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 | 2^346614+85737 | 104342 | Stefano Morozzi | 11/2024 |
8252 | 2^346611+183923 | 104341 | Stefano Morozzi | 11/2024 |
8253 | 2^346607+36209 | 104340 | Stefano Morozzi | 11/2024 |
8254 | 2^346607+65291 | 104340 | Stefano Morozzi | 11/2024 |
8255 | 2^346609+47471 | 104340 | Stefano Morozzi | 11/2024 |
8260 | (2^346606+2082)/2 | 104339 | Stefano Morozzi | 09/2020 |
8261 | (2^346607+2070)/2 | 104339 | Stefano Morozzi | 09/2020 |
8256 | 2^346605+1041 | 104339 | Stefano Morozzi | 11/2024 |
8257 | 2^346605+181167 | 104339 | Stefano Morozzi | 11/2024 |
8258 | 2^346606+1035 | 104339 | Stefano Morozzi | 11/2024 |
8259 | 2^346606+103863 | 104339 | Stefano Morozzi | 11/2024 |
8262 | 2^346601+26529 | 104338 | Stefano Morozzi | 11/2024 |
8263 | 2^346603+133431 | 104338 | Stefano Morozzi | 11/2024 |
8264 | 2^346597+97661 | 104337 | Stefano Morozzi | 11/2024 |
8265 | 2^346597+186809 | 104337 | Stefano Morozzi | 11/2024 |
8266 | 2^346598+31719 | 104337 | Stefano Morozzi | 11/2024 |
8267 | 2^346598+162513 | 104337 | Stefano Morozzi | 11/2024 |
8268 | 2^346599+45731 | 104337 | Stefano Morozzi | 11/2024 |
8269 | 2^346599+187061 | 104337 | Stefano Morozzi | 11/2024 |
8270 | 2^346600+175993 | 104337 | Stefano Morozzi | 11/2024 |
8271 | 2^346595+89753 | 104336 | Stefano Morozzi | 11/2024 |
8272 | 2^346595+114491 | 104336 | Stefano Morozzi | 11/2024 |
8273 | 2^346596+120183 | 104336 | Stefano Morozzi | 11/2024 |
8274 | 2^346591+183651 | 104335 | Stefano Morozzi | 11/2024 |
8275 | 2^346591+192149 | 104335 | Stefano Morozzi | 11/2024 |
8276 | 2^346592+77347 | 104335 | Stefano Morozzi | 11/2024 |
8277 | 2^346592+178161 | 104335 | Stefano Morozzi | 11/2024 |
8278 | 2^346592+195985 | 104335 | Stefano Morozzi | 11/2024 |
8279 | 2^346589+40607 | 104334 | Stefano Morozzi | 11/2024 |
8280 | 2^346590+151533 | 104334 | Stefano Morozzi | 11/2024 |
8281 | 2^346584+105103 | 104333 | Stefano Morozzi | 11/2024 |
8282 | 2^346585+56861 | 104333 | Stefano Morozzi | 11/2024 |
8288 | (2^346582+3202)/2 | 104332 | Stefano Morozzi | 09/2020 |
8283 | 2^346581+1601 | 104332 | Stefano Morozzi | 11/2024 |
8284 | 2^346581+82115 | 104332 | Stefano Morozzi | 11/2024 |
8285 | 2^346581+193979 | 104332 | Stefano Morozzi | 11/2024 |
8286 | 2^346582+197767 | 104332 | Stefano Morozzi | 11/2024 |
8287 | 2^346583+116579 | 104332 | Stefano Morozzi | 11/2024 |
8289 | 26092^9967+9967^26092 | 104331 | Hans Havermann | 09/2020 |
8290 | 2^346577+47501 | 104331 | Stefano Morozzi | 11/2024 |
8291 | 2^346578+163287 | 104331 | Stefano Morozzi | 11/2024 |
