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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Rank |
Probable prime |
Digits (> 50000) |
Who ? |
When ? |
3251 | 2^351460-17289 | 105801 | Enzo Doria | 05/2013 |
3252 | 19^82735+22 | 105798 | Lelio R Paula | 01/2017 |
3253 | 2^351435-109077 | 105793 | Enzo Doria | 04/2014 |
3254 | 2^351393+1089 | 105780 | Lelio R Paula | 01/2017 |
3255 | 2^351364+72631 | 105772 | Enzo Doria | 04/2016 |
3256 | 2^351305+1872467 | 105754 | Enzo Doria | 05/2016 |
3257 | 3^221649+16 | 105754 | Lelio R Paula | 11/2016 |
3258 | 8*3^221637-5 | 105749 | Lelio R Paula | 09/2014 |
3259 | 2^351279-2780449 | 105746 | Enzo Doria | 03/2016 |
3260 | 15^89903-26 | 105735 | Lelio R Paula | 02/2017 |
3261 | 2^351213-73 | 105726 | Lelio R Paula | 10/2011 |
3262 | 2^351192-4589 | 105720 | Yves Minet | 07/2011 |
3263 | 20^81250-33 | 105709 | Lelio R Paula | 12/2016 |
3264 | 2^351076-113159 | 105685 | Enzo Doria | 07/2014 |
3265 | 93^53688-2 | 105684 | Lelio R Paula | 09/2013 |
3266 | 2^351060-4559 | 105680 | Yves Minet | 07/2011 |
3267 | ((10^52836-1)*10000/9+5927)*10^52836+(10^52836-1)/9 | 105676 | Hans Havermann | 08/2019 |
3268 | 11^101473-750 | 105674 | Enzo Doria | 11/2012 |
3269 | 3*5^151181-8 | 105672 | Lelio R Paula | 11/2014 |
3270 | 15^89831-34 | 105650 | Lelio R Paula | 02/2017 |
3272 | 11^101448-360 | 105648 | Enzo Doria | 08/2012 |
3271 | 3*7^125011+4 | 105648 | Lelio R Paula | 11/2014 |
3273 | 2^350943-113269 | 105645 | Enzo Doria | 07/2014 |
3274 | 2^350868-19725 | 105622 | Enzo Doria | 06/2013 |
3275 | 2^350858-59291 | 105619 | Enzo Doria | 10/2015 |
3276 | 2^350851+135 | 105617 | Lelio R Paula | 10/2011 |
3277 | 2^350841-741 | 105614 | Lelio R Paula | 01/2017 |
3278 | 3*10^105582+77 | 105583 | Robert Price | 09/2018 |
3279 | 8*10^105571+3 | 105572 | Robert Price | 08/2015 |
3280 | 2^350674-78557 | 105564 | Jorge Menendez | 03/2018 |
3281 | 2*5^151026-3 | 105563 | Lelio R Paula | 11/2014 |
3282 | (2^350702+5)/34264674063 | 105562 | Lelio R Paula | 12/2013 |
3283 | 6^135647-5^135647 | 105554 | Jean-Louis Charton | 02/2009 |
3284 | 3^221211+236 | 105545 | Lelio R Paula | 11/2016 |
3285 | (32*10^105530-77)/9 | 105531 | Robert Price | 06/2018 |
3286 | 10^105515+33 | 105516 | Lelio R Paula | 11/2016 |
3287 | 10^105515-41033 | 105515 | Patrick De Geest | 12/2016 |
3288 | (29*2^350473-1)/267927 | 105499 | Lelio R Paula | 03/2014 |
3289 | 17^85732-72 | 105489 | Lelio R Paula | 01/2017 |
3290 | 2^350307-110329 | 105453 | Enzo Doria | 05/2014 |
3291 | 2^350253-20365 | 105437 | Enzo Doria | 06/2013 |
3292 | (3*29^72089-1075)/4 | 105423 | Curtis Bright | 05/2015 |
3293 | 2^350139-109009 | 105403 | Enzo Doria | 04/2014 |
3294 | 3*5^150763+4 | 105380 | Lelio R Paula | 11/2014 |
3295 | 12^97643+91 | 105375 | Lelio R Paula | 02/2017 |
3296 | 6*5^150744-7 | 105367 | Lelio R Paula | 11/2014 |
3297 | 2^349996-112169 | 105360 | Enzo Doria | 06/2014 |
3298 | 11^101142-1080 | 105329 | Enzo Doria | 12/2012 |
