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
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| Rank |
Probable prime |
Digits (> 50000) |
Who ? |
When ? |
| 3251 | 10^127821-700001 | 127821 | Robert Price | 08/2021 |
| 3252 | 2^424577-113755 | 127811 | Enzo Doria | 09/2014 |
| 3253 | (7*2^424512-1)/3 | 127792 | Lelio R Paula | 05/2014 |
| 3254 | (56*10^127752+691)/9 | 127753 | Robert Price | 05/2019 |
| 3255 | 11^122629-720 | 127705 | Enzo Doria | 11/2012 |
| 3256 | 22*10^127645+3 | 127647 | Robert Price | 01/2020 |
| 3257 | 28715^27844+27844^28715 | 127631 | Hans Havermann | 03/2021 |
| 3258 | (56*10^127612+187)/9 | 127613 | Robert Price | 10/2021 |
| 3259 | (5*36^81995+821)/7 | 127609 | Eric Chen | 01/2021 |
| 3260 | 4*10^127562-39 | 127563 | Robert Price | 09/2020 |
| 3261 | 32595^8186+8186^32595 | 127547 | Hans Havermann | 03/2021 |
| 3262 | 2^423696-21429 | 127546 | Enzo Doria | 07/2013 |
| 3263 | 2^423664-1864559 | 127536 | Enzo Doria | 03/2016 |
| 3264 | 37889^2322+2322^37889 | 127530 | Hans Havermann | 03/2021 |
| 3265 | 37668^2429+2429^37668 | 127523 | Hans Havermann | 03/2021 |
| 3266 | 3^267267-4 | 127519 | Henri Lifchitz | 10/2014 |
| 3267 | (103*10^127491+17)/3 | 127493 | Robert Price | 08/2020 |
| 3268 | 29376^21869+21869^29376 | 127487 | Hans Havermann | 03/2021 |
| 3269 | 31186^12241+12241^31186 | 127483 | Hans Havermann | 02/2021 |
| 3270 | (19^99689+5^99689)/24 | 127477 | Robert Price | 09/2013 |
| 3271 | (21*2^423372+1)/101 | 127447 | Lelio R Paula | 05/2014 |
| 3272 | 30594^14645+14645^30594 | 127446 | Hans Havermann | 03/2021 |
| 3273 | 2^423328-21537 | 127435 | Enzo Doria | 07/2013 |
| 3274 | (67*10^127413-7)/3 | 127415 | Robert Price | 01/2020 |
| 3275 | (2*10^127407+73)/3 | 127407 | Robert Price | 09/2020 |
| 3276 | (2^423165-7)/25 | 127384 | Lelio R Paula | 05/2015 |
| 3277 | (7726^32768+1)/13917994151414876602369 | 127379 | Kellen Shenton | 04/2021 |
| 3278 | 29512^20647+20647^29512 | 127341 | Hans Havermann | 03/2021 |
| 3279 | (112*10^127324+17)/3 | 127326 | Robert Price | 03/2020 |
| 3280 | 29565^20252+20252^29565 | 127321 | Hans Havermann | 03/2021 |
| 3281 | (F(5)^182099-F(4)^182099)/F(3) | 127282 | Wayne Halsdorf | 08/2013 |
| 3282 | (16*10^127259+197)/3 | 127260 | Robert Price | 04/2019 |
| 3283 | (26*10^127240+61)/3 | 127241 | Robert Price | 10/2019 |
| 3284 | (234483*27^88884-145)/26 | 127230 | Curtis Bright | 05/2015 |
| 3285 | 2^422515-114997 | 127190 | Enzo Doria | 06/2015 |
| 3286 | 5*10^127179-3 | 127180 | Robert Price | 07/2015 |
| 3287 | 31678^10343+10343^31678 | 127176 | Hans Havermann | 03/2021 |
| 3288 | (44*10^127169-233)/9 | 127170 | Robert Price | 01/2019 |
| 3289 | 34947^4352+4352^34947 | 127162 | Hans Havermann | 03/2021 |