8292 | 2^346579+37019 | 104331 | Stefano Morozzi | 11/2024 |
8293 | 2^346579+119645 | 104331 | Stefano Morozzi | 11/2024 |
8294 | 2^346579+157611 | 104331 | Stefano Morozzi | 11/2024 |
8295 | 2^346576+100803 | 104330 | Stefano Morozzi | 11/2024 |
8296 | 2^346576+144495 | 104330 | Stefano Morozzi | 11/2024 |
8297 | 2^346573+13859 | 104329 | Stefano Morozzi | 11/2024 |
8298 | 2^346568+110181 | 104328 | Stefano Morozzi | 11/2024 |
8300 | 5*10^104326+77 | 104327 | Robert Price | 12/2018 |
8299 | 2^346564+151101 | 104327 | Stefano Morozzi | 11/2024 |
8306 | (2^346564+2026)/2 | 104326 | Stefano Morozzi | 09/2020 |
8301 | 2^346561+53385 | 104326 | Stefano Morozzi | 11/2024 |
8302 | 2^346561+139791 | 104326 | Stefano Morozzi | 11/2024 |
8303 | 2^346562+110383 | 104326 | Stefano Morozzi | 11/2024 |
8304 | 2^346563+1013 | 104326 | Stefano Morozzi | 11/2024 |
8305 | 2^346563+9305 | 104326 | Stefano Morozzi | 11/2024 |
8307 | 2^346558+97033 | 104325 | Stefano Morozzi | 11/2024 |
8308 | 2^346556+101283 | 104324 | Stefano Morozzi | 11/2024 |
8309 | 2^346551+55043 | 104323 | Stefano Morozzi | 11/2024 |
8310 | 2^346547+71855 | 104322 | Stefano Morozzi | 11/2024 |
8311 | 2^346548+119695 | 104322 | Stefano Morozzi | 11/2024 |
8312 | 2^346550+55249 | 104322 | Stefano Morozzi | 11/2024 |
8313 | 2^346550+158655 | 104322 | Stefano Morozzi | 11/2024 |
8314 | 2^346545+87885 | 104321 | Stefano Morozzi | 11/2024 |
8315 | 2^346545+95105 | 104321 | Stefano Morozzi | 11/2024 |
8316 | 2^346546+126763 | 104321 | Stefano Morozzi | 11/2024 |
8317 | 2^346546+149397 | 104321 | Stefano Morozzi | 11/2024 |
8318 | (8925^26569-1)/(8925^163-1) | 104320 | Ryan Propper | 11/2023 |
8319 | 2^346542+128005 | 104320 | Stefano Morozzi | 11/2024 |
8320 | 2^346538+123507 | 104319 | Stefano Morozzi | 11/2024 |
8321 | 2^346540+118251 | 104319 | Stefano Morozzi | 11/2024 |
8322 | 2^346540+128965 | 104319 | Stefano Morozzi | 11/2024 |
8323 | 2^346535+138485 | 104318 | Stefano Morozzi | 11/2024 |
8324 | 2^346536+149013 | 104318 | Stefano Morozzi | 11/2024 |
8325 | 2^346531+98801 | 104317 | Stefano Morozzi | 11/2024 |
8326 | 2^346533+12035 | 104317 | Stefano Morozzi | 11/2024 |
8330 | 2^346527-111817 | 104316 | Enzo Doria | 05/2014 |
8329 | 6^134055+101 | 104316 | Lelio R Paula | 11/2016 |
8327 | fibonacci(499147)-4 | 104316 | Jon Grantham | 08/2023 |
8328 | 2^346529+101351 | 104316 | Stefano Morozzi | 11/2024 |
8331 | 2^346524+81585 | 104315 | Stefano Morozzi | 11/2024 |
8332 | 2^346524+184821 | 104315 | Stefano Morozzi | 11/2024 |
8333 | 2^346525+41051 | 104315 | Stefano Morozzi | 11/2024 |
