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 ? |
8251 | 2^338448+187167 | 101883 | Stefano Morozzi | 04/2022 |
8252 | 2^338446-160115 | 101883 | Stefano Morozzi | 06/2022 |
8253 | 2^338447-164157 | 101883 | Stefano Morozzi | 01/2023 |
8254 | 2^338447-191001 | 101883 | Stefano Morozzi | 01/2023 |
8255 | 2^338444+127623 | 101882 | Stefano Morozzi | 12/2021 |
8256 | 2^338443-113827 | 101882 | Stefano Morozzi | 12/2022 |
8257 | 2^338441-5893 | 101881 | Stefano Morozzi | 02/2022 |
8258 | 2^338439-162565 | 101881 | Stefano Morozzi | 12/2022 |
8259 | 2^338436+153657 | 101880 | Stefano Morozzi | 01/2022 |
8260 | 2^338437-153159 | 101880 | Stefano Morozzi | 01/2022 |
8261 | 2^338436-83783 | 101880 | Stefano Morozzi | 04/2022 |
8262 | 2^338435+89109 | 101880 | Stefano Morozzi | 05/2022 |
8263 | 2^338435+13871 | 101880 | Stefano Morozzi | 05/2022 |
8264 | 2^338436+149691 | 101880 | Stefano Morozzi | 02/2023 |
8265 | 2^338434+81537 | 101879 | Stefano Morozzi | 01/2022 |
8266 | 2^338432+33495 | 101879 | Stefano Morozzi | 03/2022 |
8267 | 2^338432-7043 | 101879 | Stefano Morozzi | 03/2022 |
8268 | 2^338433-32629 | 101879 | Stefano Morozzi | 03/2022 |
8269 | 2^338430-9903 | 101878 | Stefano Morozzi | 04/2022 |
8277 | 2^338426-19797 | 101877 | Enzo Doria | 06/2013 |
8270 | 2^338427-77797 | 101877 | Stefano Morozzi | 01/2022 |
8271 | 2^338427-178687 | 101877 | Stefano Morozzi | 01/2022 |
8272 | 2^338428-54873 | 101877 | Stefano Morozzi | 02/2022 |
8273 | 2^338425+41357 | 101877 | Stefano Morozzi | 06/2022 |
8274 | 2^338428+90855 | 101877 | Stefano Morozzi | 06/2022 |
8275 | 2^338428-39807 | 101877 | Stefano Morozzi | 01/2023 |
8276 | 2^338425-192381 | 101877 | Stefano Morozzi | 02/2023 |
8278 | 2^338422-188787 | 101876 | Stefano Morozzi | 12/2022 |
8279 | 2^338423-187755 | 101876 | Stefano Morozzi | 12/2022 |
8280 | 2^338422-115865 | 101876 | Stefano Morozzi | 01/2023 |
8281 | 2^338420-178829 | 101875 | Stefano Morozzi | 01/2022 |
8282 | 2^338421-105423 | 101875 | Stefano Morozzi | 02/2022 |
8283 | 2^338419-82761 | 101875 | Stefano Morozzi | 03/2022 |
8284 | 2^338420+193143 | 101875 | Stefano Morozzi | 09/2022 |
8285 | 2^338419+199641 | 101875 | Stefano Morozzi | 02/2023 |
8286 | 2^338420-143103 | 101875 | Stefano Morozzi | 02/2023 |
8287 | 2^338418-50903 | 101874 | Stefano Morozzi | 12/2021 |
8288 | 2^338418+158355 | 101874 | Stefano Morozzi | 02/2022 |
8289 | 2^338418+159339 | 101874 | Stefano Morozzi | 03/2022 |
8290 | 2^338416+14953 | 101874 | Stefano Morozzi | 05/2022 |
8291 | 2^338416+166051 | 101874 | Stefano Morozzi | 06/2022 |
