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 ? |
7254 | 25295^10744+10744^25295 | 101969 | Hans Havermann | 01/2019 |
7255 | 25712^9243+9243^25712 | 101969 | Hans Havermann | 01/2019 |
7251 | 2^338731+85863 | 101969 | Stefano Morozzi | 03/2022 |
7252 | 2^338732+185047 | 101969 | Stefano Morozzi | 03/2022 |
7253 | 2^338733+193791 | 101969 | Stefano Morozzi | 09/2022 |
7256 | 2^338729+69221 | 101968 | Stefano Morozzi | 09/2022 |
7257 | 2^338728+123355 | 101968 | Stefano Morozzi | 11/2022 |
7258 | 2^338730-87063 | 101968 | Stefano Morozzi | 12/2022 |
7259 | 2^338726+128199 | 101967 | Stefano Morozzi | 01/2022 |
7260 | 2^338727+127745 | 101967 | Stefano Morozzi | 01/2022 |
7261 | 2^338724+32971 | 101967 | Stefano Morozzi | 02/2022 |
7262 | 2^338727+189683 | 101967 | Stefano Morozzi | 05/2022 |
7263 | 2^338727+118293 | 101967 | Stefano Morozzi | 09/2022 |
7264 | 2^338723-76651 | 101966 | Stefano Morozzi | 12/2021 |
7265 | 2^338721+79037 | 101966 | Stefano Morozzi | 01/2022 |
7266 | 2^338723-132621 | 101966 | Stefano Morozzi | 03/2022 |
7267 | 2^338722+137313 | 101966 | Stefano Morozzi | 04/2022 |
7268 | 2^338722+162915 | 101966 | Stefano Morozzi | 04/2022 |
7269 | 2^338723+199161 | 101966 | Stefano Morozzi | 02/2023 |
7270 | 2^338718-126861 | 101965 | Stefano Morozzi | 12/2021 |
7271 | 2^338718-109127 | 101965 | Stefano Morozzi | 04/2022 |
7276 | (71^55079-1)/70 | 101964 | Paul Bourdelais | 08/2017 |
7272 | 2^338714+30835 | 101964 | Stefano Morozzi | 01/2022 |
7273 | 2^338714+156715 | 101964 | Stefano Morozzi | 02/2022 |
7274 | 2^338715+19923 | 101964 | Stefano Morozzi | 09/2022 |
7275 | 2^338716+173253 | 101964 | Stefano Morozzi | 11/2022 |
7277 | 2^338711+125399 | 101963 | Stefano Morozzi | 12/2021 |
7278 | 2^338713-30895 | 101963 | Stefano Morozzi | 02/2022 |
7279 | 2^338712-132545 | 101963 | Stefano Morozzi | 03/2022 |
7280 | 2^338713+87825 | 101963 | Stefano Morozzi | 04/2022 |
7281 | 2^338712+190333 | 101963 | Stefano Morozzi | 06/2022 |
7282 | 2^338709-154429 | 101962 | Stefano Morozzi | 02/2022 |
7283 | 2^338710+140545 | 101962 | Stefano Morozzi | 06/2022 |
7284 | 2^338706-102917 | 101961 | Stefano Morozzi | 01/2022 |
7285 | 2^338705+34727 | 101961 | Stefano Morozzi | 03/2022 |
7286 | 2^338706-165633 | 101961 | Stefano Morozzi | 01/2023 |
7287 | 2^338707-116115 | 101961 | Stefano Morozzi | 01/2023 |
7288 | 2^338698+104083 | 101959 | Stefano Morozzi | 01/2022 |
7289 | 2^338700-184565 | 101959 | Stefano Morozzi | 04/2022 |
7290 | 2^338700+189777 | 101959 | Stefano Morozzi | 05/2022 |
7291 | 2^338698+41779 | 101959 | Stefano Morozzi | 09/2022 |
