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
Search by form
| Rank |
Probable prime |
Digits (> 50000) |
Who ? |
When ? |
| 8251 | 2^346846+146089 | 104412 | Stefano Morozzi | 11/2024 |
| 8252 | 2^346848+14577 | 104412 | Stefano Morozzi | 11/2024 |
| 8253 | 2^346848+38901 | 104412 | Stefano Morozzi | 11/2024 |
| 8254 | 2^346849+94107 | 104412 | Stefano Morozzi | 11/2024 |
| 8255 | 2^346843+112473 | 104411 | Stefano Morozzi | 11/2024 |
| 8256 | 2^346845+186035 | 104411 | Stefano Morozzi | 11/2024 |
| 8257 | 2^346841+146711 | 104410 | Stefano Morozzi | 11/2024 |
| 8258 | 2^346839+59931 | 104409 | Stefano Morozzi | 11/2024 |
| 8259 | 2^346834+11715 | 104408 | Lelio R Paula | 04/2015 |
| 8260 | 2^346830+73129 | 104407 | Stefano Morozzi | 11/2024 |
| 8261 | 2^346832+168607 | 104407 | Stefano Morozzi | 11/2024 |
| 8262 | 2^346832+179253 | 104407 | Stefano Morozzi | 11/2024 |
| 8263 | 2^346826+73969 | 104406 | Stefano Morozzi | 11/2024 |
| 8264 | 2^346827+122901 | 104406 | Stefano Morozzi | 11/2024 |
| 8265 | 2^346823+36191 | 104405 | Stefano Morozzi | 11/2024 |
| 8266 | 2^346823+185955 | 104405 | Stefano Morozzi | 11/2024 |
| 8267 | 2^346825+3297 | 104405 | Stefano Morozzi | 11/2024 |
| 8268 | 2^346822+74757 | 104404 | Stefano Morozzi | 11/2024 |
| 8269 | 2^346822+160495 | 104404 | Stefano Morozzi | 11/2024 |
| 8270 | 2^346816+146085 | 104403 | Stefano Morozzi | 11/2024 |
| 8271 | 2^346816+158707 | 104403 | Stefano Morozzi | 11/2024 |
| 8272 | 2^346818+26689 | 104403 | Stefano Morozzi | 11/2024 |
| 8273 | 2^346818+69805 | 104403 | Stefano Morozzi | 11/2024 |
| 8274 | 2^346818+83899 | 104403 | Stefano Morozzi | 11/2024 |
| 8275 | 2^346818+110299 | 104403 | Stefano Morozzi | 11/2024 |
| 8276 | 2^346818+182793 | 104403 | Stefano Morozzi | 11/2024 |
| 8277 | 2^346819+95351 | 104403 | Stefano Morozzi | 11/2024 |
| 8278 | 2^346814+136243 | 104402 | Stefano Morozzi | 11/2024 |
| 8279 | 2^346814+188649 | 104402 | Stefano Morozzi | 11/2024 |
| 8280 | 2^346810+106309 | 104401 | Stefano Morozzi | 11/2024 |
| 8281 | 2^346807+86769 | 104400 | Stefano Morozzi | 11/2024 |
| 8282 | 2^346808+114975 | 104400 | Stefano Morozzi | 11/2024 |
| 8283 | 2^346809+61035 | 104400 | Stefano Morozzi | 11/2024 |
| 8284 | 2^346803+10845 | 104399 | Stefano Morozzi | 11/2024 |
| 8285 | 2^346803+110705 | 104399 | Stefano Morozzi | 11/2024 |
| 8286 | 2^346804+134761 | 104399 | Stefano Morozzi | 11/2024 |
| 8287 | 2^346800+137791 | 104398 | Stefano Morozzi | 11/2024 |
| 8288 | 2^346797+109589 | 104397 | Stefano Morozzi | 11/2024 |
| 8289 | 2^346798+91909 | 104397 | Stefano Morozzi | 11/2024 |
| 8290 | 2^346798+163029 | 104397 | Stefano Morozzi | 11/2024 |