8292 | 2^338418-138765 | 101874 | Stefano Morozzi | 12/2022 |
8293 | 2^338417+49737 | 101874 | Stefano Morozzi | 02/2023 |
8294 | 2^338413-125919 | 101873 | Stefano Morozzi | 12/2021 |
8295 | 2^338414+26083 | 101873 | Stefano Morozzi | 12/2021 |
8296 | 2^338412-152379 | 101873 | Stefano Morozzi | 12/2021 |
8297 | 2^338413+54797 | 101873 | Stefano Morozzi | 01/2022 |
8298 | 2^338412+157951 | 101873 | Stefano Morozzi | 02/2022 |
8299 | 2^338414+81627 | 101873 | Stefano Morozzi | 02/2022 |
8300 | 2^338413+133679 | 101873 | Stefano Morozzi | 03/2022 |
8301 | 2^338413+197735 | 101873 | Stefano Morozzi | 11/2022 |
8302 | 2^338413-114301 | 101873 | Stefano Morozzi | 01/2023 |
8303 | 11*32^67682+395 | 101873 | Eric Chen | 04/2023 |
8304 | 2^338409-52183 | 101872 | Stefano Morozzi | 12/2021 |
8305 | 2^338411-3789 | 101872 | Stefano Morozzi | 01/2022 |
8306 | 2^338409+173237 | 101872 | Stefano Morozzi | 11/2022 |
8307 | 2^338406-184175 | 101871 | Stefano Morozzi | 04/2022 |
8308 | 2^338405+94451 | 101871 | Stefano Morozzi | 09/2022 |
8309 | 2^338406-161217 | 101871 | Stefano Morozzi | 12/2022 |
8310 | 2^338406+199929 | 101871 | Stefano Morozzi | 02/2023 |
8311 | 2^338404+55717 | 101870 | Stefano Morozzi | 01/2022 |
8312 | 2^338403+36261 | 101870 | Stefano Morozzi | 04/2022 |
8313 | 2^338402-34431 | 101870 | Stefano Morozzi | 04/2022 |
8314 | 2^338404-159215 | 101870 | Stefano Morozzi | 04/2022 |
8315 | 2^338403+18363 | 101870 | Stefano Morozzi | 09/2022 |
8316 | 2^338403+170235 | 101870 | Stefano Morozzi | 11/2022 |
8317 | 2^338399+23045 | 101869 | Stefano Morozzi | 11/2022 |
8318 | 2^338399-65535 | 101869 | Stefano Morozzi | 01/2023 |
8319 | 2^338395-127449 | 101868 | Stefano Morozzi | 12/2021 |
8320 | 2^338398-127637 | 101868 | Stefano Morozzi | 01/2022 |
8321 | 2^338398-166533 | 101868 | Stefano Morozzi | 01/2023 |
8322 | 2^338394+100317 | 101867 | Stefano Morozzi | 11/2021 |
8323 | 2^338393-152749 | 101867 | Stefano Morozzi | 01/2022 |
8324 | 2^338393+163025 | 101867 | Stefano Morozzi | 04/2022 |
8325 | 2^338393+89229 | 101867 | Stefano Morozzi | 05/2022 |
8326 | 2^338393+99647 | 101867 | Stefano Morozzi | 02/2023 |
8327 | 2^338394-192471 | 101867 | Stefano Morozzi | 02/2023 |
8328 | 2^338390+76627 | 101866 | Stefano Morozzi | 12/2021 |
8329 | 2^338389-85081 | 101866 | Stefano Morozzi | 06/2022 |
8330 | 2^338390+148113 | 101866 | Stefano Morozzi | 11/2022 |
8331 | 2^338389-14253 | 101866 | Stefano Morozzi | 01/2023 |
8332 | 2^338390-114297 | 101866 | Stefano Morozzi | 01/2023 |
8333 | 2^338391-64225 | 101866 | Stefano Morozzi | 01/2023 |
