^161253-8001 | 161253 | Robert Price | 03/2018 |
| 3476 | 97*10^161247-3 | 161249 | Robert Price | 05/2020 |
| 3477 | 7*10^161192-9 | 161193 | Robert Price | 10/2015 |
| 3478 | 2^535415-19 | 161176 | Stefano Morozzi | 07/2022 |
| 3479 | 2^535269-113803 | 161133 | Enzo Doria | 09/2014 |
| 3480 | 2^535205-23295 | 161113 | Enzo Doria | 08/2013 |
| 3481 | (49*10^161105+437)/9 | 161106 | Robert Price | 09/2021 |
| 3482 | 2^534961+6561 | 161040 | Henri Lifchitz | 11/2024 |
| 3483 | (89^82609+1)/90 | 161036 | Paul Bourdelais | 10/2017 |
| 3484 | 35385^35385-17692^17692 | 160960 | Henri Lifchitz | 10/2024 |
| 3485 | 2^534429-19 | 160880 | Stefano Morozzi | 07/2022 |
| 3486 | 2^534359-23229 | 160859 | Enzo Doria | 08/2013 |
| 3487 | 10^160836-1001 | 160836 | Robert Price | 10/2022 |
| 3488 | 457^60454+60454^457 | 160803 | Norbert Schneider | 07/2021 |
| 3489 | 8*10^160782+53 | 160783 | Robert Price | 08/2020 |
| 3490 | 67^88037-66^88037 | 160763 | Robert Price | 10/2013 |
| 3491 | (88*10^160761-637)/9 | 160762 | Robert Price | 11/2020 |
| 3492 | 2^533981+81 | 160745 | Henri Lifchitz | 11/2024 |
| 3493 | 2^533948-1852559 | 160735 | Enzo Doria | 08/2015 |
| 3494 | 2^533665-23335 | 160650 | Enzo Doria | 08/2013 |
| 3495 | 2^533600+217981 | 160630 | Enzo Doria | 01/2024 |
| 3496 | (19*10^160619+77)/3 | 160620 | Robert Price | 05/2019 |
| 3497 | 2^533350-5 | 160555 | Stefano Morozzi | 07/2022 |
| 3498 | (38*10^160508+151)/9 | 160509 | Robert Price | 03/2022 |
| 3499 | 3^336353-2^336353 | 160482 | Mike Oakes | 10/2007 |
| 3500 | 26134^36315-36315^26134 | 160411 | Frank Doornink | 03/2024 |