| 8291 | 2^346793+62669 | 104396 | Stefano Morozzi | 11/2024 |
| 8292 | 2^346793+189081 | 104396 | Stefano Morozzi | 11/2024 |
| 8293 | 2^346794+109095 | 104396 | Stefano Morozzi | 11/2024 |
| 8294 | 2^346796+57285 | 104396 | Stefano Morozzi | 11/2024 |
| 8295 | 2^346791+184833 | 104395 | Stefano Morozzi | 11/2024 |
| 8296 | 2^346787+81005 | 104394 | Stefano Morozzi | 11/2024 |
| 8297 | 2^346787+81605 | 104394 | Stefano Morozzi | 11/2024 |
| 8298 | 2^346789+2015 | 104394 | Stefano Morozzi | 11/2024 |
| 8299 | 2^346789+19595 | 104394 | Stefano Morozzi | 11/2024 |
| 8300 | 2^346784+84771 | 104393 | Stefano Morozzi | 11/2024 |
| 8301 | 2^346784+124243 | 104393 | Stefano Morozzi | 11/2024 |
| 8302 | 2^346784+143707 | 104393 | Stefano Morozzi | 11/2024 |
| 8303 | 2^346786+66117 | 104393 | Stefano Morozzi | 11/2024 |
| 8304 | 2^346786+194725 | 104393 | Stefano Morozzi | 11/2024 |
| 8308 | 24276^19961+19961^24276 | 104392 | Hans Havermann | 09/2020 |
| 8305 | 2^346780+81517 | 104392 | Stefano Morozzi | 11/2024 |
| 8306 | 2^346780+121341 | 104392 | Stefano Morozzi | 11/2024 |
| 8307 | 2^346780+171943 | 104392 | Stefano Morozzi | 11/2024 |
| 8309 | 2^346777+28991 | 104391 | Stefano Morozzi | 11/2024 |
| 8310 | 2^346777+110021 | 104391 | Stefano Morozzi | 11/2024 |
| 8311 | 2^346778+53769 | 104391 | Stefano Morozzi | 11/2024 |
| 8312 | 2^346779+134115 | 104391 | Stefano Morozzi | 11/2024 |
| 8313 | 2^346779+172961 | 104391 | Stefano Morozzi | 11/2024 |
| 8314 | 2^346773+81797 | 104390 | Stefano Morozzi | 11/2024 |
| 8315 | 2^346774+164119 | 104390 | Stefano Morozzi | 11/2024 |
| 8316 | 2^346775+72063 | 104390 | Stefano Morozzi | 11/2024 |
| 8317 | 2^346775+197315 | 104390 | Stefano Morozzi | 11/2024 |
| 8318 | 2^346776+32233 | 104390 | Stefano Morozzi | 11/2024 |
| 8319 | 2^346776+187777 | 104390 | Stefano Morozzi | 11/2024 |
| 8320 | 2^346770+98719 | 104389 | Stefano Morozzi | 11/2024 |
| 8321 | 2^346770+110437 | 104389 | Stefano Morozzi | 11/2024 |
| 8322 | 2^346771+1205 | 104389 | Stefano Morozzi | 11/2024 |
| 8323 | 2^346771+3465 | 104389 | Stefano Morozzi | 11/2024 |
| 8324 | 2^346771+129543 | 104389 | Stefano Morozzi | 11/2024 |
| 8325 | 2^346772+41143 | 104389 | Stefano Morozzi | 11/2024 |
| 8326 | 2^346772+69865 | 104389 | Stefano Morozzi | 11/2024 |
| 8327 | 2^346767+168441 | 104388 | Stefano Morozzi | 11/2024 |
| 8328 | 2^346768+37897 | 104388 | Stefano Morozzi | 11/2024 |
| 8329 | 2^346768+80977 | 104388 | Stefano Morozzi | 11/2024 |
| 8330 | 2^346769+158745 | 104388 | Stefano Morozzi | 11/2024 |
| 8336 | 79^55009+78 | 104387 | Norbert Schneider | 02/2015 |
| 8331 | 2^346763+14723 | 104387 | Stefano Morozzi | 11/2024 |