| 3290 | 6*10^127158+19 | 127159 | Robert Price | 11/2021 |
| 3291 | 30469^14902+14902^30469 | 127155 | Hans Havermann | 03/2021 |
| 3292 | 5*10^127153+77 | 127154 | Robert Price | 12/2018 |
| 3293 | 29941^17620+17620^29941 | 127130 | Hans Havermann | 02/2021 |
| 3294 | 31607^10516+10516^31607 | 127119 | Hans Havermann | 03/2021 |
| 3295 | (19*10^127118-97)/3 | 127119 | Robert Price | 10/2021 |
| 3296 | (29*10^127111+691)/9 | 127112 | Robert Price | 08/2021 |
| 3297 | 736^44335+44335^736 | 127104 | Norbert Schneider | 07/2019 |
| 3298 | 33040^7023+7023^33040 | 127090 | Hans Havermann | 03/2021 |
| 3299 | 29748^18661+18661^29748 | 127052 | Hans Havermann | 03/2021 |
| 3300 | -516776642557847117490*Bern(37960)/34256837217082767928421792453 | 127042 | Thomas Ritschel | 06/2017 |
| 3301 | (78^67141-1)/77 | 127036 | Paul Bourdelais | 09/2017 |
| 3302 | (14*10^127014-137)/3 | 127015 | Robert Price | 04/2021 |
| 3303 | 31436^10965+10965^31436 | 127002 | Hans Havermann | 03/2021 |
| 3304 | 28905^24758+24758^28905 | 127001 | Hans Havermann | 03/2021 |
| 3305 | 2^421860-113285 | 126993 | Enzo Doria | 07/2014 |
| 3306 | (10^127030+7)/81234833/9230384921/6092460488946445358851 | 126991 | Alfred Reich | 07/2021 |
| 3307 | (2^421827-7)/11 | 126982 | Lelio R Paula | 05/2015 |
| 3308 | 11^121910-840 | 126957 | Enzo Doria | 12/2012 |
| 3309 | (56*10^126935+187)/9 | 126936 | Robert Price | 10/2021 |
| 3310 | 28915^24538+24538^28915 | 126933 | Hans Havermann | 03/2021 |
| 3311 | (29*10^126928-77)/3 | 126929 | Robert Price | 02/2020 |
| 3312 | (259*10^126919-1)/3 | 126921 | Robert Price | 12/2020 |
| 3313 | 10^126919+204567 | 126920 | Patrick De Geest | 05/2021 |
| 3314 | 10^126919-100001 | 126919 | Robert Price | 07/2020 |
| 3315 | 28340^28503+28503^28340 | 126907 | Norbert Schneider | 02/2021 |
| 3316 | (71^68539+1)/72 | 126882 | Paul Bourdelais | 09/2017 |
| 3317 | (5*10^126871-119)/3 | 126872 | Robert Price | 03/2018 |
| 3318 | 331^50339-10004 | 126846 | Enzo Doria | 07/2012 |
| 3319 | 2^421363-2790757 | 126843 | Enzo Doria | 03/2016 |
| 3320 | (106*10^126839-1)/3 | 126841 | Serge Batalov | 12/2014 |
| 3321 | 37938^2203+2203^37938 | 126828 | Hans Havermann | 03/2021 |
| 3322 | (7*2^421243+1)/39 | 126807 | Lelio R Paula | 05/2014 |
| 3323 | (14*10^126784-83)/3 | 126785 | Robert Price | 12/2018 |
| 3324 | 2^421161-286183 | 126783 | Enzo Doria | 06/2015 |
| 3325 | (106*10^126726+17)/3 | 126728 | Robert Price | 04/2021 |
| 3326 | 30718^13347+13347^30718 | 126724 | Hans Havermann | 03/2021 |
| 3327 | 2^420939-113935 | 126716 | Enzo Doria | 10/2014 |
| 3328 | 177^56363-2 | 126703 | Lelio R Paula | 10/2017 |
| 3329 | 2^420741-113659 | 126656 | Enzo Doria | 08/2014 |
| 3330 | 2^420694-21 | 126642 | Lelio R Paula | 05/2017 |