8334 | 2^338389-16971 | 101866 | Stefano Morozzi | 02/2023 |
8335 | 2^338387-75685 | 101865 | Stefano Morozzi | 12/2021 |
8336 | 2^338388-53459 | 101865 | Stefano Morozzi | 01/2022 |
8337 | 2^338388-36575 | 101865 | Stefano Morozzi | 12/2022 |
8338 | 2^338385-190311 | 101865 | Stefano Morozzi | 01/2023 |
8339 | 2^338384+131563 | 101864 | Stefano Morozzi | 01/2022 |
8340 | 2^338382+109069 | 101864 | Stefano Morozzi | 03/2022 |
8341 | 2^338384+168987 | 101864 | Stefano Morozzi | 09/2022 |
8342 | 2^338383-42367 | 101864 | Stefano Morozzi | 02/2023 |
8343 | 2^338380+77125 | 101863 | Stefano Morozzi | 12/2021 |
8344 | 2^338381-35539 | 101863 | Stefano Morozzi | 06/2022 |
8345 | 2^338378-125841 | 101862 | Stefano Morozzi | 12/2021 |
8346 | 2^338375+27815 | 101862 | Stefano Morozzi | 01/2022 |
8347 | 2^338375-28509 | 101862 | Stefano Morozzi | 01/2022 |
8348 | 2^338375+29985 | 101862 | Stefano Morozzi | 01/2022 |
8349 | 2^338377+157881 | 101862 | Stefano Morozzi | 02/2022 |
8350 | 2^338375+59589 | 101862 | Stefano Morozzi | 03/2022 |
8351 | 2^338378+36399 | 101862 | Stefano Morozzi | 04/2022 |
8352 | 2^338378-159773 | 101862 | Stefano Morozzi | 04/2022 |
8353 | 2^338378+14883 | 101862 | Stefano Morozzi | 05/2022 |
8354 | 2^338376+140173 | 101862 | Stefano Morozzi | 06/2022 |
8355 | 2^338375+18761 | 101862 | Stefano Morozzi | 09/2022 |
8356 | 2^338373-75103 | 101861 | Stefano Morozzi | 12/2021 |
8357 | 2^338372+128877 | 101861 | Stefano Morozzi | 01/2022 |
8358 | 2^338374-28731 | 101861 | Stefano Morozzi | 01/2022 |
8359 | 2^338374-128427 | 101861 | Stefano Morozzi | 01/2022 |
8360 | 2^338372+37875 | 101861 | Stefano Morozzi | 04/2022 |
8361 | 2^338373+161541 | 101861 | Stefano Morozzi | 04/2022 |
8362 | 2^338374+37759 | 101861 | Stefano Morozzi | 04/2022 |
8363 | 2^338372+93235 | 101861 | Stefano Morozzi | 09/2022 |
8364 | 2^338373-63273 | 101861 | Stefano Morozzi | 12/2022 |
8365 | 2^338369+29427 | 101860 | Stefano Morozzi | 01/2022 |
8366 | 2^338370+179133 | 101860 | Stefano Morozzi | 01/2022 |
8367 | 2^338369+131501 | 101860 | Stefano Morozzi | 01/2022 |
8368 | 2^338369+181649 | 101860 | Stefano Morozzi | 02/2022 |
8369 | 2^338370-4787 | 101860 | Stefano Morozzi | 02/2022 |
8370 | 2^338371-133491 | 101860 | Stefano Morozzi | 04/2022 |
8371 | 2^338371+42023 | 101860 | Stefano Morozzi | 09/2022 |
8372 | 2^338371+145323 | 101860 | Stefano Morozzi | 11/2022 |
8373 | 2^338371-138145 | 101860 | Stefano Morozzi | 12/2022 |
8380 | 2^338368-20369 | 101859 | Enzo Doria | 06/2013 |
8381 | 2^338366+74179 | 101859 | Enzo Doria | 04/2016 |