8334 | 2^346525+61845 | 104315 | Stefano Morozzi | 11/2024 |
8335 | 2^346521+47439 | 104314 | Stefano Morozzi | 11/2024 |
8336 | 2^346522+34689 | 104314 | Stefano Morozzi | 11/2024 |
8337 | 2^346519+24543 | 104313 | Stefano Morozzi | 11/2024 |
8338 | 2^346519+75119 | 104313 | Stefano Morozzi | 11/2024 |
8342 | 92105!4+8 | 104312 | Robert Price | 09/2019 |
8339 | 2^346514+11023 | 104312 | Stefano Morozzi | 11/2024 |
8340 | 2^346514+22009 | 104312 | Stefano Morozzi | 11/2024 |
8341 | 2^346516+107031 | 104312 | Stefano Morozzi | 11/2024 |
8343 | 2^346511+65675 | 104311 | Stefano Morozzi | 11/2024 |
8344 | 2^346512+105345 | 104311 | Stefano Morozzi | 11/2024 |
8345 | 2^346513+80387 | 104311 | Stefano Morozzi | 11/2024 |
8346 | 2^346510+104955 | 104310 | Stefano Morozzi | 11/2024 |
8347 | 2^346510+145347 | 104310 | Stefano Morozzi | 11/2024 |
8348 | 2^346506+105537 | 104309 | Stefano Morozzi | 11/2024 |
8349 | 2^346506+145353 | 104309 | Stefano Morozzi | 11/2024 |
8350 | 2^346503+160109 | 104308 | Stefano Morozzi | 11/2024 |
8351 | 2^346494+155215 | 104306 | Stefano Morozzi | 11/2024 |
8352 | 2^346495+26243 | 104306 | Stefano Morozzi | 11/2024 |
8353 | 2^346497+108749 | 104306 | Stefano Morozzi | 11/2024 |
8354 | 2^346488+146631 | 104304 | Stefano Morozzi | 11/2024 |
8355 | 2^346489+6035 | 104304 | Stefano Morozzi | 11/2024 |
8356 | 2^346489+16389 | 104304 | Stefano Morozzi | 11/2024 |
8357 | 2^346489+175959 | 104304 | Stefano Morozzi | 11/2024 |
8358 | 2^346484+119491 | 104303 | Stefano Morozzi | 11/2024 |
8359 | 2^346487+12125 | 104303 | Stefano Morozzi | 11/2024 |
8360 | 2^346487+92103 | 104303 | Stefano Morozzi | 11/2024 |
8361 | 2^346481+199815 | 104302 | Stefano Morozzi | 11/2024 |
8362 | 2^346478+2335 | 104301 | Stefano Morozzi | 11/2024 |
8363 | 2^346478+121773 | 104301 | Stefano Morozzi | 11/2024 |
8364 | 2^346479+80703 | 104301 | Stefano Morozzi | 11/2024 |
8365 | 2^346479+164693 | 104301 | Stefano Morozzi | 11/2024 |
8366 | 2^346480+156951 | 104301 | Stefano Morozzi | 11/2024 |
8367 | 2^346480+176247 | 104301 | Stefano Morozzi | 11/2024 |
8368 | 2^346475+178953 | 104300 | Stefano Morozzi | 11/2024 |
8369 | 2^346476+83935 | 104300 | Stefano Morozzi | 11/2024 |
8370 | 2^346470+182623 | 104298 | Stefano Morozzi | 11/2024 |
8371 | 2^346464+54007 | 104297 | Stefano Morozzi | 11/2024 |
8372 | 2^346464+55287 | 104297 | Stefano Morozzi | 11/2024 |
8373 | 2^346464+84411 | 104297 | Stefano Morozzi | 11/2024 |
8374 | 2^346465+15905 | 104297 | Stefano Morozzi | 11/2024 |
8375 | 2^346465+27797 | 104297 | Stefano Morozzi | 11/2024 |