3299 | (68*10^105320-41)/9 | 105321 | Robert Price | 10/2013 |
3300 | 3^220712-9934 | 105307 | Enzo Doria | 05/2014 |
3301 | 7*10^105296+9 | 105297 | Robert Price | 09/2015 |
3302 | 2^349739+1873373 | 105282 | Enzo Doria | 06/2016 |
3303 | 7^124574+24 | 105278 | Lelio R Paula | 11/2016 |
3304 | 2^349708-20957 | 105273 | Enzo Doria | 06/2013 |
3305 | 2^349649-20469 | 105255 | Enzo Doria | 06/2013 |
3306 | 2^349607-20109 | 105243 | Enzo Doria | 06/2013 |
3307 | 2^349594-19085 | 105239 | Enzo Doria | 05/2013 |
3308 | 2^349530+1874479 | 105220 | Enzo Doria | 06/2016 |
3309 | (3^220528+8)/8081 | 105215 | Lelio R Paula | 12/2013 |
3310 | 3^220464-112852 | 105189 | Enzo Doria | 07/2014 |
3311 | 2^349419-17349 | 105186 | Enzo Doria | 05/2013 |
3312 | 2^349400-2579 | 105180 | Yves Minet | 07/2014 |
3313 | 8*5^150471+3 | 105176 | Lelio R Paula | 11/2014 |
3314 | 655^37342+37342^655 | 105165 | Norbert Schneider | 08/2018 |
3315 | 13^94403+94 | 105160 | Lelio R Paula | 12/2016 |
3316 | 2^349301-112309 | 105151 | Enzo Doria | 06/2014 |
3317 | 9*2^349220+5 | 105127 | Lelio R Paula | 09/2014 |
3318 | 7*3^220317+8 | 105119 | Lelio R Paula | 09/2014 |
3319 | 7^124386+88 | 105119 | Lelio R Paula | 11/2016 |
3320 | 2^349171-19657 | 105111 | Enzo Doria | 06/2013 |
3321 | (2^(6*58185+1)-5)/3 | 105093 | Kevin Acres | 11/2013 |
3322 | (2^349111-5)/3 | 105093 | Lelio R Paula | 12/2013 |
3323 | 675^37142+37142^675 | 105087 | Norbert Schneider | 08/2018 |
3324 | 2^348981-2797573 | 105054 | Enzo Doria | 04/2016 |
3325 | 2^348869-6555 | 105021 | Lelio R Paula | 01/2017 |
3326 | 5^150217+78 | 104998 | Lelio R Paula | 11/2016 |
3327 | (28*10^104972+149)/3 | 104973 | Robert Price | 12/2019 |
3328 | 2^348703-113005 | 104971 | Enzo Doria | 06/2014 |
3330 | 2^348612-809 | 104943 | Yves Minet | 05/2013 |
3329 | (73*10^104942-1)/9 | 104943 | Robert Price | 01/2015 |
3331 | 2^348583-350407 | 104934 | Enzo Doria | 06/2015 |
3332 | 2^348531-949 | 104919 | Yves Minet | 05/2012 |
3333 | 20^80636-59 | 104910 | Lelio R Paula | 12/2016 |
3334 | 8*10^104893-13 | 104894 | Robert Price | 08/2019 |
3335 | 2^348437+35 | 104890 | Lelio R Paula | 09/2011 |
3336 | 2^348348+135 | 104864 | Lelio R Paula | 09/2011 |
3337 | (2^348284+9)/25 | 104843 | Lelio R Paula | 12/2013 |
3338 | 75^55914-74 | 104843 | Norbert Schneider | 01/2015 |
3339 | 2^348268+255255 | 104840 | Lelio R Paula | 01/2017 |
3340 | 5^149985-52 | 104836 | Lelio R Paula | 11/2016 |
3341 | 2^348224-20249 | 104826 | Enzo Doria | 06/2013 |
3342 | 2^348212-20105 | 104823 | Enzo Doria | 06/2013 |
3343 | 20^80562+19 | 104814 | Lelio R Paula | 12/2016 |
3344 | 2*10^104811-87 | 104812 | Robert Price | 04/2018 |
3345 | 2^348149-20053 | 104804 | Enzo Doria | 06/2013 |
3346 | 2^348095-171 | 104788 | Lelio R Paula | 09/2011 |
3347 | 2^348003-20377 | 104760 | Enzo Doria | 06/2013 |
3348 | 2^347994-741 | 104757 | Lelio R Paula | 12/2016 |
3349 | (13*2^347972-1)/282309 | 104746 | Lelio R Paula | 03/2014 |
3350 | 2^347910-109937 | 104732 | Enzo Doria | 04/2014 |