7292 | 2^338699+148533 | 101959 | Stefano Morozzi | 11/2022 |
7293 | 2^338700+97381 | 101959 | Stefano Morozzi | 11/2022 |
7294 | 2^338698-142181 | 101959 | Stefano Morozzi | 02/2023 |
7295 | 2^338696+181671 | 101958 | Stefano Morozzi | 02/2022 |
7296 | 2^338697+146651 | 101958 | Stefano Morozzi | 11/2022 |
7297 | 2^338695-116977 | 101958 | Stefano Morozzi | 02/2023 |
7298 | 2^338692+106297 | 101957 | Stefano Morozzi | 01/2022 |
7299 | 2^338692+33195 | 101957 | Stefano Morozzi | 02/2022 |
7300 | 2^338692+110505 | 101957 | Stefano Morozzi | 03/2022 |
7301 | 2^338692+190093 | 101957 | Stefano Morozzi | 05/2022 |
7302 | 2^338692+173343 | 101957 | Stefano Morozzi | 11/2022 |
7303 | 2^338693+144975 | 101957 | Stefano Morozzi | 11/2022 |
7304 | 2^338692+149281 | 101957 | Stefano Morozzi | 02/2023 |
7305 | 2^338688+82203 | 101956 | Stefano Morozzi | 02/2022 |
7306 | 2^338689+82365 | 101956 | Stefano Morozzi | 02/2022 |
7307 | 2^338688-92159 | 101956 | Stefano Morozzi | 02/2023 |
7308 | 2^338686-81303 | 101955 | Stefano Morozzi | 03/2022 |
7309 | 2^338687+40461 | 101955 | Stefano Morozzi | 06/2022 |
7310 | 2^338687+65283 | 101955 | Stefano Morozzi | 06/2022 |
7316 | 2^338682-19865 | 101954 | Enzo Doria | 06/2013 |
7317 | (2^(112895*3+1)+243)/7 | 101954 | Kevin Acres | 12/2013 |
7311 | (8*10^101954-269)/9 | 101954 | Robert Price | 09/2021 |
7312 | 2^338683+50303 | 101954 | Stefano Morozzi | 11/2021 |
7313 | 2^338682-107205 | 101954 | Stefano Morozzi | 03/2022 |
7314 | 2^338682+13839 | 101954 | Stefano Morozzi | 05/2022 |
7315 | 2^338683-42837 | 101954 | Stefano Morozzi | 02/2023 |
7318 | 2^338678-180005 | 101953 | Stefano Morozzi | 02/2022 |
7319 | 2^338680+15855 | 101953 | Stefano Morozzi | 06/2022 |
7320 | 2^338678+93175 | 101953 | Stefano Morozzi | 09/2022 |
7321 | 2^338680+99217 | 101953 | Stefano Morozzi | 02/2023 |
7322 | 2^338674-175967 | 101952 | Stefano Morozzi | 12/2021 |
7323 | 2^338677-177373 | 101952 | Stefano Morozzi | 12/2021 |
7324 | 2^338677+102999 | 101952 | Stefano Morozzi | 01/2022 |
7325 | 2^338676+33381 | 101952 | Stefano Morozzi | 03/2022 |
7326 | 2^338677-82699 | 101952 | Stefano Morozzi | 03/2022 |
7327 | 2^338676-34299 | 101952 | Stefano Morozzi | 04/2022 |
7328 | 2^338675+188445 | 101952 | Stefano Morozzi | 05/2022 |
7329 | 2^338676+165271 | 101952 | Stefano Morozzi | 06/2022 |
7330 | 2^338674-187551 | 101952 | Stefano Morozzi | 12/2022 |
7331 | 2^338676-42243 | 101952 | Stefano Morozzi | 02/2023 |
7332 | 2^338671-55041 | 101951 | Stefano Morozzi | 02/2022 |