8376 | 2^346465+85815 | 104297 | Stefano Morozzi | 11/2024 |
8377 | 2^346465+92787 | 104297 | Stefano Morozzi | 11/2024 |
8378 | 2^346466+133369 | 104297 | Stefano Morozzi | 11/2024 |
8379 | 2^346461+30591 | 104296 | Stefano Morozzi | 11/2024 |
8380 | 2^346462+74067 | 104296 | Stefano Morozzi | 11/2024 |
8381 | 2^346458+68947 | 104295 | Stefano Morozzi | 11/2024 |
8382 | 2^346459+39333 | 104295 | Stefano Morozzi | 11/2024 |
8383 | 2^346459+110355 | 104295 | Stefano Morozzi | 11/2024 |
8384 | 2^346454+166035 | 104294 | Stefano Morozzi | 11/2024 |
8385 | 2^346456+132385 | 104294 | Stefano Morozzi | 11/2024 |
8386 | 2^346456+138727 | 104294 | Stefano Morozzi | 11/2024 |
8387 | 2^346456+176767 | 104294 | Stefano Morozzi | 11/2024 |
8388 | 2^346451+72969 | 104293 | Stefano Morozzi | 11/2024 |
8389 | 2^346452+10441 | 104293 | Stefano Morozzi | 11/2024 |
8390 | 2^346449+170595 | 104292 | Stefano Morozzi | 11/2024 |
8391 | 2^346450+70143 | 104292 | Stefano Morozzi | 11/2024 |
8392 | (7^123407-5^123407)/2 | 104291 | Jon Grantham | 08/2023 |
8393 | 2^346445+194585 | 104291 | Stefano Morozzi | 11/2024 |
8394 | 2^346447+13715 | 104291 | Stefano Morozzi | 11/2024 |
8395 | 2^346447+188493 | 104291 | Stefano Morozzi | 11/2024 |
8396 | 2^346441+43529 | 104290 | Stefano Morozzi | 11/2024 |
8397 | 2^346441+105707 | 104290 | Stefano Morozzi | 11/2024 |
8398 | 2^346443+97995 | 104290 | Stefano Morozzi | 11/2024 |
8399 | 2^346438+125667 | 104289 | Stefano Morozzi | 11/2024 |
8400 | 2^346438+173595 | 104289 | Stefano Morozzi | 11/2024 |
8401 | 2^346434+155605 | 104288 | Stefano Morozzi | 11/2024 |
8402 | 2^346435+110823 | 104288 | Stefano Morozzi | 11/2024 |
8403 | 2^346435+139281 | 104288 | Stefano Morozzi | 11/2024 |
8404 | 2^346431+2543 | 104287 | Stefano Morozzi | 11/2024 |
8405 | 2^346432+177181 | 104287 | Stefano Morozzi | 11/2024 |
8406 | 2^346433+35699 | 104287 | Stefano Morozzi | 11/2024 |
8407 | 2^346433+108015 | 104287 | Stefano Morozzi | 11/2024 |
8408 | 2^346429+100365 | 104286 | Stefano Morozzi | 11/2024 |
8409 | 2^346424+104841 | 104285 | Stefano Morozzi | 11/2024 |
8410 | 2^346425+136095 | 104285 | Stefano Morozzi | 11/2024 |
8411 | 2^346425+184971 | 104285 | Stefano Morozzi | 11/2024 |
8412 | 2^346426+74325 | 104285 | Stefano Morozzi | 11/2024 |
8413 | 2^346427+30795 | 104285 | Stefano Morozzi | 11/2024 |
8414 | 2^346421+42971 | 104284 | Stefano Morozzi | 11/2024 |
8415 | 2^346421+82577 | 104284 | Stefano Morozzi | 11/2024 |
8416 | 2^346423+142533 | 104284 | Stefano Morozzi | 11/2024 |
