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 | 2^346449+170595 | 104292 | Stefano Morozzi | 11/2024 |
8252 | 2^346450+70143 | 104292 | Stefano Morozzi | 11/2024 |
8253 | (7^123407-5^123407)/2 | 104291 | Jon Grantham | 08/2023 |
8254 | 2^346445+194585 | 104291 | Stefano Morozzi | 11/2024 |
8255 | 2^346447+13715 | 104291 | Stefano Morozzi | 11/2024 |
8256 | 2^346447+188493 | 104291 | Stefano Morozzi | 11/2024 |
8257 | 2^346441+43529 | 104290 | Stefano Morozzi | 11/2024 |
8258 | 2^346441+105707 | 104290 | Stefano Morozzi | 11/2024 |
8259 | 2^346443+97995 | 104290 | Stefano Morozzi | 11/2024 |
8260 | 2^346438+125667 | 104289 | Stefano Morozzi | 11/2024 |
8261 | 2^346438+173595 | 104289 | Stefano Morozzi | 11/2024 |
8262 | 2^346434+155605 | 104288 | Stefano Morozzi | 11/2024 |
8263 | 2^346435+110823 | 104288 | Stefano Morozzi | 11/2024 |
8264 | 2^346435+139281 | 104288 | Stefano Morozzi | 11/2024 |
8265 | 2^346431+2543 | 104287 | Stefano Morozzi | 11/2024 |
8266 | 2^346432+177181 | 104287 | Stefano Morozzi | 11/2024 |
8267 | 2^346433+35699 | 104287 | Stefano Morozzi | 11/2024 |
8268 | 2^346433+108015 | 104287 | Stefano Morozzi | 11/2024 |
8269 | 2^346429+100365 | 104286 | Stefano Morozzi | 11/2024 |
8270 | 2^346424+104841 | 104285 | Stefano Morozzi | 11/2024 |
8271 | 2^346425+136095 | 104285 | Stefano Morozzi | 11/2024 |
8272 | 2^346425+184971 | 104285 | Stefano Morozzi | 11/2024 |
8273 | 2^346426+74325 | 104285 | Stefano Morozzi | 11/2024 |
8274 | 2^346427+30795 | 104285 | Stefano Morozzi | 11/2024 |
8275 | 2^346421+42971 | 104284 | Stefano Morozzi | 11/2024 |
8276 | 2^346421+82577 | 104284 | Stefano Morozzi | 11/2024 |
8277 | 2^346423+142533 | 104284 | Stefano Morozzi | 11/2024 |
8278 | 6^134013+163 | 104283 | Lelio R Paula | 11/2016 |
8279 | 2^346414+165775 | 104282 | Stefano Morozzi | 11/2024 |
8280 | 10^(2*52140+1)-10^52140-1 | 104281 | Robert Price | 07/2023 |
8281 | 2^346411+106893 | 104281 | Stefano Morozzi | 11/2024 |
8282 | 2^346412+157935 | 104281 | Stefano Morozzi | 11/2024 |
8283 | 2^346413+117485 | 104281 | Stefano Morozzi | 11/2024 |
8284 | 2^346408+8085 | 104280 | Stefano Morozzi | 11/2024 |
8285 | 2^346408+24423 | 104280 | Stefano Morozzi | 11/2024 |
8286 | 2^346409+145047 | 104280 | Stefano Morozzi | 11/2024 |
8287 | 2^346410+172533 | 104280 | Stefano Morozzi | 11/2024 |
8288 | 2^346406+58417 | 104279 | Stefano Morozzi | 11/2024 |
8289 | 2^346406+198315 | 104279 | Stefano Morozzi | 11/2024 |
8290 | 2^346407+172509 | 104279 | Stefano Morozzi | 11/2024 |
8291 | 2^346401+180129 | 104278 | Stefano Morozzi | 11/2024 |