3351 | 5^149794+28 | 104702 | Lelio R Paula | 11/2016 |
3352 | 105^51800-2 | 104698 | Lelio R Paula | 10/2017 |
3353 | (16^86939+3^86939)/19 | 104684 | Robert Price | 06/2013 |
3354 | (15^89009-1)/14 | 104682 | Paul Bourdelais | 03/2010 |
3355 | 2^347731-18609 | 104678 | Enzo Doria | 05/2013 |
3356 | 4*6^134519+7 | 104677 | Lelio R Paula | 11/2014 |
3357 | 2^347612-18545 | 104642 | Enzo Doria | 05/2013 |
3358 | 6^134465+95 | 104635 | Lelio R Paula | 11/2016 |
3359 | 2^347517-17301 | 104614 | Enzo Doria | 05/2013 |
3360 | 3^219222-310 | 104596 | Lelio R Paula | 11/2016 |
3361 | (15*2^347399-1)/13 | 104578 | Lelio R Paula | 03/2014 |
3362 | 2^347372-17853 | 104570 | Enzo Doria | 05/2013 |
3363 | 2^347314+99 | 104552 | Lelio R Paula | 09/2011 |
3364 | 2^347300-22233 | 104548 | Enzo Doria | 06/2013 |
3365 | 2^347287-19845 | 104544 | Enzo Doria | 06/2013 |
3366 | (31*2^347254-1)/891 | 104533 | Lelio R Paula | 03/2014 |
3367 | 5*F(250091)*(F(250091)-1)+1 | 104532 | Serge Batalov | 04/2015 |
3368 | 7*2^347239-3 | 104531 | Lelio R Paula | 09/2014 |
3369 | (3^219098-8)/514147439969 | 104525 | Lelio R Paula | 12/2013 |
3370 | 5*3^219047+8 | 104513 | Lelio R Paula | 09/2014 |
3371 | 2^347148-109073 | 104502 | Enzo Doria | 04/2014 |
3372 | 2^347129-20145 | 104497 | Enzo Doria | 06/2013 |
3373 | 4*10^104461-57 | 104462 | Robert Price | 10/2018 |
3374 | 2^346923-19585 | 104435 | Enzo Doria | 05/2013 |
3375 | (11*2^346864-1)/175 | 104416 | Lelio R Paula | 03/2014 |
3376 | 2^346854+346854^2+1 | 104414 | Robert Price | 06/2014 |
3377 | 2^346834+11715 | 104408 | Lelio R Paula | 04/2015 |
3378 | 79^55009+78 | 104387 | Norbert Schneider | 02/2015 |
3379 | 3^218744+58 | 104368 | Lelio R Paula | 11/2016 |
3380 | 9*10^104361+89 | 104362 | Robert Price | 11/2019 |
3381 | 2^346649+65 | 104352 | Lelio R Paula | 09/2011 |
3382 | 2^346638-17265 | 104349 | Enzo Doria | 05/2013 |
3383 | 5*10^104326+77 | 104327 | Robert Price | 12/2018 |
3385 | 2^346527-111817 | 104316 | Enzo Doria | 05/2014 |
3384 | 6^134055+101 | 104316 | Lelio R Paula | 11/2016 |
3386 | 92105!4+8 | 104312 | Robert Price | 09/2019 |
3387 | 6^134013+163 | 104283 | Lelio R Paula | 11/2016 |
3388 | 18^83049-89 | 104250 | Lelio R Paula | 01/2017 |
3389 | 2^346213+484049 | 104221 | Enzo Doria | 04/2017 |
3390 | 18^83021-91 | 104214 | Lelio R Paula | 01/2017 |
3391 | 10^104212+128779 | 104213 | Patrick De Geest | 05/2016 |
3392 | 10^104212+237447 | 104213 | Patrick De Geest | 05/2016 |
3393 | 10^104212+242139 | 104213 | Patrick De Geest | 05/2016 |
3394 | 10^104212+269199 | 104213 | Patrick De Geest | 05/2016 |
3395 | (10^104212-71)/1 | 104212 | Serge Batalov | 12/2014 |
3396 | 2^346078+7695 | 104180 | Lelio R Paula | 12/2016 |
3397 | 2^346055-19537 | 104173 | Enzo Doria | 05/2013 |
3398 | (3*2^346057+1)/77 | 104173 | Lelio R Paula | 12/2013 |
3399 | 2^346037-20125 | 104168 | Enzo Doria | 06/2013 |
3400 | (34*10^104168-7)/9/13/551179 | 104162 | Makoto Morimoto | 05/2016 |
3401 | 6^133854-17993 | 104159 | Enzo Doria | 03/2013 |
