## PRP Records

### Probable Primes Top 10000

#### (295756 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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See the Latest PRPs
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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 ? 3251 2^515227-114997 155099 Enzo Doria 06/2015 3252 26510^35061-35061^26510 155090 Frank Doornink 03/2024 3254 EPrime(155025) 155025 Eric W. Weisstein 10/2010 3253 (14*10^155024-221)/9 155025 Robert Price 04/2018 3255 (4*10^155022+173)/3 155023 Robert Price 02/2018 3256 (266*10^154897+1)/3 154899 Robert Price 04/2020 3257 (115*10^154869-1)/3 154871 Serge Batalov 12/2014 3258 (86*10^154853-221)/9 154854 Robert Price 09/2019 3259 2^514361+78167 154839 Enzo Doria 05/2016 3260 2^514281-115033 154815 Enzo Doria 06/2015 3261 25701^35104-35104^25701 154807 Frank Doornink 02/2024 3262 2^514194-3311 154788 Yves Minet 12/2014 3263 25930^35067-35067^25930 154779 Frank Doornink 03/2024 3264 (14*10^154773+37)/3 154774 Robert Price 12/2018 3265 (16*10^154748+131)/3 154749 Robert Price 03/2022 3266 6*10^154742-31 154743 Robert Price 07/2020 3267 (14*10^154645+139)/9 154646 Robert Price 11/2021 3268 2^513690+216949 154637 Enzo Doria 12/2023 3269 5*10^154618-79 154619 Robert Price 03/2021 3270 (167*10^154595+1)/3 154597 Robert Price 04/2021 3271 2^513437+1879337 154560 Enzo Doria 09/2016 3272 2^513306-113201 154521 Enzo Doria 07/2014 3273 26415^34942-34942^26415 154509 Frank Doornink 03/2024 3274 18^120818+19^120818-2 154497 Harsh Aggarwal 05/2024 3275 (10^154494-13)/3 154494 Robert Price 12/2017 3276 23462^35343+35343^23462 154462 Norbert Schneider 04/2023 3277 2^513042-113787 154442 Enzo Doria 09/2014 3278 (151*10^154434-7)/9 154436 Robert Price 01/2020 3279 (118*10^154428+11)/3 154430 Robert Price 03/2022 3280 2^512987+29153 154425 Enzo Doria 02/2024 3281 (14*10^154413+139)/9 154414 Robert Price 11/2021 3282 (77*10^154389-149)/9 154390 Robert Price 03/2022 3283 32184^34247-34247^32184 154374 Frank Doornink 02/2024 3284 10^154359+49 154360 Robert Price 02/2023 3285 2^512628-114053 154317 Enzo Doria 11/2014 3286 2^512529-49783 154287 Enzo Doria 10/2015 3287 (355573#+6991)/(6991*2031599) 154285 Makoto Morimoto 06/2019 3288 2^512315-115297 154223 Enzo Doria 06/2015 3289 (47*10^154221+241)/9 154222 Robert Price 06/2022 3290 (7*10^154211+173)/9 154211 Robert Price 01/2022 3291 2^512243+22703 154201 Enzo Doria 09/2023 3292 2^512168+79561 154178 Enzo Doria 06/2016 3293 (77*10^154175+67)/9 154176 Robert Price 12/2021 3294 (59*19^120562-5)/18 154170 Anonymous 12/2023 3295 (5*10^154158-311)/9 154158 Robert Price 12/2021 3296 27169^34758-34758^27169 154120 Frank Doornink 01/2024 3297 (89*10^154103-737)/9 154104 Robert Price 01/2022 3298 2^511857+23327 154085 Enzo Doria 10/2023 3299 4*10^154078-57 154079 Robert Price 10/2018 3300 26242^34863-34863^26242 154060 Frank Doornink 03/2024 3301 (355049#+1859)/(11*13*10148891*62587751) 154051 Makoto Morimoto 06/2019 3302 7*10^154038-57 154039 Robert Price 06/2020 3303 2^511658-114371 154025 Enzo Doria 02/2015 3304 (57^87719+1)/58 154022 Paul Bourdelais 11/2017 3305 2^511580-1846679 154001 Enzo Doria 07/2015 3306 (259*10^153998-1)/3 154000 Robert Price 12/2020 3307 2^511541-113713 153990 Enzo Doria 09/2014 3308 49958^32768+49957^32768 153965 Kellen Shenton 11/2020 3309 10^153935+970801 153936 Patrick De Geest 05/2021 3310 10^153935-1000001 153935 