8292 | 2^346402+16897 | 104278 | Stefano Morozzi | 11/2024 |
8293 | 2^346402+114829 | 104278 | Stefano Morozzi | 11/2024 |
8294 | 2^346398+91623 | 104277 | Stefano Morozzi | 11/2024 |
8295 | 2^346398+117369 | 104277 | Stefano Morozzi | 11/2024 |
8296 | 2^346400+100141 | 104277 | Stefano Morozzi | 11/2024 |
8297 | 2^346400+183625 | 104277 | Stefano Morozzi | 11/2024 |
8298 | 2^346395+87281 | 104276 | Stefano Morozzi | 11/2024 |
8299 | 2^346391+28833 | 104275 | Stefano Morozzi | 11/2024 |
8300 | 2^346392+33715 | 104275 | Stefano Morozzi | 11/2024 |
8301 | 2^346392+37507 | 104275 | Stefano Morozzi | 11/2024 |
8302 | 2^346392+197617 | 104275 | Stefano Morozzi | 11/2024 |
8303 | 2^346393+45929 | 104275 | Stefano Morozzi | 11/2024 |
8304 | 2^346388+27223 | 104274 | Stefano Morozzi | 11/2024 |
8305 | 2^346388+29187 | 104274 | Stefano Morozzi | 11/2024 |
8306 | 2^346388+114657 | 104274 | Stefano Morozzi | 11/2024 |
8307 | 2^346388+158667 | 104274 | Stefano Morozzi | 11/2024 |
8308 | (22*10^104272-61)/3 | 104273 | Robert Price | 03/2022 |
8309 | 2^346385+150947 | 104273 | Stefano Morozzi | 11/2024 |
8310 | 2^346385+179309 | 104273 | Stefano Morozzi | 11/2024 |
8311 | 2^346387+80549 | 104273 | Stefano Morozzi | 11/2024 |
8312 | 2^346387+90309 | 104273 | Stefano Morozzi | 11/2024 |
8313 | 2^346387+157473 | 104273 | Stefano Morozzi | 11/2024 |
8314 | 2^346381+67497 | 104272 | Stefano Morozzi | 11/2024 |
8315 | 2^346379+72419 | 104271 | Stefano Morozzi | 11/2024 |
8316 | 2^346379+118811 | 104271 | Stefano Morozzi | 11/2024 |
8317 | 2^346377+97379 | 104270 | Stefano Morozzi | 11/2024 |
8318 | 2^346371+144159 | 104269 | Stefano Morozzi | 11/2024 |
8319 | 2^346371+167213 | 104269 | Stefano Morozzi | 11/2024 |
8320 | 2^346373+31301 | 104269 | Stefano Morozzi | 11/2024 |
8321 | 2^346373+103665 | 104269 | Stefano Morozzi | 11/2024 |
8322 | 2^346368+19155 | 104268 | Stefano Morozzi | 11/2024 |
8323 | 2^346370+10107 | 104268 | Stefano Morozzi | 11/2024 |
8324 | 2^346370+38649 | 104268 | Stefano Morozzi | 11/2024 |
8325 | 2^346365+8411 | 104267 | Stefano Morozzi | 11/2024 |
8326 | 2^346367+6735 | 104267 | Stefano Morozzi | 11/2024 |
8327 | 2^346367+140303 | 104267 | Stefano Morozzi | 11/2024 |
8328 | 2^346361+17507 | 104266 | Stefano Morozzi | 11/2024 |
8329 | 2^346361+46401 | 104266 | Stefano Morozzi | 11/2024 |
8330 | 2^346361+64875 | 104266 | Stefano Morozzi | 11/2024 |
8331 | 2^346364+182271 | 104266 | Stefano Morozzi | 11/2024 |
8332 | 2^346360+33403 | 104265 | Stefano Morozzi | 11/2024 |
8333 | 2^346355+7121 | 104264 | Stefano Morozzi | 11/2024 |