7333 | 2^338673-80203 | 101951 | Stefano Morozzi | 02/2022 |
7334 | 2^338672-182063 | 101951 | Stefano Morozzi | 03/2022 |
7335 | 2^338672+36667 | 101951 | Stefano Morozzi | 04/2022 |
7336 | 2^338668+2583 | 101950 | Stefano Morozzi | 12/2021 |
7337 | 2^338670-157001 | 101950 | Stefano Morozzi | 03/2022 |
7338 | 2^338669-8353 | 101950 | Stefano Morozzi | 04/2022 |
7339 | 2^338670+40635 | 101950 | Stefano Morozzi | 06/2022 |
7347 | (2^338666+3154)/2 | 101949 | Stefano Morozzi | 09/2020 |
7340 | 2^338665+1577 | 101949 | Stefano Morozzi | 12/2021 |
7341 | 2^338665-51133 | 101949 | Stefano Morozzi | 12/2021 |
7342 | 2^338664+4345 | 101949 | Stefano Morozzi | 01/2022 |
7343 | 2^338666-128943 | 101949 | Stefano Morozzi | 01/2022 |
7344 | 2^338664+131535 | 101949 | Stefano Morozzi | 01/2022 |
7345 | 2^338667+14943 | 101949 | Stefano Morozzi | 05/2022 |
7346 | 2^338665+166637 | 101949 | Stefano Morozzi | 09/2022 |
7348 | 2^338662+31587 | 101948 | Stefano Morozzi | 02/2022 |
7349 | 2^338663-58375 | 101948 | Stefano Morozzi | 04/2022 |
7350 | 2^338663-107869 | 101948 | Stefano Morozzi | 04/2022 |
7351 | 2^338663+90435 | 101948 | Stefano Morozzi | 06/2022 |
7352 | 2^338661+70457 | 101948 | Stefano Morozzi | 11/2022 |
7353 | 2^338662+70519 | 101948 | Stefano Morozzi | 11/2022 |
7354 | 2^338663-39447 | 101948 | Stefano Morozzi | 01/2023 |
7355 | 2^338658-159191 | 101947 | Stefano Morozzi | 04/2022 |
7356 | 2^338659-159687 | 101947 | Stefano Morozzi | 04/2022 |
7357 | 2^338659+15543 | 101947 | Stefano Morozzi | 05/2022 |
7358 | 2^338658+44395 | 101947 | Stefano Morozzi | 09/2022 |
7359 | 2^338658+192537 | 101947 | Stefano Morozzi | 09/2022 |
7360 | 2^338659-90531 | 101947 | Stefano Morozzi | 01/2023 |
7361 | 2^338659-114759 | 101947 | Stefano Morozzi | 01/2023 |
7362 | 2^338659+124079 | 101947 | Stefano Morozzi | 02/2023 |
7363 | 2^338654+51027 | 101946 | Stefano Morozzi | 12/2021 |
7364 | 2^338656-152115 | 101946 | Stefano Morozzi | 12/2021 |
7365 | 2^338654+32415 | 101946 | Stefano Morozzi | 02/2022 |
7366 | 2^338654+39799 | 101946 | Stefano Morozzi | 05/2022 |
7367 | 2^338655+144579 | 101946 | Stefano Morozzi | 09/2022 |
7368 | 2^338657+97509 | 101946 | Stefano Morozzi | 11/2022 |
7369 | 2^338653+126629 | 101945 | Stefano Morozzi | 12/2021 |
7370 | 2^338653+33279 | 101945 | Stefano Morozzi | 02/2022 |
7371 | 2^338652-107097 | 101945 | Stefano Morozzi | 03/2022 |
7372 | 2^338653+94475 | 101945 | Stefano Morozzi | 09/2022 |
7373 | 2^338651+194073 | 101945 | Stefano Morozzi | 09/2022 |
7374 | 2^338652-89157 | 101945 | Stefano Morozzi | 01/2023 |