8374 | 2^338366+53853 | 101859 | Stefano Morozzi | 01/2022 |
8375 | 2^338365-31665 | 101859 | Stefano Morozzi | 03/2022 |
8376 | 2^338368-156345 | 101859 | Stefano Morozzi | 03/2022 |
8377 | 2^338366-159867 | 101859 | Stefano Morozzi | 04/2022 |
8378 | 2^338368-63509 | 101859 | Stefano Morozzi | 12/2022 |
8379 | 2^338365-190975 | 101859 | Stefano Morozzi | 01/2023 |
8382 | 2^338362-180845 | 101858 | Stefano Morozzi | 02/2022 |
8383 | 2^338364-155769 | 101858 | Stefano Morozzi | 02/2022 |
8384 | 2^338362+142843 | 101858 | Stefano Morozzi | 09/2022 |
8385 | 2^338362+170019 | 101858 | Stefano Morozzi | 11/2022 |
8386 | 2^338361-100875 | 101857 | Stefano Morozzi | 12/2021 |
8387 | 2^338361+154169 | 101857 | Stefano Morozzi | 01/2022 |
8388 | 2^338359-189645 | 101857 | Stefano Morozzi | 01/2023 |
8389 | 2^338356+101271 | 101856 | Stefano Morozzi | 12/2021 |
8390 | 2^338356+53383 | 101856 | Stefano Morozzi | 01/2022 |
8391 | 2^338355+59393 | 101856 | Stefano Morozzi | 03/2022 |
8392 | 2^338356+60775 | 101856 | Stefano Morozzi | 03/2022 |
8393 | 2^338356-106257 | 101856 | Stefano Morozzi | 03/2022 |
8394 | 2^338357-58921 | 101856 | Stefano Morozzi | 04/2022 |
8395 | 2^338356+94605 | 101856 | Stefano Morozzi | 09/2022 |
8396 | 2^338356+117813 | 101856 | Stefano Morozzi | 09/2022 |
8397 | 2^338358-38475 | 101856 | Stefano Morozzi | 12/2022 |
8398 | 2^338353-190291 | 101855 | Stefano Morozzi | 01/2023 |
8399 | 2^338350-152933 | 101854 | Stefano Morozzi | 01/2022 |
8400 | 2^338350+6337 | 101854 | Stefano Morozzi | 01/2022 |
8401 | 2^338350+168759 | 101854 | Stefano Morozzi | 09/2022 |
8404 | 27088^5755+5755^27088 | 101853 | Hans Havermann | 01/2019 |
8402 | 2^338347+125901 | 101853 | Stefano Morozzi | 11/2021 |
8403 | 2^338346-10643 | 101853 | Stefano Morozzi | 06/2022 |
8405 | 2^338343+152271 | 101852 | Stefano Morozzi | 12/2021 |
8406 | 2^338345+154107 | 101852 | Stefano Morozzi | 01/2022 |
8407 | 2^338342+155397 | 101852 | Stefano Morozzi | 01/2022 |
8408 | 2^338342-130767 | 101852 | Stefano Morozzi | 02/2022 |
8409 | 2^338345-30123 | 101852 | Stefano Morozzi | 02/2022 |
8410 | 2^338345+35747 | 101852 | Stefano Morozzi | 03/2022 |
8411 | 2^338345-133131 | 101852 | Stefano Morozzi | 04/2022 |
8412 | 2^338345-134559 | 101852 | Stefano Morozzi | 04/2022 |
8413 | 2^338342+170073 | 101852 | Stefano Morozzi | 11/2022 |
8414 | 2^338344+46567 | 101852 | Stefano Morozzi | 11/2022 |
8415 | 2^338344+97141 | 101852 | Stefano Morozzi | 11/2022 |
8416 | 2^338342-162213 | 101852 | Stefano Morozzi | 12/2022 |