Robert Price 08/2020 3311 (16*10^153868-73)/3 153869 Robert Price 07/2020 3312 9*10^153851-67 153852 Robert Price 11/2020 3313 2^511077-112723 153850 Enzo Doria 06/2014 3314 69^83653-68^83653 153826 Robert Price 12/2013 3315 2^510963-113707 153816 Enzo Doria 09/2014 3316 (154*10^153810-1)/9 153812 Serge Batalov 12/2014 3317 (181*25^109991-75077)/8 153763 Curtis Bright 05/2015 3318 2*10^153746-3 153747 Robert Price 07/2015 3319 2^510626+1179379 153714 Enzo Doria 05/2016 3320 (7*10^153664+113)/3 153665 Robert Price 02/2018 3321 2^510448+24991 153661 Enzo Doria 11/2023 3322 2^510420+81121 153652 Enzo Doria 07/2016 3323 (197*7^181761-1)/2 153608 Karsten Bonath 05/2017 3324 2^509894-459161 153494 Enzo Doria 05/2015 3325 (74*10^153489+673)/9 153490 Robert Price 02/2022 3326 (49*10^153484-211)/9 153485 Robert Price 06/2022 3327 2^509841+71657 153478 Enzo Doria 04/2016 3328 9*10^153446+41 153447 Robert Price 08/2020 3329 2^509533-1846723 153385 Enzo Doria 07/2015 3330 2^509468-39989 153366 Enzo Doria 09/2015 3331 70^83117-69^83117 153360 Robert Price 01/2014 3332 (209246*34^99997-81)/11 153148 Eric Chen 08/2023 3333 (7*10^153116-1)/3 153117 Robert Price 08/2022 3334 (112*10^153025-1)/3 153027 Serge Batalov 12/2014 3335 31912^33975-33975^31912 153022 Frank Doornink 01/2024 3336 (19*10^153010+131)/3 153011 Robert Price 06/2020 3337 2^508174-1855151 152976 Enzo Doria 09/2015 3338 181^67757-2 152974 Lelio R Paula 12/2017 3339 2^508160-1864829 152972 Enzo Doria 01/2016 3340 10^152960+412563 152961 Patrick De Geest 05/2021 3341 10^152960-50000000001 152960 Robert Price 12/2020 3342 10^152960-423749 152960 Patrick De Geest 05/2021 3343 (71*10^152933-143)/9 152934 Robert Price 10/2021 3344 32109^33932-33932^32109 152919 Frank Doornink 02/2024 3345 2^507857-1848199 152881 Enzo Doria 07/2015 3346 2^507638-115361 152815 Enzo Doria 07/2015 3347 2^507551-114025 152789 Enzo Doria 11/2014 3348 (6^196337+1)/7 152780 Paul Bourdelais 02/2010 3349 (22*10^152670-13)/9 152671 Robert Price 06/2018 3350 2^507085+28517 152648 Enzo Doria 01/2024 3351 2^506917+28847 152598 Enzo Doria 02/2024 3352 2^506451-22339 152457 Enzo Doria 07/2013 3353 26463^34460-34460^26463 152405 Frank Doornink 03/2024 3354 31898^33837-33837^31898 152394 Frank Doornink 01/2024 3355 2^505995-113185 152320 Enzo Doria 07/2014 3356 (8*10^152260-17)/9 152260 Serge Batalov 11/2022 3357 (4*10^152253+149)/9 152253 Robert Price 04/2018 3358 33530^33643-33643^33530 152250 Norbert Schneider 04/2024 3359 578^55117-577^55117 152230 Jean-Louis Charton 08/2012 3360 2^505431-505431 152150 Henri Lifchitz 04/2005 3361 (203*10^152143+1)/3 152145 Robert Price 03/2020 3362 31730^33787-33787^31730 152092 Frank Doornink 01/2024 3363 2^505089+217787 152047 Enzo Doria 01/2024 3364 33565^33594-33594^33565 152043 Norbert Schneider 04/2024 3365 2^505053+73097 152037 Enzo Doria 04/2016 3366 22*10^151998+3 152000 Robert Price 01/2020 3367 (238*10^151979-1)/3 151981 Robert Price 04/2020 3368 (2^504793-7)/46765 151954 Lelio R Paula 12/2017 3369 350377#+797581 151937 Nicolas PALAU 08/2017 3370 (79*10^151906-529)/9 151907 Robert Price 01/2022 3371 2^504618-343991 151906 Enzo Doria 07/2015 3372 2^504259+211193 151798 Enzo Doria 08/2023 3373 2^504212-461939 151783 Enzo Doria 07/2015 3374 7*10^151772-41 151773 Robert Price 08/2021 3375 2^504054-2231 151736 Yves Minet 10/2011 3376 25237^34458-34458^25237 151686 Frank Doornink 11/2023 3377 (28*10^151682+191)/3 