7375 | 2^338649-154663 | 101944 | Stefano Morozzi | 02/2022 |
7376 | 2^338650+61399 | 101944 | Stefano Morozzi | 04/2022 |
7377 | 2^338650-35655 | 101944 | Stefano Morozzi | 06/2022 |
7378 | 2^338650+169623 | 101944 | Stefano Morozzi | 09/2022 |
7379 | 2^338649-40743 | 101944 | Stefano Morozzi | 01/2023 |
7380 | 2^338645+150311 | 101943 | Stefano Morozzi | 11/2021 |
7381 | 2^338645+28481 | 101943 | Stefano Morozzi | 01/2022 |
7382 | 2^338647-77895 | 101943 | Stefano Morozzi | 01/2022 |
7383 | 2^338647-84607 | 101943 | Stefano Morozzi | 04/2022 |
7384 | 2^338647+164523 | 101943 | Stefano Morozzi | 05/2022 |
7385 | 2^338645+64845 | 101943 | Stefano Morozzi | 05/2022 |
7386 | 2^338644-35969 | 101943 | Stefano Morozzi | 12/2022 |
7387 | 2^338645-15715 | 101943 | Stefano Morozzi | 01/2023 |
7388 | 2^338641-152541 | 101942 | Stefano Morozzi | 12/2021 |
7389 | 2^338643-56487 | 101942 | Stefano Morozzi | 03/2022 |
7390 | 2^338642-186525 | 101942 | Stefano Morozzi | 12/2022 |
7391 | 2^338643-41715 | 101942 | Stefano Morozzi | 02/2023 |
7392 | 2^338638+100575 | 101941 | Stefano Morozzi | 12/2021 |
7393 | 2^338639-127461 | 101941 | Stefano Morozzi | 12/2021 |
7394 | 2^338640+187657 | 101941 | Stefano Morozzi | 04/2022 |
7395 | 2^338640+44431 | 101941 | Stefano Morozzi | 09/2022 |
7396 | 2^338635+1961 | 101940 | Stefano Morozzi | 12/2021 |
7397 | 2^338637+102125 | 101940 | Stefano Morozzi | 12/2021 |
7398 | 2^338636-135329 | 101940 | Stefano Morozzi | 06/2022 |
7399 | 2^338635+199485 | 101940 | Stefano Morozzi | 02/2023 |
7404 | 28594^3673+3673^28594 | 101939 | Hans Havermann | 02/2019 |
7400 | 2^338631+110741 | 101939 | Stefano Morozzi | 03/2022 |
7401 | 2^338631+112119 | 101939 | Stefano Morozzi | 04/2022 |
7402 | 2^338634-83097 | 101939 | Stefano Morozzi | 04/2022 |
7403 | 2^338633+139701 | 101939 | Stefano Morozzi | 05/2022 |
7405 | 2^338630-150341 | 101938 | Stefano Morozzi | 12/2021 |
7406 | 2^338630+12867 | 101938 | Stefano Morozzi | 04/2022 |
7407 | 2^338629+42147 | 101938 | Stefano Morozzi | 09/2022 |
7408 | 2^338628+121083 | 101938 | Stefano Morozzi | 11/2022 |
7409 | 2^338630+147235 | 101938 | Stefano Morozzi | 11/2022 |
7410 | 2^338628-37679 | 101938 | Stefano Morozzi | 12/2022 |
7411 | 2^338629-41383 | 101938 | Stefano Morozzi | 01/2023 |
7412 | 2^338628-91877 | 101938 | Stefano Morozzi | 02/2023 |
7413 | 2^338626-105875 | 101937 | Stefano Morozzi | 02/2022 |
7414 | 2^338625-111729 | 101937 | Stefano Morozzi | 12/2022 |
7415 | 2^338627+49299 | 101937 | Stefano Morozzi | 02/2023 |
7416 | 2^338621+33069 | 101936 | Stefano Morozzi | 02/2022 |