8417 | 2^338339+2753 | 101851 | Stefano Morozzi | 12/2021 |
8418 | 2^338341+128415 | 101851 | Stefano Morozzi | 01/2022 |
8419 | 2^338338+2677 | 101850 | Stefano Morozzi | 12/2021 |
8420 | 2^338336+54607 | 101850 | Stefano Morozzi | 01/2022 |
8421 | 2^338338+109999 | 101850 | Stefano Morozzi | 03/2022 |
8422 | 2^338336+161575 | 101850 | Stefano Morozzi | 04/2022 |
8423 | 2^338335+51975 | 101849 | Stefano Morozzi | 12/2021 |
8424 | 2^338335-152607 | 101849 | Stefano Morozzi | 01/2022 |
8425 | 2^338334+55273 | 101849 | Stefano Morozzi | 01/2022 |
8426 | 2^338332+34315 | 101849 | Stefano Morozzi | 03/2022 |
8427 | 2^338335+158759 | 101849 | Stefano Morozzi | 03/2022 |
8428 | 2^338332+67621 | 101849 | Stefano Morozzi | 09/2022 |
8429 | 2^338332-66099 | 101849 | Stefano Morozzi | 01/2023 |
8430 | 2^338334-191043 | 101849 | Stefano Morozzi | 01/2023 |
8431 | 2^338331+83403 | 101848 | Stefano Morozzi | 02/2022 |
8432 | 2^338330-110865 | 101848 | Stefano Morozzi | 06/2022 |
8433 | 2^338330+71047 | 101848 | Stefano Morozzi | 11/2022 |
8434 | 2^338328-5295 | 101847 | Stefano Morozzi | 02/2022 |
8435 | 2^338327+143585 | 101847 | Stefano Morozzi | 09/2022 |
8436 | 2^338324-179667 | 101846 | Stefano Morozzi | 02/2022 |
8437 | 2^338322+21903 | 101846 | Stefano Morozzi | 11/2022 |
8438 | 2^338324+98047 | 101846 | Stefano Morozzi | 11/2022 |
8439 | 2^338323-87729 | 101846 | Stefano Morozzi | 12/2022 |
8440 | 2^338322-16667 | 101846 | Stefano Morozzi | 01/2023 |
8441 | 2^338325-142159 | 101846 | Stefano Morozzi | 02/2023 |
8442 | 2^338316-175857 | 101844 | Stefano Morozzi | 12/2021 |
8443 | 2^338318+54405 | 101844 | Stefano Morozzi | 01/2022 |
8444 | 2^338316+32961 | 101844 | Stefano Morozzi | 02/2022 |
8445 | 2^338317+68175 | 101844 | Stefano Morozzi | 09/2022 |
8446 | 2^338318-86171 | 101844 | Stefano Morozzi | 12/2022 |
8447 | 2^338315-178635 | 101843 | Stefano Morozzi | 01/2022 |
8448 | 2^338315+34899 | 101843 | Stefano Morozzi | 03/2022 |
8449 | 2^338314-106973 | 101843 | Stefano Morozzi | 03/2022 |
8450 | 2^338313+170411 | 101843 | Stefano Morozzi | 11/2022 |
8451 | 2^338315-88807 | 101843 | Stefano Morozzi | 12/2022 |
8452 | 2^338311-51799 | 101842 | Stefano Morozzi | 12/2021 |
8453 | 2^338309+157259 | 101842 | Stefano Morozzi | 02/2022 |
8454 | 2^338310+40903 | 101842 | Stefano Morozzi | 06/2022 |
8455 | 2^338309-168051 | 101842 | Stefano Morozzi | 02/2023 |
8456 | 2^338308-55853 | 101841 | Stefano Morozzi | 02/2022 |
8457 | 2^338307+134871 | 101841 | Stefano Morozzi | 03/2022 |
8458 | 2^338307+19689 | 101841 | Stefano Morozzi | 09/2022 |