8417 | 6^134013+163 | 104283 | Lelio R Paula | 11/2016 |
8418 | 2^346414+165775 | 104282 | Stefano Morozzi | 11/2024 |
8419 | 10^(2*52140+1)-10^52140-1 | 104281 | Robert Price | 07/2023 |
8420 | 2^346411+106893 | 104281 | Stefano Morozzi | 11/2024 |
8421 | 2^346412+157935 | 104281 | Stefano Morozzi | 11/2024 |
8422 | 2^346413+117485 | 104281 | Stefano Morozzi | 11/2024 |
8423 | 2^346408+8085 | 104280 | Stefano Morozzi | 11/2024 |
8424 | 2^346408+24423 | 104280 | Stefano Morozzi | 11/2024 |
8425 | 2^346409+145047 | 104280 | Stefano Morozzi | 11/2024 |
8426 | 2^346410+172533 | 104280 | Stefano Morozzi | 11/2024 |
8427 | 2^346406+58417 | 104279 | Stefano Morozzi | 11/2024 |
8428 | 2^346406+198315 | 104279 | Stefano Morozzi | 11/2024 |
8429 | 2^346407+172509 | 104279 | Stefano Morozzi | 11/2024 |
8430 | 2^346401+180129 | 104278 | Stefano Morozzi | 11/2024 |
8431 | 2^346402+16897 | 104278 | Stefano Morozzi | 11/2024 |
8432 | 2^346402+114829 | 104278 | Stefano Morozzi | 11/2024 |
8433 | 2^346398+91623 | 104277 | Stefano Morozzi | 11/2024 |
8434 | 2^346398+117369 | 104277 | Stefano Morozzi | 11/2024 |
8435 | 2^346400+100141 | 104277 | Stefano Morozzi | 11/2024 |
8436 | 2^346400+183625 | 104277 | Stefano Morozzi | 11/2024 |
8437 | 2^346395+87281 | 104276 | Stefano Morozzi | 11/2024 |
8438 | 2^346391+28833 | 104275 | Stefano Morozzi | 11/2024 |
8439 | 2^346392+33715 | 104275 | Stefano Morozzi | 11/2024 |
8440 | 2^346392+37507 | 104275 | Stefano Morozzi | 11/2024 |
8441 | 2^346392+197617 | 104275 | Stefano Morozzi | 11/2024 |
8442 | 2^346393+45929 | 104275 | Stefano Morozzi | 11/2024 |
8443 | 2^346388+27223 | 104274 | Stefano Morozzi | 11/2024 |
8444 | 2^346388+29187 | 104274 | Stefano Morozzi | 11/2024 |
8445 | 2^346388+114657 | 104274 | Stefano Morozzi | 11/2024 |
8446 | 2^346388+158667 | 104274 | Stefano Morozzi | 11/2024 |
8447 | (22*10^104272-61)/3 | 104273 | Robert Price | 03/2022 |
8448 | 2^346385+150947 | 104273 | Stefano Morozzi | 11/2024 |
8449 | 2^346385+179309 | 104273 | Stefano Morozzi | 11/2024 |
8450 | 2^346387+80549 | 104273 | Stefano Morozzi | 11/2024 |
8451 | 2^346387+90309 | 104273 | Stefano Morozzi | 11/2024 |
8452 | 2^346387+157473 | 104273 | Stefano Morozzi | 11/2024 |
8453 | 2^346381+67497 | 104272 | Stefano Morozzi | 11/2024 |
8454 | 2^346379+72419 | 104271 | Stefano Morozzi | 11/2024 |
8455 | 2^346379+118811 | 104271 | Stefano Morozzi | 11/2024 |
8456 | 2^346377+97379 | 104270 | Stefano Morozzi | 11/2024 |
8457 | 2^346371+144159 | 104269 | Stefano Morozzi | 11/2024 |
8458 | 2^346371+167213 | 104269 | Stefano Morozzi | 11/2024 |