151683 Robert Price 02/2020 3378 2^503817+23961 151665 Enzo Doria 10/2023 3379 2^503475-933075 151562 Paul Bourdelais 06/2021 3380 2^503371+26289 151530 Enzo Doria 12/2023 3381 2^503361-39883 151527 Enzo Doria 09/2015 3382 2^503225+382667 151486 Enzo Doria 10/2016 3383 (206*10^151483-11)/3 151485 Robert Price 02/2022 3384 (844*10^151396-7)/9 151398 Robert Price 05/2021 3385 (26*10^151391-503)/9 151392 Robert Price 07/2018 3386 2^502769+1877567 151349 Enzo Doria 08/2016 3387 2^502576-4019 151291 Yves Minet 10/2011 3388 5*10^151257+41 151258 Robert Price 03/2019 3389 2^502290-2792501 151205 Enzo Doria 02/2016 3390 2^502181+1868417 151172 Enzo Doria 04/2016 3391 2^502055+22583 151134 Enzo Doria 09/2023 3392 (3*23^110967+41)/22 151106 Anonymous 12/2023 3393 6*10^151063-77 151064 Robert Price 09/2021 3394 2^501781-1850503 151052 Enzo Doria 08/2015 3395 (5*10^151007+37)/3 151008 Robert Price 03/2018 3396 3^316494+5*2^316494 151007 Jon Grantham 08/2023 3397 2^501627-991 151005 Yves Minet 02/2014 3398 2^501577-115333 150990 Enzo Doria 07/2015 3399 25239^34298-34298^25239 150983 Frank Doornink 12/2023 3400 (19*10^150977-7)/3 150978 Robert Price 12/2023 3401 8*10^150975+3 150976 Robert Price 08/2015 3402 2^501512-113669 150971 Enzo Doria 09/2014 3403 34180^26101+26101^34180 150962 Norman Luhn 04/2024 3404 U(1083477)/2166953 150949 Serge Batalov 07/2024 3405 (83*10^150908+493)/9 150909 Robert Price 12/2021 3406 36267^14482+14482^36267 150901 Norman Luhn 04/2024 3407 2*10^150818+83 150819 Robert Price 12/2021 3408 48753^1240+1240^48753 150814 Norman Luhn 04/2024 3409 (12^139739+1)/13 150803 Paul Bourdelais 09/2011 3410 (31^101111-1)/30 150792 Alexander Zhirkov 11/2010 3411 2^500899-500899 150786 Henri Lifchitz 04/2005 3412 2^500832+1876801 150766 Enzo Doria 07/2016 3413 (23*10^150763-59)/9 150764 Robert Price 05/2018 3414 46002^1891+1891^46002 150735 Norman Luhn 04/2024 3415 32001^33458-33458^32001 150734 Frank Doornink 01/2024 3416 2^500699+1884953 150726 Enzo Doria 02/2017 3417 (13*10^150675-37)/3 150676 Robert Price 01/2019 3418 (2^500527+lucasV(1,2,500527)+1)/4 150674 Mike Oakes 11/2016 3419 35365^18204+18204^35365 150661 Norman Luhn 05/2024 3421 2^500337-71101 150617 Enzo Doria 04/2016 3420 (74*10^150616+133)/9 150617 Robert Price 06/2019 3422 (2*10^150612-17)/3 150612 Serge Batalov 11/2022 3423 4*10^150577+91 150578 Robert Price 08/2018 3424 5649^40132+40132^5649 150575 Norbert Schneider 04/2024 3425 2^500160+80071 150564 Enzo Doria 06/2016 3426 (2^500120+5)/9 150551 Lelio R Paula 12/2017 3428 (43*10^150515-421)/9 150516 Robert Price 01/2019 3427 4695^40994+40994^4695 150516 Norbert Schneider 11/2023 3429 2^499999+15981 150515 Norman Luhn 08/2023 3430 (10^150551-1)/9/385207015049/57498437921/7808738631274081 150512 Maksym Voznyy 08/2014 3431 (10^150551-1)/1556587827131683185788921941743157225041 150512 Robert Price 07/2016 3432 26614^34005-34005^26614 150476 Frank Doornink 03/2024 3433 2^499861-29503 150474 Enzo Doria 08/2015 3434 2^499653-113533 150411 Enzo Doria 08/2014 3435 (14*10^150391-191)/3 150392 Robert Price 10/2020 3436 29033^33696+33696^29033 150382 Norbert Schneider 10/2023 3437 2^499534-221 150375 Yves Minet 06/2012 3438 30110^33567+33567^30110 150337 Norbert Schneider 10/2023 3439 26212^34023-34023^26212 150331 Frank Doornink 03/2024 3440 (28*10^150294+41)/3 150295 Robert Price 07/2021 3441 2^499225+49727 150282 Enzo Doria 09/2016 3442 (695*10^150274+7)/9 150276 Robert Price 12/2021 3443 2^499054-29261 150231 Enzo Doria 07/2015 3444 18580^35187+35187^18580 150215 Norbert Schneider 10/2023 3445 (844*10^150196-7)/9 150198 Robert Price 05/2021 3446 2^498907-933075 150186 Paul Bourdelais 06/2021 3447 (2^498898-7)/9 150183 Lelio R Paula 10/2015 3448 3*10^150182+17 150183 Robert Price 07/2018 3449 5*10^150175+63 150176 Robert Price 09/2020 3450 29273^33618-33618^29273 150154 Frank Doornink 06/2024 3451 32363^33292+33292^32363 150149 Norbert Schneider 07/2022 3452 32^99753-99753^32 150144 Henri Lifchitz 08/2024 3453 (77*10^150128+67)/9 150129 Robert Price 12/2021 3454 (7*10^(2*75062+1)-9*10^75062-7)/9 150125 Robert Price 12/2023 3455 2^498623+1866983 150101 Enzo Doria 03/2016 3456 33194^33194-213^213 150073 Serge Batalov 04/2024 3457 27868^33759-33759^27868 150063 Frank Doornink 06/2024 3458 (25*10^150050-403)/9 150051 Robert Price 12/2020 3459 numbpart(18140942830) 150033 Serge Batalov 04/2017 3460 10^150029+4381 150030 Patrick De Geest 05/2016 3461 10^150029-41 150029 Serge Batalov 12/2014 3462 33185^33185+618^618 150028 Serge Batalov 04/2024 3463 9*34^97952+529 150013 Eric Chen 08/2023 3464 10^150000+1158603 150001 Patrick De Geest 09/2018 3465 10^150000-245703 150000 Patrick De Geest 09/2018 3466 (38*10^149999+691)/9 150000 Robert Price 10/2018 3467 2043563126843649194^8192+2043563126843649185^8192 150000 Youcef Lemsafer 01/2023 3468 (2043563126843649232^8192+2043563126843649201^8192)/147457 149994 Youcef Lemsafer 01/2023 3469 2^498238-53 149985 Lelio R Paula 12/2017 3470 45728^1905+1905^45728 149984 Hans Havermann 10/2020 3471 (211^65024+1)/(211^512+1) 149945 Martin Hopf 12/2023 3472 5*10^149907+23 149908 Robert Price 03/2019 3473 32^99585-829 149891 Eric Chen 11/2023 3474 39347^6442+6442^39347 149874 Hans Havermann 09/2020 3475 2^497850+81049 149868 Enzo Doria 07/2016 3476 V(1075416) 149830 Serge Batalov 07/2024 3477 37228^10575+10575^37228 149816 Hans Havermann 10/2020 3478 (5*2^497673+1)/2743 149812 Lelio R Paula 10/2015 3479 (5*2^497671+1)/373703 149810 Lelio R Paula 10/2015 3480 (2*10^149803-143)/3 149803 Robert Price 03/2018 3481 33845^26604+26604^33845 149763 Hans Havermann 09/2020 3482 2^497434-2784191 149743 Enzo Doria 10/2015 3483 (865*10^149737-1)/9 149739 Robert Price 04/2020 3484 10^149695-7000001 149695 Robert Price 06/2021 3485 38237^8214+8214^38237 149681 Hans Havermann 09/2020 3486 (23*10^149655+19)/3 149656 Robert Price 07/2019 3487 2^497068-113579 149633 Enzo Doria 08/2014 3488 2^497037+73727 149624 Enzo Doria 04/2016 3489 11*10^149618+3 149620 Robert Price 07/2021 3490 34942^19067+19067^34942 149562 Hans Havermann 09/2020 3491 33696^27449+27449^33696 149561 Hans Havermann 09/2020 3492 2^496773+77747 149544 Enzo Doria 05/2016 3493 29937^33400-33400^29937 149506 Frank Doornink 06/2024 3494 (7*10^149483-493)/9 149483 Robert Price 04/2021 3495 (206*10^149459+7)/3 149461 Robert Price 07/2020 3496 34589^20940+20940^34589 149459 Hans Havermann 09/2020 3497 2^496477-113485 149455 Enzo Doria 08/2014 3498 3*2^496411-5 149436 Jon Grantham 07/2023 3499 ((10^74703-1)*10000/9+7481)*10^74703+(10^74703-1)/9 149410 Hans Havermann 09/2019 3500 2^496270-49451 149393 Enzo Doria 10/2015

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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: September, 12 2024 08:27 (Time in France)

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