7417 | 2^338623-106405 | 101936 | Stefano Morozzi | 03/2022 |
7418 | 2^338621+61751 | 101936 | Stefano Morozzi | 04/2022 |
7419 | 2^338623-86577 | 101936 | Stefano Morozzi | 12/2022 |
7420 | 2^338620-150735 | 101935 | Stefano Morozzi | 12/2021 |
7421 | 2^338619-27765 | 101935 | Stefano Morozzi | 01/2022 |
7422 | 2^338619-77959 | 101935 | Stefano Morozzi | 01/2022 |
7423 | 2^338619-186367 | 101935 | Stefano Morozzi | 12/2022 |
7424 | 2^338618-64905 | 101935 | Stefano Morozzi | 01/2023 |
7425 | 2^338615+151655 | 101934 | Stefano Morozzi | 12/2021 |
7426 | 2^338616+5047 | 101934 | Stefano Morozzi | 01/2022 |
7427 | 2^338616+39705 | 101934 | Stefano Morozzi | 05/2022 |
7428 | 2^338617+149321 | 101934 | Stefano Morozzi | 02/2023 |
7429 | 2^338611+76659 | 101933 | Stefano Morozzi | 12/2021 |
7430 | 2^338613-109791 | 101933 | Stefano Morozzi | 04/2022 |
7431 | 2^338612+119583 | 101933 | Stefano Morozzi | 09/2022 |
7432 | 2^338611-140397 | 101933 | Stefano Morozzi | 01/2023 |
7433 | 2^338614-39653 | 101933 | Stefano Morozzi | 01/2023 |
7434 | 2^338609+130139 | 101932 | Stefano Morozzi | 01/2022 |
7435 | 2^338609+131327 | 101932 | Stefano Morozzi | 01/2022 |
7436 | 2^338608-155453 | 101932 | Stefano Morozzi | 02/2022 |
7437 | 2^338609+161721 | 101932 | Stefano Morozzi | 04/2022 |
7438 | 2^338609-10405 | 101932 | Stefano Morozzi | 06/2022 |
7439 | 2^338608+94017 | 101932 | Stefano Morozzi | 09/2022 |
7440 | 2^338610+170515 | 101932 | Stefano Morozzi | 11/2022 |
7441 | 2^338607+30611 | 101931 | Stefano Morozzi | 01/2022 |
7442 | 2^338607+106695 | 101931 | Stefano Morozzi | 02/2022 |
7443 | 2^338606-32291 | 101931 | Stefano Morozzi | 03/2022 |
7444 | 2^338606+15195 | 101931 | Stefano Morozzi | 05/2022 |
7445 | 2^338605+197789 | 101931 | Stefano Morozzi | 11/2022 |
7446 | 2^338607-90621 | 101931 | Stefano Morozzi | 01/2023 |
7447 | 2^338603-1195 | 101930 | Stefano Morozzi | 12/2021 |
7448 | 2^338601+108867 | 101930 | Stefano Morozzi | 03/2022 |
7449 | 2^338603+34311 | 101930 | Stefano Morozzi | 03/2022 |
7450 | 2^338598+57127 | 101929 | Stefano Morozzi | 02/2022 |
7451 | 2^338598+162645 | 101929 | Stefano Morozzi | 04/2022 |
7452 | 2^338599+43445 | 101929 | Stefano Morozzi | 09/2022 |
7453 | 2^338599+19485 | 101929 | Stefano Morozzi | 09/2022 |
7454 | 2^338598+46195 | 101929 | Stefano Morozzi | 11/2022 |
7455 | 2^338600-36393 | 101929 | Stefano Morozzi | 12/2022 |
7456 | 2^338596-1739 | 101928 | Stefano Morozzi | 12/2021 |
7457 | 2^338595-78687 | 101928 | Stefano Morozzi | 01/2022 |
7458 | 2^338595+181683 | 101928 | Stefano Morozzi | 02/2022 |