| 3331 | (13*10^126638+437)/9 | 126639 | Robert Price | 04/2018 |
| 3332 | (167*10^126637-17)/3 | 126639 | Robert Price | 03/2020 |
| 3333 | 4*10^126625+87 | 126626 | Robert Price | 08/2018 |
| 3334 | (31*2^420556+1)/7 | 126601 | Lelio R Paula | 05/2014 |
| 3335 | 7*10^126600-99 | 126601 | Robert Price | 06/2019 |
| 3336 | 2^420424-59189 | 126561 | Enzo Doria | 10/2015 |
| 3337 | 28717^25534+25534^28717 | 126560 | Hans Havermann | 03/2021 |
| 3338 | 28922^23655+23655^28922 | 126503 | Hans Havermann | 03/2021 |
| 3339 | 2^420126+71893 | 126471 | Enzo Doria | 04/2016 |
| 3340 | (43*10^126441+47)/9 | 126442 | Robert Price | 12/2018 |
| 3341 | 2^419866+1877059 | 126393 | Enzo Doria | 07/2016 |
| 3342 | 29315^20484+20484^29315 | 126390 | Hans Havermann | 03/2021 |
| 3343 | 29433^19676+19676^29433 | 126384 | Hans Havermann | 03/2021 |
| 3344 | F(604711) | 126377 | Henri Lifchitz | 02/2005 |
| 3345 | 2^419757+72707 | 126360 | Enzo Doria | 04/2016 |
| 3346 | 2^419720-21569 | 126349 | Enzo Doria | 07/2013 |
| 3347 | 2^419637+29 | 126324 | Henri Lifchitz | 02/2006 |
| 3348 | 31004^11865+11865^31004 | 126319 | Hans Havermann | 03/2021 |
| 3349 | 2^419612+1876741 | 126316 | Enzo Doria | 07/2016 |
| 3350 | 2^419520+2793271 | 126289 | Enzo Doria | 03/2016 |
| 3351 | (2^419447-5)/369 | 126264 | Lelio R Paula | 05/2014 |
| 3352 | 2^419328-1859939 | 126231 | Enzo Doria | 03/2016 |
| 3353 | 2^419282-1851507 | 126217 | Enzo Doria | 08/2015 |
| 3354 | (133*10^126212+17)/3 | 126214 | Robert Price | 11/2021 |
| 3355 | 2^419251+1866143 | 126208 | Enzo Doria | 03/2016 |
| 3356 | 11^121185+2 | 126202 | Robert Price | 05/2014 |
| 3357 | 28203^28352+28352^28203 | 126175 | Norbert Schneider | 01/2021 |
| 3358 | (23*2^419036-1)/1393 | 126141 | Lelio R Paula | 05/2014 |
| 3359 | 2^418851+23 | 126087 | Robert Price | 09/2015 |
| 3360 | (2^418849-9)/2681 | 126083 | Lelio R Paula | 05/2014 |
| 3361 | 2^418829+167 | 126081 | Lelio R Paula | 01/2012 |
| 3362 | 31037^11530+11530^31037 | 126067 | Hans Havermann | 03/2021 |
| 3363 | (31*2^418782-1)/75891 | 126063 | Lelio R Paula | 05/2014 |
| 3364 | (19*2^418754-1)/15 | 126058 | Lelio R Paula | 05/2014 |
| 3365 | (35*10^126048-323)/9 | 126049 | Robert Price | 10/2021 |
| 3366 | 33016^6551+6551^33016 | 126000 | Hans Havermann | 03/2021 |
| 3367 | 2^418548-111546435 | 125996 | Paul Bourdelais | 10/2021 |
| 3368 | 34736^4227+4227^34736 | 125954 | Hans Havermann | 03/2021 |
| 3369 | 2^418319-109501 | 125927 | Enzo Doria | 04/2014 |
| 3370 | 2^418316-112373 | 125926 | Enzo Doria | 06/2014 |
| 3371 | 40398^1309+1309^40398 | 125919 | Hans Havermann | 03/2021 |
| 3372 | (8*10^125894-29)/3 | 125895 | Robert Price | 07/2018 |
| 3373 | (26*10^125886-413)/9 | 125887 | Robert Price | 05/2018 |
| 3374 | 2^417968+1869811 | 125821 | Enzo Doria | 06/2016 |