8334 | 2^346356+128607 | 104264 | Stefano Morozzi | 11/2024 |
8335 | 2^346356+152841 | 104264 | Stefano Morozzi | 11/2024 |
8336 | 2^346351+12735 | 104263 | Stefano Morozzi | 11/2024 |
8337 | 2^346354+12247 | 104263 | Stefano Morozzi | 11/2024 |
8338 | 2^346354+93177 | 104263 | Stefano Morozzi | 11/2024 |
8339 | 2^346354+152067 | 104263 | Stefano Morozzi | 11/2024 |
8340 | 2^346348+55023 | 104262 | Stefano Morozzi | 11/2024 |
8341 | 2^346349+92945 | 104262 | Stefano Morozzi | 11/2024 |
8342 | 2^346350+124873 | 104262 | Stefano Morozzi | 11/2024 |
8343 | 2^346350+141253 | 104262 | Stefano Morozzi | 11/2024 |
8344 | 2^346345+36681 | 104261 | Stefano Morozzi | 11/2024 |
8345 | 2^346346+142767 | 104261 | Stefano Morozzi | 11/2024 |
8346 | 2^346331+13743 | 104257 | Stefano Morozzi | 11/2024 |
8347 | 2^346333+100331 | 104257 | Stefano Morozzi | 11/2024 |
8348 | 2^346333+157209 | 104257 | Stefano Morozzi | 11/2024 |
8349 | 2^346330+186837 | 104256 | Stefano Morozzi | 11/2024 |
8350 | 2^346325+144891 | 104255 | Stefano Morozzi | 11/2024 |
8351 | 2^346326+148237 | 104255 | Stefano Morozzi | 11/2024 |
8352 | 2^346321+5877 | 104254 | Stefano Morozzi | 11/2024 |
8353 | 2^346323+35999 | 104254 | Stefano Morozzi | 11/2024 |
8354 | 2^346323+133109 | 104254 | Stefano Morozzi | 11/2024 |
8355 | 2^346318+50695 | 104253 | Stefano Morozzi | 11/2024 |
8356 | 2^346319+78975 | 104253 | Stefano Morozzi | 11/2024 |
8361 | (2^346318+862)/2 | 104252 | Stefano Morozzi | 02/2021 |
8357 | 2^346315+46235 | 104252 | Stefano Morozzi | 11/2024 |
8358 | 2^346316+84571 | 104252 | Stefano Morozzi | 11/2024 |
8359 | 2^346316+168015 | 104252 | Stefano Morozzi | 11/2024 |
8360 | 2^346317+431 | 104252 | Stefano Morozzi | 11/2024 |
8369 | 18^83049-89 | 104250 | Lelio R Paula | 01/2017 |
8368 | (2^346311+606)/2 | 104250 | Stefano Morozzi | 09/2020 |
8362 | 2^346308+92347 | 104250 | Stefano Morozzi | 11/2024 |
8363 | 2^346308+182521 | 104250 | Stefano Morozzi | 11/2024 |
8364 | 2^346309+128897 | 104250 | Stefano Morozzi | 11/2024 |
8365 | 2^346309+184955 | 104250 | Stefano Morozzi | 11/2024 |
8366 | 2^346310+303 | 104250 | Stefano Morozzi | 11/2024 |
8367 | 2^346311+32693 | 104250 | Stefano Morozzi | 11/2024 |
8370 | 2^346305+165741 | 104249 | Stefano Morozzi | 11/2024 |
8371 | 2^346302+75075 | 104248 | Stefano Morozzi | 11/2024 |
8372 | 2^346304+33411 | 104248 | Stefano Morozzi | 11/2024 |
8373 | 2^346298+147849 | 104247 | Stefano Morozzi | 11/2024 |
8374 | 2^346300+144855 | 104247 | Stefano Morozzi | 11/2024 |
8375 | 2^346296+44865 | 104246 | Stefano Morozzi | 11/2024 |