7459 | 2^338597-106045 | 101928 | Stefano Morozzi | 02/2022 |
7460 | 2^338595+119565 | 101928 | Stefano Morozzi | 09/2022 |
7461 | 2^338595+19623 | 101928 | Stefano Morozzi | 09/2022 |
7462 | 2^338595+21711 | 101928 | Stefano Morozzi | 11/2022 |
7463 | 2^338596-111129 | 101928 | Stefano Morozzi | 12/2022 |
7464 | 2^338591+53769 | 101927 | Stefano Morozzi | 01/2022 |
7465 | 2^338593+156989 | 101927 | Stefano Morozzi | 02/2022 |
7466 | 2^338592+36157 | 101927 | Stefano Morozzi | 03/2022 |
7467 | 2^338593+42099 | 101927 | Stefano Morozzi | 09/2022 |
7468 | 2^338591+46685 | 101927 | Stefano Morozzi | 11/2022 |
7469 | 2^338593+120437 | 101927 | Stefano Morozzi | 11/2022 |
7470 | 2^338591-165517 | 101927 | Stefano Morozzi | 01/2023 |
7471 | 2^338592-166107 | 101927 | Stefano Morozzi | 01/2023 |
7472 | 2^338592-189249 | 101927 | Stefano Morozzi | 01/2023 |
7473 | 2^338594-40493 | 101927 | Stefano Morozzi | 01/2023 |
7474 | 2^338590+182007 | 101926 | Stefano Morozzi | 02/2022 |
7475 | 2^338590+60747 | 101926 | Stefano Morozzi | 03/2022 |
7476 | 2^338588+62397 | 101926 | Stefano Morozzi | 04/2022 |
7477 | 2^338589-9685 | 101926 | Stefano Morozzi | 04/2022 |
7478 | 2^338588+73765 | 101926 | Stefano Morozzi | 02/2023 |
7479 | 2^338589-16915 | 101926 | Stefano Morozzi | 02/2023 |
7486 | (2^338587+2306)/2 | 101925 | Stefano Morozzi | 02/2021 |
7480 | 2^338586+1153 | 101925 | Stefano Morozzi | 12/2021 |
7481 | 2^338587-51709 | 101925 | Stefano Morozzi | 12/2021 |
7482 | 2^338586+105303 | 101925 | Stefano Morozzi | 01/2022 |
7483 | 2^338585-131773 | 101925 | Stefano Morozzi | 03/2022 |
7484 | 2^338587+168039 | 101925 | Stefano Morozzi | 09/2022 |
7485 | 2^338585-140719 | 101925 | Stefano Morozzi | 01/2023 |
7487 | 2^338584+100771 | 101924 | Stefano Morozzi | 11/2021 |
7488 | 2^338581-150415 | 101924 | Stefano Morozzi | 12/2021 |
7489 | 2^338581-2349 | 101924 | Stefano Morozzi | 12/2021 |
7490 | 2^338582+42933 | 101924 | Stefano Morozzi | 09/2022 |
7491 | 2^338584+93267 | 101924 | Stefano Morozzi | 09/2022 |
7492 | 2^338582-86697 | 101924 | Stefano Morozzi | 12/2022 |
7493 | 2^338582-138035 | 101924 | Stefano Morozzi | 12/2022 |
7494 | 2^338584-115569 | 101924 | Stefano Morozzi | 01/2023 |
7495 | 2^338581-92793 | 101924 | Stefano Morozzi | 02/2023 |
7496 | 2^338578+67593 | 101923 | Stefano Morozzi | 09/2022 |
7497 | 2^338580+142201 | 101923 | Stefano Morozzi | 09/2022 |
7498 | 2^338579-14635 | 101923 | Stefano Morozzi | 01/2023 |
7499 | 2^338579-164985 | 101923 | Stefano Morozzi | 01/2023 |
7500 | 2^338575-28815 | 101922 | Stefano Morozzi | 01/2022 |