| 3375 | 2^417902+63 | 125802 | Lelio R Paula | 09/2015 |
| 3376 | (10^125792-91)/9 | 125792 | Serge Batalov | 12/2014 |
| 3377 | 30438^13573+13573^30438 | 125791 | Hans Havermann | 03/2021 |
| 3378 | 32867^6714+6714^32867 | 125782 | Hans Havermann | 03/2021 |
| 3379 | 31155^10892+10892^31155 | 125777 | Hans Havermann | 03/2021 |
| 3380 | (35*10^125754-593)/9 | 125755 | Robert Price | 07/2018 |
| 3381 | 30455^13464+13464^30455 | 125754 | Hans Havermann | 03/2021 |
| 3382 | (32*10^125751-77)/9 | 125752 | Robert Price | 06/2018 |
| 3383 | 2^417704+77011 | 125742 | Enzo Doria | 05/2016 |
| 3384 | 29755^16816+16816^29755 | 125737 | Hans Havermann | 03/2021 |
| 3385 | (22*10^125734+203)/9 | 125735 | Robert Price | 10/2021 |
| 3386 | 29918^15915+15915^29918 | 125710 | Hans Havermann | 03/2021 |
| 3387 | (10^125706+149)/3 | 125706 | Serge Batalov | 12/2014 |
| 3388 | 28531^25368+25368^28531 | 125659 | Hans Havermann | 03/2021 |
| 3389 | 2^417419-115309 | 125656 | Enzo Doria | 07/2015 |
| 3390 | 2^417300+77281 | 125620 | Enzo Doria | 05/2016 |
| 3391 | 30638^12537+12537^30638 | 125561 | Hans Havermann | 03/2021 |
| 3392 | 2^417095-1657 | 125559 | Yves Minet | 07/2014 |
| 3393 | 30162^14525+14525^30162 | 125538 | Hans Havermann | 03/2021 |
| 3394 | (56*10^125535+583)/9 | 125536 | Robert Price | 08/2021 |
| 3395 | (88*10^125492-637)/9 | 125493 | Robert Price | 11/2020 |
| 3396 | 28958^21525+21525^28958 | 125474 | Hans Havermann | 02/2021 |
| 3398 | 2^416773-25 | 125462 | Lelio R Paula | 09/2015 |
| 3397 | (10^125482+7)/162685667/1639829194459 | 125462 | Alfred Reich | 07/2021 |
| 3399 | 33889^5032+5032^33889 | 125449 | Hans Havermann | 03/2021 |
| 3400 | (289511#+292834)/(2^3*146417) | 125444 | Makoto Morimoto | 10/2017 |
| 3401 | (11*2^416691+1)/43 | 125436 | Lelio R Paula | 05/2014 |
| 3402 | (289511#+1896)/(2*3^3*79*780193*9911849) | 125434 | Makoto Morimoto | 06/2019 |
| 3403 | 2^416641-2*416641+1 | 125422 | Robert Price | 05/2018 |
| 3404 | 33392^5697+5697^33392 | 125409 | Hans Havermann | 03/2021 |
| 3405 | (21*2^416566-1)/17 | 125399 | Lelio R Paula | 05/2014 |
| 3406 | 2^416530+1870429 | 125389 | Enzo Doria | 05/2016 |
| 3407 | (56*10^125385+691)/9 | 125386 | Robert Price | 05/2019 |
| 3408 | 27953^28198+28198^27953 | 125381 | Norbert Schneider | 01/2021 |
| 3409 | 31074^10837+10837^31074 | 125381 | Hans Havermann | 03/2021 |
| 3410 | 33745^5194+5194^33745 | 125380 | Hans Havermann | 03/2021 |
| 3411 | 2^416490+1875109 | 125376 | Enzo Doria | 09/2016 |
| 3412 | 28360^26331+26331^28360 | 125365 | Hans Havermann | 03/2021 |
| 3413 | 2^416416-114929 | 125354 | Enzo Doria | 05/2015 |
| 3414 | (77*10^125330-293)/9 | 125331 | Robert Price | 09/2019 |