8376 | 2^346297+116291 | 104246 | Stefano Morozzi | 11/2024 |
8377 | 2^346297+142667 | 104246 | Stefano Morozzi | 11/2024 |
8378 | 2^346293+39285 | 104245 | Stefano Morozzi | 11/2024 |
8379 | 2^346293+58929 | 104245 | Stefano Morozzi | 11/2024 |
8380 | 2^346294+151075 | 104245 | Stefano Morozzi | 11/2024 |
8381 | 2^346290+162153 | 104244 | Stefano Morozzi | 11/2024 |
8382 | 2^346286+139935 | 104243 | Stefano Morozzi | 11/2024 |
8383 | 2^346282+184705 | 104242 | Stefano Morozzi | 11/2024 |
8384 | 2^346283+116913 | 104242 | Stefano Morozzi | 11/2024 |
8385 | 2^346284+118191 | 104242 | Stefano Morozzi | 11/2024 |
8386 | 2^346284+186595 | 104242 | Stefano Morozzi | 11/2024 |
8387 | 2^346279+29591 | 104241 | Stefano Morozzi | 11/2024 |
8388 | 2^346279+122385 | 104241 | Stefano Morozzi | 11/2024 |
8389 | 2^346280+18925 | 104241 | Stefano Morozzi | 11/2024 |
8390 | 2^346281+69725 | 104241 | Stefano Morozzi | 11/2024 |
8391 | 2^346281+156401 | 104241 | Stefano Morozzi | 11/2024 |
8392 | 2^346275+182519 | 104240 | Stefano Morozzi | 11/2024 |
8393 | 2^346276+14101 | 104240 | Stefano Morozzi | 11/2024 |
8394 | 2^346276+189937 | 104240 | Stefano Morozzi | 11/2024 |
8395 | 2^346273+121425 | 104239 | Stefano Morozzi | 11/2024 |
8396 | 2^346274+72363 | 104239 | Stefano Morozzi | 11/2024 |
8397 | 2^346274+92047 | 104239 | Stefano Morozzi | 11/2024 |
8398 | 2^346268+44233 | 104238 | Stefano Morozzi | 11/2024 |
8399 | 2^346270+19539 | 104238 | Stefano Morozzi | 11/2024 |
8400 | 2^346265+133877 | 104237 | Stefano Morozzi | 11/2024 |
8401 | 2^346267+64613 | 104237 | Stefano Morozzi | 11/2024 |
8402 | 2^346267+70461 | 104237 | Stefano Morozzi | 11/2024 |
8403 | 2^346267+118715 | 104237 | Stefano Morozzi | 11/2024 |
8404 | 2^346263+110721 | 104236 | Stefano Morozzi | 11/2024 |
8405 | 2^346263+165009 | 104236 | Stefano Morozzi | 11/2024 |
8406 | 2^346264+50481 | 104236 | Stefano Morozzi | 11/2024 |
8407 | 2^346264+134047 | 104236 | Stefano Morozzi | 11/2024 |
8408 | 2^346264+179617 | 104236 | Stefano Morozzi | 11/2024 |
8409 | 2^346260+176391 | 104235 | Stefano Morozzi | 11/2024 |
8410 | 2^346256+36111 | 104234 | Stefano Morozzi | 11/2024 |
8411 | 2^346254+52299 | 104233 | Stefano Morozzi | 11/2024 |
8417 | (166*10^104230+11)/3 | 104232 | Robert Price | 03/2021 |
8412 | 2^346248+3075 | 104232 | Stefano Morozzi | 11/2024 |
8413 | 2^346248+39081 | 104232 | Stefano Morozzi | 11/2024 |
8414 | 2^346249+38339 | 104232 | Stefano Morozzi | 11/2024 |
8415 | 2^346251+32831 | 104232 | Stefano Morozzi | 11/2024 |
8416 | 2^346251+116175 | 104232 | Stefano Morozzi | 11/2024 |