3402 | 2^345990+1874239 | 104154 | Enzo Doria | 06/2016 |
3403 | 2^345988-20373 | 104153 | Enzo Doria | 06/2013 |
3404 | (26*10^104132-503)/9 | 104133 | Robert Price | 07/2018 |
3405 | 3*5^148968+8 | 104125 | Lelio R Paula | 11/2014 |
3406 | (7*10^104113+53)/3 | 104114 | Robert Price | 05/2018 |
3407 | p(21253)#/2+8 | 104113 | Robert Price | 01/2017 |
3408 | 322^41507+41507^322 | 104094 | Norbert Schneider | 12/2014 |
3409 | 6^133768-17423 | 104092 | Enzo Doria | 03/2013 |
3410 | 2^345786-19557 | 104092 | Enzo Doria | 05/2013 |
3411 | 171^46606-2 | 104072 | Lelio R Paula | 10/2017 |
3412 | 2^345704-149 | 104068 | Lelio R Paula | 09/2011 |
3413 | 6^133704-17273 | 104042 | Enzo Doria | 02/2013 |
3414 | (3*2^345590-1)/23 | 104033 | Lelio R Paula | 03/2014 |
3415 | (19*2^345590+1)/33859 | 104030 | Lelio R Paula | 12/2013 |
3416 | 2^345547+11 | 104021 | Lelio R Paula | 09/2011 |
3417 | (19*10^104014-49)/3 | 104015 | Robert Price | 05/2019 |
3418 | 2^345504+723 | 104008 | Lelio R Paula | 09/2011 |
3419 | 2^345498-20037 | 104006 | Enzo Doria | 06/2013 |
3420 | 18^82854-37 | 104005 | Lelio R Paula | 01/2017 |
3421 | 2^345486-109065 | 104002 | Enzo Doria | 04/2014 |
3422 | 2^345487-1851507 | 104002 | Enzo Doria | 08/2015 |
3423 | 2^345476+777 | 103999 | Lelio R Paula | 09/2011 |
3424 | 4*10^103981-83 | 103982 | Robert Price | 10/2018 |
3425 | (5*2^345321-1)/3 | 103953 | Lelio R Paula | 03/2014 |
3426 | (2^345267-9)/539049127 | 103927 | Lelio R Paula | 12/2013 |
3427 | (19*10^103907+77)/3 | 103908 | Robert Price | 05/2019 |
3428 | (78557*2^345163+1)/78589 | 103905 | Lelio R Paula | 07/2014 |
3429 | 2^345106-112181 | 103888 | Enzo Doria | 06/2014 |
3430 | 2^345079+99 | 103880 | Lelio R Paula | 09/2011 |
3431 | 11^99736-1500 | 103865 | Enzo Doria | 12/2012 |
3432 | 2^344842-20157 | 103808 | Enzo Doria | 06/2013 |
3433 | (47*2^344822+1)/1071 | 103801 | Lelio R Paula | 05/2015 |
3434 | 2^344802-20765 | 103796 | Enzo Doria | 06/2013 |
3435 | 2^344794-3821 | 103794 | Yves Minet | 05/2011 |
3436 | 2^344782-109103 | 103790 | Enzo Doria | 04/2014 |
3437 | 3^217521-112292 | 103784 | Enzo Doria | 06/2014 |
3438 | 2^344759-3505 | 103783 | Lelio R Paula | 11/2016 |
3439 | 2^344735-147 | 103776 | Lelio R Paula | 09/2011 |
3440 | L(496533)-p(496533) | 103770 | Robert Price | 02/2018 |
3441 | 2*10^103749-69 | 103750 | Robert Price | 03/2018 |
3442 | (55459*2^344617+1)/3 | 103745 | Lelio R Paula | 07/2014 |
3443 | 2^344607-108891 | 103738 | Enzo Doria | 03/2014 |
3444 | 2^344541-19561 | 103718 | Enzo Doria | 05/2013 |
3445 | (1017*2^344529-1)/569 | 103714 | Lelio R Paula | 05/2015 |
3446 | (4*10^103703-1)/3 | 103704 | Serge Batalov | 08/2009 |
3447 | 2^344444-455 | 103688 | Yves Minet | 03/2012 |
3448 | (13*53^238539*617^9)/10^307661 | 103673 | Hans Havermann | 06/2017 |
3449 | 2^344317-109933 | 103650 | Enzo Doria | 04/2014 |
3450 | 2^344309-1852033 | 103648 | Enzo Doria | 08/2015 |
3451 | 2^344213-21253 | 103619 | Enzo Doria | 06/2013 |
3452 | 2^344196-465 | 103614 | Lelio R Paula | 11/2016 |