8459 | 2^338308+66873 | 101841 | Stefano Morozzi | 09/2022 |
8460 | 2^338306+124399 | 101841 | Stefano Morozzi | 02/2023 |
8461 | 2^338306-91913 | 101841 | Stefano Morozzi | 02/2023 |
8462 | 2^338304+78757 | 101840 | Stefano Morozzi | 01/2022 |
8463 | 2^338304-5807 | 101840 | Stefano Morozzi | 02/2022 |
8464 | 2^338305+110879 | 101840 | Stefano Morozzi | 03/2022 |
8465 | 2^338304+91147 | 101840 | Stefano Morozzi | 06/2022 |
8466 | 2^338304-64475 | 101840 | Stefano Morozzi | 01/2023 |
8467 | 2^338299+85611 | 101839 | Stefano Morozzi | 03/2022 |
8468 | 2^338299-189985 | 101839 | Stefano Morozzi | 01/2023 |
8469 | 2^338298-25571 | 101838 | Stefano Morozzi | 12/2021 |
8470 | 2^338297+35547 | 101838 | Stefano Morozzi | 03/2022 |
8471 | 2^338298+111199 | 101838 | Stefano Morozzi | 03/2022 |
8472 | 2^338297+145455 | 101838 | Stefano Morozzi | 11/2022 |
8473 | 2^338297-166285 | 101838 | Stefano Morozzi | 01/2023 |
8474 | 2^338294-150711 | 101837 | Stefano Morozzi | 12/2021 |
8475 | 2^338294+177597 | 101837 | Stefano Morozzi | 12/2021 |
8476 | 2^338294-177807 | 101837 | Stefano Morozzi | 01/2022 |
8477 | 2^338295-52929 | 101837 | Stefano Morozzi | 01/2022 |
8478 | 2^338293+37407 | 101837 | Stefano Morozzi | 04/2022 |
8479 | 2^338292+40573 | 101837 | Stefano Morozzi | 06/2022 |
8480 | 2^338294+172425 | 101837 | Stefano Morozzi | 11/2022 |
8481 | 2^338293-191799 | 101837 | Stefano Morozzi | 02/2023 |
8482 | 2^338289+30957 | 101836 | Stefano Morozzi | 01/2022 |
8483 | 2^338291+131825 | 101836 | Stefano Morozzi | 02/2022 |
8484 | 2^338291+110111 | 101836 | Stefano Morozzi | 03/2022 |
8485 | 2^338290-156423 | 101836 | Stefano Morozzi | 03/2022 |
8486 | 2^338291-157845 | 101836 | Stefano Morozzi | 03/2022 |
8487 | 2^338290+69243 | 101836 | Stefano Morozzi | 09/2022 |
8488 | 2^338291-189327 | 101836 | Stefano Morozzi | 01/2023 |
8489 | 2^338291+74079 | 101836 | Stefano Morozzi | 02/2023 |
8490 | 2^338288+26623 | 101835 | Stefano Morozzi | 12/2021 |
8491 | 2^338286+33325 | 101835 | Stefano Morozzi | 02/2022 |
8492 | 2^338287+132633 | 101835 | Stefano Morozzi | 02/2022 |
8493 | 2^338287+157149 | 101835 | Stefano Morozzi | 02/2022 |
8494 | 2^338288-107193 | 101835 | Stefano Morozzi | 03/2022 |
8495 | 2^338286-83333 | 101835 | Stefano Morozzi | 04/2022 |
8496 | 2^338287+114425 | 101835 | Stefano Morozzi | 05/2022 |
8497 | 2^338288+194403 | 101835 | Stefano Morozzi | 09/2022 |
8498 | 2^338288-113177 | 101835 | Stefano Morozzi | 12/2022 |
8499 | 2^338288-65747 | 101835 | Stefano Morozzi | 01/2023 |
8500 | 2^338285+82131 | 101834 | Stefano Morozzi | 02/2022 |