| 8332 | 2^346763+90743 | 104387 | Stefano Morozzi | 11/2024 |
| 8333 | 2^346764+95503 | 104387 | Stefano Morozzi | 11/2024 |
| 8334 | 2^346766+31645 | 104387 | Stefano Morozzi | 11/2024 |
| 8335 | 2^346766+51115 | 104387 | Stefano Morozzi | 11/2024 |
| 8337 | 2^346760+90225 | 104386 | Stefano Morozzi | 11/2024 |
| 8338 | 2^346762+31825 | 104386 | Stefano Morozzi | 11/2024 |
| 8339 | 2^346762+192817 | 104386 | Stefano Morozzi | 11/2024 |
| 8340 | 2^346757+97691 | 104385 | Stefano Morozzi | 11/2024 |
| 8341 | 2^346758+111415 | 104385 | Stefano Morozzi | 11/2024 |
| 8342 | 2^346759+86331 | 104385 | Stefano Morozzi | 11/2024 |
| 8343 | 2^346755+22085 | 104384 | Stefano Morozzi | 11/2024 |
| 8344 | 2^346750+140967 | 104383 | Stefano Morozzi | 11/2024 |
| 8345 | 2^346751+48515 | 104383 | Stefano Morozzi | 11/2024 |
| 8346 | 2^346751+74481 | 104383 | Stefano Morozzi | 11/2024 |
| 8347 | 2^346752+103497 | 104383 | Stefano Morozzi | 11/2024 |
| 8348 | 2^346747+4589 | 104382 | Stefano Morozzi | 11/2024 |
| 8349 | 2^346747+29969 | 104382 | Stefano Morozzi | 11/2024 |
| 8350 | 2^346747+130973 | 104382 | Stefano Morozzi | 11/2024 |
| 8351 | 2^346748+184387 | 104382 | Stefano Morozzi | 11/2024 |
| 8352 | 2^346743+39545 | 104381 | Stefano Morozzi | 11/2024 |
| 8353 | 2^346743+61335 | 104381 | Stefano Morozzi | 11/2024 |
| 8354 | 2^346746+99025 | 104381 | Stefano Morozzi | 11/2024 |
| 8355 | 2^346737+39431 | 104379 | Stefano Morozzi | 11/2024 |
| 8356 | 2^346733+96437 | 104378 | Stefano Morozzi | 11/2024 |
| 8357 | 2^346736+83025 | 104378 | Stefano Morozzi | 11/2024 |
| 8358 | 2^346736+196405 | 104378 | Stefano Morozzi | 11/2024 |
| 8359 | 2^346732+72685 | 104377 | Stefano Morozzi | 11/2024 |
| 8360 | 2^346727+86903 | 104376 | Stefano Morozzi | 11/2024 |
| 8361 | 2^346727+89829 | 104376 | Stefano Morozzi | 11/2024 |
| 8362 | 2^346729+199319 | 104376 | Stefano Morozzi | 11/2024 |
| 8363 | 2^346723+73521 | 104375 | Stefano Morozzi | 11/2024 |
| 8364 | 2^346724+91177 | 104375 | Stefano Morozzi | 11/2024 |
| 8365 | 2^346726+191527 | 104375 | Stefano Morozzi | 11/2024 |
| 8366 | 2^346720+235 | 104374 | Stefano Morozzi | 11/2024 |
| 8367 | 2^346720+189435 | 104374 | Stefano Morozzi | 11/2024 |
| 8368 | 2^346718+124833 | 104373 | Stefano Morozzi | 11/2024 |
| 8369 | 2^346718+127029 | 104373 | Stefano Morozzi | 11/2024 |
| 8370 | 2^346719+129291 | 104373 | Stefano Morozzi | 11/2024 |
| 8371 | 2^346719+183033 | 104373 | Stefano Morozzi | 11/2024 |
| 8372 | 2^346714+81909 | 104372 | Stefano Morozzi | 11/2024 |
| 8373 | 2^346714+174493 | 104372 | Stefano Morozzi | 11/2024 |
| 8374 | 2^346716+174123 | 104372 | Stefano Morozzi | 11/2024 |