3453 | 2^344187-20001 | 103611 | Enzo Doria | 06/2013 |
3454 | (117191#+(355573#)/(117191#))/(200233679) | 103602 | Makoto Morimoto | 10/2017 |
3455 | 20^79621-19^79621 | 103590 | Jean-Louis Charton | 03/2011 |
3456 | Phi(155391,10)/1243129 | 103586 | Maksym Voznyy | 09/2015 |
3457 | 2^344085-20365 | 103580 | Enzo Doria | 06/2013 |
3458 | 5^148169+54 | 103566 | Lelio R Paula | 11/2016 |
3459 | 2^344017-108795 | 103560 | Enzo Doria | 03/2014 |
3460 | 2^343971-5077 | 103546 | Lelio R Paula | 09/2011 |
3461 | (7*10^103531+71)/3 | 103532 | Robert Price | 05/2018 |
3462 | 2^343899+141 | 103524 | Lelio R Paula | 08/2011 |
3463 | (2^343933+1)/(3*98294339989393) | 103520 | Gord Palameta | 08/2018 |
3464 | 6^133029-67 | 103517 | Lelio R Paula | 11/2016 |
3465 | (17*2^343877+1)/13625 | 103515 | Lelio R Paula | 12/2013 |
3466 | (136*10^103474-1)/9 | 103476 | Serge Batalov | 12/2014 |
3467 | 5^148014-24 | 103458 | Lelio R Paula | 11/2016 |
3468 | (22*10^103450+53)/3 | 103451 | Robert Price | 07/2019 |
3469 | 2^343604+9931 | 103436 | Yves Minet | 01/2011 |
3470 | 2^343601-21189 | 103435 | Enzo Doria | 06/2013 |
3471 | 2^343508-115229 | 103407 | Enzo Doria | 06/2015 |
3472 | (509203*2^343491-1)/16147 | 103403 | Lelio R Paula | 05/2015 |
3473 | 3^216685-113056 | 103386 | Enzo Doria | 07/2014 |
3474 | 91355!4+1024 | 103381 | Robert Price | 09/2019 |
3475 | 44^62903-43^62903 | 103379 | Jean-Louis Charton | 08/2012 |
3476 | 11^99262-20 | 103371 | Lelio R Paula | 12/2016 |
3477 | (509203*2^343357-1)/5 | 103366 | Lelio R Paula | 05/2015 |
3478 | 2^343356-2791889 | 103361 | Enzo Doria | 03/2016 |
3479 | (25*10^103360-241)/9 | 103361 | Robert Price | 05/2018 |
3480 | Phi(104989,10)/2939693 | 103350 | Maksym Voznyy | 09/2015 |
3481 | 2^343182-171 | 103309 | Lelio R Paula | 08/2011 |
3482 | (23619^23619+23620^23620)/7187 | 103294 | David Broadhurst | 09/2009 |
3483 | 2^343079-1835611 | 103278 | Enzo Doria | 05/2015 |
3484 | 2^343063-1147 | 103273 | Yves Minet | 06/2013 |
3485 | 9*6^132689+7 | 103254 | Lelio R Paula | 11/2014 |
3486 | 2^342979-18085 | 103247 | Enzo Doria | 05/2013 |
3487 | (16*10^103244-31)/3 | 103245 | Robert Price | 03/2019 |
3488 | 2^342966-16995 | 103244 | Lelio R Paula | 11/2016 |
3489 | (16*10^103214-31)/3 | 103215 | Robert Price | 03/2019 |
3490 | (37*10^103211+611)/9 | 103212 | Robert Price | 11/2018 |
3491 | 5^147650+16 | 103203 | Lelio R Paula | 11/2016 |
3492 | gcd(Phi(852060,10),(10^42603+1)^3*(10^42603+1-10^21302)+(10^85206+10^42603)*(10^21302+1)+10^127809) | 103201 | Serge Batalov | 04/2015 |
3493 | 2^342817+2707067 | 103199 | Enzo Doria | 03/2016 |
3494 | 43^63177-42 | 103198 | Theodore Burton | 02/2007 |
3495 | 2^342805-21025 | 103195 | Enzo Doria | 06/2013 |
3496 | 2^342714+12285 | 103168 | Lelio R Paula | 11/2016 |
3497 | 18^82178-4481 | 103156 | Enzo Doria | 03/2013 |
3498 | 2^342665-17349 | 103153 | Enzo Doria | 05/2013 |
3499 | 2^342612+175 | 103137 | Lelio R Paula | 08/2011 |
3500 | 5*2^342585-3 | 103130 | Lelio R Paula | 09/2014 |