| 3415 | (172*10^125292-1)/9 | 125294 | Serge Batalov | 12/2014 |
| 3416 | 2^416134+1865899 | 125269 | Enzo Doria | 03/2016 |
| 3417 | 153^57337-152 | 125264 | Norbert Schneider | 12/2018 |
| 3418 | (9*2^415992+1)/13560845 | 125220 | Lelio R Paula | 05/2014 |
| 3419 | 30054^14657+14657^30054 | 125207 | Hans Havermann | 03/2021 |
| 3420 | (23^91943-1)/22 | 125201 | Robert Price | 01/2012 |
| 3421 | 2^415884-933075 | 125194 | Paul Bourdelais | 06/2021 |
| 3422 | 43125^27010-106 | 125185 | Enzo Doria | 08/2012 |
| 3423 | (38*10^125166+349)/9 | 125167 | Robert Price | 10/2018 |
| 3424 | 2^415765-112603 | 125158 | Enzo Doria | 06/2014 |
| 3425 | 8*10^125088-13 | 125089 | Robert Price | 08/2019 |
| 3426 | (25*10^125076-13)/3 | 125077 | Robert Price | 09/2019 |
| 3427 | (11*10^125054+73)/3 | 125055 | Robert Price | 08/2021 |
| 3428 | (29*10^125021-113)/3 | 125022 | Robert Price | 10/2019 |
| 3429 | 2^415290-113591 | 125015 | Enzo Doria | 08/2014 |
| 3430 | 2^415276-460919 | 125011 | Enzo Doria | 06/2015 |
| 3431 | 2^415259+77243 | 125006 | Enzo Doria | 05/2016 |
| 3432 | (67*10^124990+77)/9 | 124991 | Robert Price | 10/2021 |
| 3433 | 2^415144-3683 | 124971 | Yves Minet | 10/2011 |
| 3434 | 2^415092+111546435 | 124956 | Paul Bourdelais | 10/2021 |
| 3435 | 31936^8173+8173^31936 | 124946 | Hans Havermann | 03/2021 |
| 3436 | 5^178715-4 | 124916 | Tyler NeSmith | 07/2021 |
| 3437 | 29767^15700+15700^29767 | 124900 | Hans Havermann | 03/2021 |
| 3438 | 2^414874+79 | 124890 | Lelio R Paula | 01/2015 |
| 3439 | (2^414765+7)/1389 | 124854 | Lelio R Paula | 05/2014 |
| 3440 | 2^414618+79459 | 124813 | Enzo Doria | 06/2016 |
| 3441 | (61*10^124809-1)/3 | 124811 | Robert Price | 01/2020 |
| 3442 | (29*10^124765-71)/3 | 124766 | Robert Price | 07/2021 |
| 3443 | 2^414432-1846709 | 124757 | Enzo Doria | 07/2015 |
| 3444 | 2*10^124751-51 | 124752 | Robert Price | 04/2018 |
| 3445 | (56*10^124735+367)/9 | 124736 | Robert Price | 06/2019 |
| 3446 | (13*2^414274-1)/153 | 124708 | Lelio R Paula | 05/2014 |
| 3447 | 56*10^124656-3 | 124658 | Robert Price | 03/2020 |
| 3448 | (7*10^124648+197)/3 | 124649 | Robert Price | 07/2018 |
| 3450 | 2^414032-5 | 124637 | Henri Lifchitz | 07/2006 |
| 3449 | 2^414032+1872331 | 124637 | Enzo Doria | 05/2016 |
| 3451 | 37373^2158+2158^37373 | 124604 | Hans Havermann | 03/2021 |
| 3452 | 29811^15112+15112^29811 | 124590 | Hans Havermann | 03/2021 |
| 3453 | 14120^30009-30009^14120 | 124533 | Norbert Schneider | 02/2015 |
| 3454 | 29757^15296+15296^29757 | 124521 | Hans Havermann | 03/2021 |
| 3455 | 35056^3561+3561^35056 | 124504 | Hans Havermann | 03/2021 |
| 3456 | 40588^1167+1167^40588 | 124487 | Hans Havermann | 02/2021 |
| 3457 | (85*10^124485-49)/9 | 124486 | Robert Price | 12/2020 |
| 3458 | 64^68909-63^68909 | 124463 | Robert Price | 07/2013 |