| 8375 | 2^346711+160659 | 104371 | Stefano Morozzi | 11/2024 |
| 8376 | 2^346710+143649 | 104371 | Stefano Morozzi | 11/2024 |
| 8377 | 2^346712+52063 | 104371 | Stefano Morozzi | 11/2024 |
| 8378 | 2^346707+27099 | 104370 | Stefano Morozzi | 11/2024 |
| 8379 | 2^346708+26217 | 104370 | Stefano Morozzi | 11/2024 |
| 8380 | 2^346708+165715 | 104370 | Stefano Morozzi | 11/2024 |
| 8381 | 2^346705+6581 | 104369 | Stefano Morozzi | 11/2024 |
| 8382 | 2^346705+39851 | 104369 | Stefano Morozzi | 11/2024 |
| 8383 | 2^346706+172963 | 104369 | Stefano Morozzi | 11/2024 |
| 8386 | 3^218744+58 | 104368 | Lelio R Paula | 11/2016 |
| 8384 | 2^346700+191515 | 104368 | Stefano Morozzi | 11/2024 |
| 8385 | 2^346701+164841 | 104368 | Stefano Morozzi | 11/2024 |
| 8387 | 2^346694+20437 | 104366 | Stefano Morozzi | 11/2024 |
| 8388 | 2^346694+131557 | 104366 | Stefano Morozzi | 11/2024 |
| 8389 | 2^346695+6795 | 104366 | Stefano Morozzi | 11/2024 |
| 8390 | 2^346691+158613 | 104365 | Stefano Morozzi | 11/2024 |
| 8391 | 2^346692+122623 | 104365 | Stefano Morozzi | 11/2024 |
| 8392 | 2^346687+188033 | 104364 | Stefano Morozzi | 11/2024 |
| 8393 | 2^346688+71005 | 104364 | Stefano Morozzi | 11/2024 |
| 8394 | 2^346688+89811 | 104364 | Stefano Morozzi | 11/2024 |
| 8395 | 2^346688+122115 | 104364 | Stefano Morozzi | 11/2024 |
| 8396 | 2^346689+100829 | 104364 | Stefano Morozzi | 11/2024 |
| 8397 | 2^346689+172847 | 104364 | Stefano Morozzi | 11/2024 |
| 8398 | 2^346685+136145 | 104363 | Stefano Morozzi | 11/2024 |
| 8401 | 9*10^104361+89 | 104362 | Robert Price | 11/2019 |
| 8399 | 2^346681+58601 | 104362 | Stefano Morozzi | 11/2024 |
| 8400 | 2^346681+186111 | 104362 | Stefano Morozzi | 11/2024 |
| 8402 | 2^346676+82285 | 104360 | Stefano Morozzi | 11/2024 |
| 8403 | 2^346670+69985 | 104359 | Stefano Morozzi | 11/2024 |
| 8404 | 2^346672+85371 | 104359 | Stefano Morozzi | 11/2024 |
| 8405 | 2^346673+47231 | 104359 | Stefano Morozzi | 11/2024 |
| 8411 | 25048^14665+14665^25048 | 104358 | Hans Havermann | 09/2020 |
| 8406 | 2^346667+84359 | 104358 | Stefano Morozzi | 11/2024 |
| 8407 | 2^346668+26391 | 104358 | Stefano Morozzi | 11/2024 |
| 8408 | 2^346668+138987 | 104358 | Stefano Morozzi | 11/2024 |
| 8409 | 2^346669+27735 | 104358 | Stefano Morozzi | 11/2024 |
| 8410 | 2^346669+33989 | 104358 | Stefano Morozzi | 11/2024 |
| 8412 | 2^346664+16377 | 104357 | Stefano Morozzi | 11/2024 |
| 8413 | 2^346666+29595 | 104357 | Stefano Morozzi | 11/2024 |
| 8414 | 2^346660+61095 | 104356 | Stefano Morozzi | 11/2024 |
| 8415 | 2^346661+114311 | 104356 | Stefano Morozzi | 11/2024 |
| 8416 | 2^346662+75745 | 104356 | Stefano Morozzi | 11/2024 |