8418 | 2^346247+197309 | 104231 | Stefano Morozzi | 11/2024 |
8419 | 2^346245+95429 | 104231 | Stefano Morozzi | 11/2024 |
8420 | 2^346243+58163 | 104230 | Stefano Morozzi | 11/2024 |
8421 | 2^346243+130931 | 104230 | Stefano Morozzi | 11/2024 |
8422 | 2^346244+10381 | 104230 | Stefano Morozzi | 11/2024 |
8423 | 2^346241+41057 | 104229 | Stefano Morozzi | 11/2024 |
8424 | 2^346235+152303 | 104228 | Stefano Morozzi | 11/2024 |
8425 | 2^346236+106617 | 104228 | Stefano Morozzi | 11/2024 |
8426 | 2^346232+103317 | 104227 | Stefano Morozzi | 11/2024 |
8427 | 2^346232+193681 | 104227 | Stefano Morozzi | 11/2024 |
8428 | 2^346233+115671 | 104227 | Stefano Morozzi | 11/2024 |
8429 | 2^346229+73157 | 104226 | Stefano Morozzi | 11/2024 |
8430 | 2^346229+145377 | 104226 | Stefano Morozzi | 11/2024 |
8431 | 2^346230+171103 | 104226 | Stefano Morozzi | 11/2024 |
8432 | 2^346225+55527 | 104225 | Stefano Morozzi | 11/2024 |
8433 | 2^346225+132251 | 104225 | Stefano Morozzi | 11/2024 |
8434 | 2^346225+140637 | 104225 | Stefano Morozzi | 11/2024 |
8435 | 2^346223+27335 | 104224 | Stefano Morozzi | 11/2024 |
8436 | 2^346223+74591 | 104224 | Stefano Morozzi | 11/2024 |
8437 | 2^346224+70905 | 104224 | Stefano Morozzi | 11/2024 |
8438 | 2^346220+12355 | 104223 | Stefano Morozzi | 11/2024 |
8439 | 2^346220+110805 | 104223 | Stefano Morozzi | 11/2024 |
8440 | 2^346220+161361 | 104223 | Stefano Morozzi | 11/2024 |
8441 | 2^346220+176523 | 104223 | Stefano Morozzi | 11/2024 |
8442 | 2^346220+185625 | 104223 | Stefano Morozzi | 11/2024 |
8443 | 2^346216+62973 | 104222 | Stefano Morozzi | 11/2024 |
8444 | 2^346217+88391 | 104222 | Stefano Morozzi | 11/2024 |
8445 | 2^346217+170121 | 104222 | Stefano Morozzi | 11/2024 |
8446 | 2^346217+111567 | 104222 | Stefano Morozzi | 11/2024 |
8450 | 2^346213+484049 | 104221 | Enzo Doria | 04/2017 |
8447 | 2^346212+31773 | 104221 | Stefano Morozzi | 11/2024 |
8448 | 2^346213+37151 | 104221 | Stefano Morozzi | 11/2024 |
8449 | 2^346213+162399 | 104221 | Stefano Morozzi | 11/2024 |
8451 | 2^346209+173231 | 104220 | Stefano Morozzi | 11/2024 |
8452 | 2^346207+125243 | 104219 | Stefano Morozzi | 11/2024 |
8453 | 2^346208+79825 | 104219 | Stefano Morozzi | 11/2024 |
8454 | 2^346208+176463 | 104219 | Stefano Morozzi | 11/2024 |
8455 | 2^346206+195363 | 104219 | Stefano Morozzi | 11/2024 |
8456 | 2^346202+67065 | 104218 | Stefano Morozzi | 11/2024 |
8457 | 2^346202+107377 | 104218 | Stefano Morozzi | 11/2024 |
8458 | 2^346204+127677 | 104218 | Stefano Morozzi | 11/2024 |