| 3459 | 35016^3581+3581^35016 | 124448 | Hans Havermann | 03/2021 |
| 3460 | 2^413387+76253 | 124442 | Enzo Doria | 04/2016 |
| 3461 | 28749^21298+21298^28749 | 124436 | Hans Havermann | 03/2021 |
| 3462 | 2^413352+524287 | 124432 | Paul Underwood | 09/2018 |
| 3463 | 287117#+391613 | 124424 | Nicolas PALAU | 01/2017 |
| 3464 | (4*10^124420+83)/3 | 124421 | Robert Price | 02/2018 |
| 3465 | 34578^3965+3965^34578 | 124421 | Hans Havermann | 03/2021 |
| 3466 | (68*10^124392-329)/9 | 124393 | Robert Price | 03/2021 |
| 3467 | (27*2^413207-1)/108335 | 124385 | Lelio R Paula | 05/2014 |
| 3468 | 10^124383+58407 | 124384 | Patrick De Geest | 08/2021 |
| 3470 | 10^124383-8000001 | 124383 | Robert Price | 04/2021 |
| 3469 | 10^124383-5801 | 124383 | Patrick De Geest | 08/2021 |
| 3471 | (41*10^124335-383)/9 | 124336 | Robert Price | 11/2018 |
| 3472 | (304*10^124329-43)/9 | 124331 | Robert Price | 02/2020 |
| 3473 | 34716^3811+3811^34716 | 124320 | Hans Havermann | 03/2021 |
| 3474 | 2^412868-120599 | 124286 | Paul Bourdelais | 02/2012 |
| 3475 | 10^124248+899089 | 124249 | Patrick De Geest | 05/2021 |
| 3477 | 10^124248-1000001 | 124248 | Robert Price | 08/2020 |
| 3476 | 10^124248-501903 | 124248 | Patrick De Geest | 05/2021 |
| 3478 | 45^75145-2 | 124231 | Lelio R Paula | 08/2015 |
| 3479 | 29901^14272+14272^29901 | 124224 | Hans Havermann | 03/2021 |
| 3480 | 2^412645-112213 | 124219 | Enzo Doria | 06/2014 |
| 3481 | 29837^14500+14500^29837 | 124163 | Hans Havermann | 03/2021 |
| 3482 | 28074^26455+26455^28074 | 124158 | Hans Havermann | 03/2021 |
| 3483 | 2^412248+74611 | 124100 | Enzo Doria | 04/2016 |
| 3484 | (22*10^124096-13)/9 | 124097 | Robert Price | 06/2018 |
| 3485 | (455*10^124093+31)/9 | 124095 | Robert Price | 06/2021 |
| 3486 | 2^412192-3329 | 124083 | Yves Minet | 12/2014 |
| 3487 | (25*2^412191-1)/23 | 124082 | Lelio R Paula | 05/2014 |
| 3489 | (25*10^124076-67)/3 | 124077 | Robert Price | 06/2019 |
| 3488 | 28132^25735+25735^28132 | 124077 | Hans Havermann | 03/2021 |
| 3490 | F(593689) | 124074 | Henri Lifchitz | 01/2005 |
| 3491 | (11*2^412161+1)/19 | 124073 | Lelio R Paula | 05/2014 |
| 3492 | 35364^3215+3215^35364 | 124028 | Hans Havermann | 03/2021 |
| 3494 | (266*10^124022-11)/3 | 124024 | Robert Price | 04/2020 |
| 3493 | 29987^13674+13674^29987 | 124024 | Hans Havermann | 03/2021 |
| 3495 | 2^411932-111546435 | 124004 | Paul Bourdelais | 10/2021 |
| 3496 | 2^411884-113279 | 123990 | Enzo Doria | 07/2014 |
| 3497 | (2^411832+1)/257 | 123972 | Lelio R Paula | 05/2014 |
| 3498 | (2^411833+2)/514 | 123972 | Stefano Morozzi | 03/2020 |
| 3499 | (26*10^123970-89)/9 | 123971 | Robert Price | 06/2018 |
| 3500 | 2^411790-1853531 | 123962 | Enzo Doria | 08/2015 |