| 8417 | 2^346663+123305 | 104356 | Stefano Morozzi | 11/2024 |
| 8418 | 2^346662+150475 | 104356 | Stefano Morozzi | 11/2024 |
| 8419 | 2^346658+28393 | 104355 | Stefano Morozzi | 11/2024 |
| 8420 | 2^346658+137619 | 104355 | Stefano Morozzi | 11/2024 |
| 8421 | 2^346659+86415 | 104355 | Stefano Morozzi | 11/2024 |
| 8422 | 2^346659+117849 | 104355 | Stefano Morozzi | 11/2024 |
| 8423 | 2^346655+199859 | 104354 | Stefano Morozzi | 11/2024 |
| 8424 | 2^346656+100627 | 104354 | Stefano Morozzi | 11/2024 |
| 8425 | 2^346651+88491 | 104353 | Stefano Morozzi | 11/2024 |
| 8426 | 2^346652+32971 | 104353 | Stefano Morozzi | 11/2024 |
| 8427 | 2^346652+85321 | 104353 | Stefano Morozzi | 11/2024 |
| 8428 | 2^346652+100627 | 104353 | Stefano Morozzi | 11/2024 |
| 8429 | 2^346652+190255 | 104353 | Stefano Morozzi | 11/2024 |
| 8430 | 2^346652+194667 | 104353 | Stefano Morozzi | 11/2024 |
| 8431 | 2^346652+197073 | 104353 | Stefano Morozzi | 11/2024 |
| 8435 | 2^346649+65 | 104352 | Lelio R Paula | 09/2011 |
| 8432 | 2^346647+128475 | 104352 | Stefano Morozzi | 11/2024 |
| 8433 | 2^346647+181169 | 104352 | Stefano Morozzi | 11/2024 |
| 8434 | 2^346648+97381 | 104352 | Stefano Morozzi | 11/2024 |
| 8436 | (19*33^68718-600883)/32 | 104350 | Eric Chen | 05/2023 |
| 8437 | 2^346640+73723 | 104350 | Stefano Morozzi | 11/2024 |
| 8438 | 2^346641+169667 | 104350 | Stefano Morozzi | 11/2024 |
| 8439 | 2^346642+100395 | 104350 | Stefano Morozzi | 11/2024 |
| 8440 | 2^346643+61025 | 104350 | Stefano Morozzi | 11/2024 |
| 8441 | 2^346643+160785 | 104350 | Stefano Morozzi | 11/2024 |
| 8443 | 2^346638-17265 | 104349 | Enzo Doria | 05/2013 |
| 8442 | 2^346637+34139 | 104349 | Stefano Morozzi | 11/2024 |
| 8444 | 2^346635+13071 | 104348 | Stefano Morozzi | 11/2024 |
| 8445 | 2^346630+66003 | 104347 | Stefano Morozzi | 11/2024 |
| 8446 | 2^346630+187137 | 104347 | Stefano Morozzi | 11/2024 |
| 8447 | 2^346631+27393 | 104347 | Stefano Morozzi | 11/2024 |
| 8448 | 2^346632+21883 | 104347 | Stefano Morozzi | 11/2024 |
| 8449 | 2^346632+136015 | 104347 | Stefano Morozzi | 11/2024 |
| 8450 | 2^346628+87907 | 104346 | Stefano Morozzi | 11/2024 |
| 8451 | 2^346624+174075 | 104345 | Stefano Morozzi | 11/2024 |
| 8452 | 2^346620+87451 | 104344 | Stefano Morozzi | 11/2024 |
| 8453 | 2^346622+12247 | 104344 | Stefano Morozzi | 11/2024 |
| 8454 | 2^346623+69161 | 104344 | Stefano Morozzi | 11/2024 |
| 8455 | 2^346614+85737 | 104342 | Stefano Morozzi | 11/2024 |
| 8456 | 2^346611+183923 | 104341 | Stefano Morozzi | 11/2024 |
| 8457 | 2^346607+36209 | 104340 | Stefano Morozzi | 11/2024 |
| 8458 | 2^346607+65291 | 104340 | Stefano Morozzi | 11/2024 |