8459 | 2^346204+19573 | 104218 | Stefano Morozzi | 11/2024 |
8460 | 2^346204+161997 | 104218 | Stefano Morozzi | 11/2024 |
8461 | 2^346204+152665 | 104218 | Stefano Morozzi | 11/2024 |
8462 | 2^346199+90995 | 104217 | Stefano Morozzi | 11/2024 |
8463 | 2^346199+189629 | 104217 | Stefano Morozzi | 11/2024 |
8464 | 2^346200+159591 | 104217 | Stefano Morozzi | 11/2024 |
8465 | 2^346195+19733 | 104216 | Stefano Morozzi | 11/2024 |
8466 | 2^346196+141117 | 104216 | Stefano Morozzi | 11/2024 |
8467 | 2^346196+195171 | 104216 | Stefano Morozzi | 11/2024 |
8468 | 2^346197+113751 | 104216 | Stefano Morozzi | 11/2024 |
8469 | 2^346198+95305 | 104216 | Stefano Morozzi | 11/2024 |
8470 | 2^346198+106735 | 104216 | Stefano Morozzi | 11/2024 |
8472 | 18^83021-91 | 104214 | Lelio R Paula | 01/2017 |
8471 | 2^346189+194831 | 104214 | Stefano Morozzi | 11/2024 |
8473 | 10^104212+128779 | 104213 | Patrick De Geest | 05/2016 |
8474 | 10^104212+237447 | 104213 | Patrick De Geest | 05/2016 |
8475 | 10^104212+242139 | 104213 | Patrick De Geest | 05/2016 |
8476 | 10^104212+269199 | 104213 | Patrick De Geest | 05/2016 |
8480 | 24254^19803+19803^24254 | 104213 | Hans Havermann | 09/2020 |
8477 | 2^346186+93813 | 104213 | Stefano Morozzi | 11/2024 |
8478 | 2^346186+153687 | 104213 | Stefano Morozzi | 11/2024 |
8479 | 2^346187+102195 | 104213 | Stefano Morozzi | 11/2024 |
8485 | (10^104212-71)/1 | 104212 | Serge Batalov | 12/2014 |
8481 | 2^346182+118065 | 104212 | Stefano Morozzi | 11/2024 |
8482 | 2^346184+155085 | 104212 | Stefano Morozzi | 11/2024 |
8483 | 2^346184+187513 | 104212 | Stefano Morozzi | 11/2024 |
8484 | 2^346184+188455 | 104212 | Stefano Morozzi | 11/2024 |
8486 | 2^346180+82735 | 104211 | Stefano Morozzi | 11/2024 |
8487 | 2^346180+160593 | 104211 | Stefano Morozzi | 11/2024 |
8488 | 2^346180+192333 | 104211 | Stefano Morozzi | 11/2024 |
8489 | 2^346181+199821 | 104211 | Stefano Morozzi | 11/2024 |
8490 | 2^346176+123667 | 104210 | Stefano Morozzi | 11/2024 |
8491 | 2^346178+37455 | 104210 | Stefano Morozzi | 11/2024 |
8492 | 2^346178+95865 | 104210 | Stefano Morozzi | 11/2024 |
8493 | 2^346178+159517 | 104210 | Stefano Morozzi | 11/2024 |
8494 | 2^346174+12543 | 104209 | Stefano Morozzi | 11/2024 |
8495 | 2^346169+56049 | 104208 | Stefano Morozzi | 11/2024 |
8496 | 2^346169+118965 | 104208 | Stefano Morozzi | 11/2024 |
8497 | 2^346170+31363 | 104208 | Stefano Morozzi | 11/2024 |
8498 | 2^346165+61767 | 104207 | Stefano Morozzi | 11/2024 |
8499 | 2^346166+189919 | 104207 | Stefano Morozzi | 11/2024 |
8500 | 2^346167+41681 | 104207 | Stefano Morozzi | 11/2024 |