8459 | 2^346373+31301 | 104269 | Stefano Morozzi | 11/2024 |
8460 | 2^346373+103665 | 104269 | Stefano Morozzi | 11/2024 |
8461 | 2^346368+19155 | 104268 | Stefano Morozzi | 11/2024 |
8462 | 2^346370+10107 | 104268 | Stefano Morozzi | 11/2024 |
8463 | 2^346370+38649 | 104268 | Stefano Morozzi | 11/2024 |
8464 | 2^346365+8411 | 104267 | Stefano Morozzi | 11/2024 |
8465 | 2^346367+6735 | 104267 | Stefano Morozzi | 11/2024 |
8466 | 2^346367+140303 | 104267 | Stefano Morozzi | 11/2024 |
8467 | 2^346361+17507 | 104266 | Stefano Morozzi | 11/2024 |
8468 | 2^346361+46401 | 104266 | Stefano Morozzi | 11/2024 |
8469 | 2^346361+64875 | 104266 | Stefano Morozzi | 11/2024 |
8470 | 2^346364+182271 | 104266 | Stefano Morozzi | 11/2024 |
8471 | 2^346360+33403 | 104265 | Stefano Morozzi | 11/2024 |
8472 | 2^346355+7121 | 104264 | Stefano Morozzi | 11/2024 |
8473 | 2^346356+128607 | 104264 | Stefano Morozzi | 11/2024 |
8474 | 2^346356+152841 | 104264 | Stefano Morozzi | 11/2024 |
8475 | 2^346351+12735 | 104263 | Stefano Morozzi | 11/2024 |
8476 | 2^346354+12247 | 104263 | Stefano Morozzi | 11/2024 |
8477 | 2^346354+93177 | 104263 | Stefano Morozzi | 11/2024 |
8478 | 2^346354+152067 | 104263 | Stefano Morozzi | 11/2024 |
8479 | 2^346348+55023 | 104262 | Stefano Morozzi | 11/2024 |
8480 | 2^346349+92945 | 104262 | Stefano Morozzi | 11/2024 |
8481 | 2^346350+124873 | 104262 | Stefano Morozzi | 11/2024 |
8482 | 2^346350+141253 | 104262 | Stefano Morozzi | 11/2024 |
8483 | 2^346345+36681 | 104261 | Stefano Morozzi | 11/2024 |
8484 | 2^346346+142767 | 104261 | Stefano Morozzi | 11/2024 |
8485 | 2^346331+13743 | 104257 | Stefano Morozzi | 11/2024 |
8486 | 2^346333+100331 | 104257 | Stefano Morozzi | 11/2024 |
8487 | 2^346333+157209 | 104257 | Stefano Morozzi | 11/2024 |
8488 | 2^346330+186837 | 104256 | Stefano Morozzi | 11/2024 |
8489 | 2^346325+144891 | 104255 | Stefano Morozzi | 11/2024 |
8490 | 2^346326+148237 | 104255 | Stefano Morozzi | 11/2024 |
8491 | 2^346321+5877 | 104254 | Stefano Morozzi | 11/2024 |
8492 | 2^346323+35999 | 104254 | Stefano Morozzi | 11/2024 |
8493 | 2^346323+133109 | 104254 | Stefano Morozzi | 11/2024 |
8494 | 2^346318+50695 | 104253 | Stefano Morozzi | 11/2024 |
8495 | 2^346319+78975 | 104253 | Stefano Morozzi | 11/2024 |
8500 | (2^346318+862)/2 | 104252 | Stefano Morozzi | 02/2021 |
8496 | 2^346315+46235 | 104252 | Stefano Morozzi | 11/2024 |
8497 | 2^346316+84571 | 104252 | Stefano Morozzi | 11/2024 |
8498 | 2^346316+168015 | 104252 | Stefano Morozzi | 11/2024 |
8499 | 2^346317+431 | 104252 | Stefano Morozzi | 11/2024 |