| 8459 | 2^346609+47471 | 104340 | Stefano Morozzi | 11/2024 |
| 8464 | (2^346606+2082)/2 | 104339 | Stefano Morozzi | 09/2020 |
| 8465 | (2^346607+2070)/2 | 104339 | Stefano Morozzi | 09/2020 |
| 8460 | 2^346605+1041 | 104339 | Stefano Morozzi | 11/2024 |
| 8461 | 2^346605+181167 | 104339 | Stefano Morozzi | 11/2024 |
| 8462 | 2^346606+1035 | 104339 | Stefano Morozzi | 11/2024 |
| 8463 | 2^346606+103863 | 104339 | Stefano Morozzi | 11/2024 |
| 8466 | 2^346601+26529 | 104338 | Stefano Morozzi | 11/2024 |
| 8467 | 2^346603+133431 | 104338 | Stefano Morozzi | 11/2024 |
| 8468 | 2^346597+97661 | 104337 | Stefano Morozzi | 11/2024 |
| 8469 | 2^346597+186809 | 104337 | Stefano Morozzi | 11/2024 |
| 8470 | 2^346598+31719 | 104337 | Stefano Morozzi | 11/2024 |
| 8471 | 2^346598+162513 | 104337 | Stefano Morozzi | 11/2024 |
| 8472 | 2^346599+45731 | 104337 | Stefano Morozzi | 11/2024 |
| 8473 | 2^346599+187061 | 104337 | Stefano Morozzi | 11/2024 |
| 8474 | 2^346600+175993 | 104337 | Stefano Morozzi | 11/2024 |
| 8475 | 2^346595+89753 | 104336 | Stefano Morozzi | 11/2024 |
| 8476 | 2^346595+114491 | 104336 | Stefano Morozzi | 11/2024 |
| 8477 | 2^346596+120183 | 104336 | Stefano Morozzi | 11/2024 |
| 8478 | 2^346591+183651 | 104335 | Stefano Morozzi | 11/2024 |
| 8479 | 2^346591+192149 | 104335 | Stefano Morozzi | 11/2024 |
| 8480 | 2^346592+77347 | 104335 | Stefano Morozzi | 11/2024 |
| 8481 | 2^346592+178161 | 104335 | Stefano Morozzi | 11/2024 |
| 8482 | 2^346592+195985 | 104335 | Stefano Morozzi | 11/2024 |
| 8483 | 2^346589+40607 | 104334 | Stefano Morozzi | 11/2024 |
| 8484 | 2^346590+151533 | 104334 | Stefano Morozzi | 11/2024 |
| 8485 | 2^346584+105103 | 104333 | Stefano Morozzi | 11/2024 |
| 8486 | 2^346585+56861 | 104333 | Stefano Morozzi | 11/2024 |
| 8492 | (2^346582+3202)/2 | 104332 | Stefano Morozzi | 09/2020 |
| 8487 | 2^346581+1601 | 104332 | Stefano Morozzi | 11/2024 |
| 8488 | 2^346581+82115 | 104332 | Stefano Morozzi | 11/2024 |
| 8489 | 2^346581+193979 | 104332 | Stefano Morozzi | 11/2024 |
| 8490 | 2^346582+197767 | 104332 | Stefano Morozzi | 11/2024 |
| 8491 | 2^346583+116579 | 104332 | Stefano Morozzi | 11/2024 |
| 8493 | 26092^9967+9967^26092 | 104331 | Hans Havermann | 09/2020 |
| 8494 | 2^346577+47501 | 104331 | Stefano Morozzi | 11/2024 |
| 8495 | 2^346578+163287 | 104331 | Stefano Morozzi | 11/2024 |
| 8496 | 2^346579+37019 | 104331 | Stefano Morozzi | 11/2024 |
| 8497 | 2^346579+119645 | 104331 | Stefano Morozzi | 11/2024 |
| 8498 | 2^346579+157611 | 104331 | Stefano Morozzi | 11/2024 |
| 8499 | 2^346576+100803 | 104330 | Stefano Morozzi | 11/2024 |
| 8500 | 2^346576+144495 | 104330 | Stefano Morozzi | 11/2024 |