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 ? |
7251 | 3^219222-310 | 104596 | Lelio R Paula | 11/2016 |
7252 | 25993^10554+10554^25993 | 104581 | Hans Havermann | 09/2020 |
7253 | (15*2^347399-1)/13 | 104578 | Lelio R Paula | 03/2014 |
7254 | 2^347372-17853 | 104570 | Enzo Doria | 05/2013 |
7255 | 2^347314+99 | 104552 | Lelio R Paula | 09/2011 |
7256 | 2^347300-22233 | 104548 | Enzo Doria | 06/2013 |
7257 | 2^347287-19845 | 104544 | Enzo Doria | 06/2013 |
7258 | 2^347258-231191 | 104536 | Harrison Mesh | 06/2022 |
7259 | (31*2^347254-1)/891 | 104533 | Lelio R Paula | 03/2014 |
7260 | 5*F(250091)*(F(250091)-1)+1 | 104532 | Serge Batalov | 04/2015 |
7261 | 7*2^347239-3 | 104531 | Lelio R Paula | 09/2014 |
7262 | (3^219098-8)/514147439969 | 104525 | Lelio R Paula | 12/2013 |
7263 | 5*3^219047+8 | 104513 | Lelio R Paula | 09/2014 |
7264 | 2^347148-109073 | 104502 | Enzo Doria | 04/2014 |
7265 | 2^347129-20145 | 104497 | Enzo Doria | 06/2013 |
7266 | 4*10^104461-57 | 104462 | Robert Price | 10/2018 |
7267 | 2^346999+198831 | 104458 | Stefano Morozzi | 11/2024 |
7268 | 2^346996+166273 | 104457 | Stefano Morozzi | 11/2024 |
7269 | 2^346997+105755 | 104457 | Stefano Morozzi | 11/2024 |
7270 | 2^346997+115259 | 104457 | Stefano Morozzi | 11/2024 |
7271 | 2^346992+97515 | 104456 | Stefano Morozzi | 11/2024 |
7272 | 2^346992+169593 | 104456 | Stefano Morozzi | 11/2024 |
7273 | 2^346994+182215 | 104456 | Stefano Morozzi | 11/2024 |
7274 | 2^346994+187933 | 104456 | Stefano Morozzi | 11/2024 |
7275 | (7*10^(2*52227+1)+9*10^52227-7)/9 | 104455 | Robert Price | 10/2023 |
7278 | (2^346989+590)/2 | 104454 | Stefano Morozzi | 09/2020 |
7276 | 2^346988+295 | 104454 | Stefano Morozzi | 11/2024 |
7277 | 2^346988+47241 | 104454 | Stefano Morozzi | 11/2024 |
7279 | 2^346983+4203 | 104453 | Stefano Morozzi | 11/2024 |
7280 | 2^346983+119259 | 104453 | Stefano Morozzi | 11/2024 |
7281 | 2^346983+47729 | 104453 | Stefano Morozzi | 11/2024 |
7282 | 2^346985+124437 | 104453 | Stefano Morozzi | 11/2024 |
7283 | 2^346979+72443 | 104452 | Stefano Morozzi | 11/2024 |
7284 | 2^346980+167731 | 104452 | Stefano Morozzi | 11/2024 |
7285 | 2^346978+64933 | 104451 | Stefano Morozzi | 11/2024 |
7286 | 2^346974+105865 | 104450 | Stefano Morozzi | 11/2024 |
7287 | 2^346972+95343 | 104449 | Stefano Morozzi | 11/2024 |
7288 | 2^346966+63519 | 104448 | Stefano Morozzi | 11/2024 |
7289 | 2^346963+42825 | 104447 | Stefano Morozzi | 11/2024 |
7290 | 2^346963+140153 | 104447 | Stefano Morozzi | 11/2024 |
7291 | 2^346965+144537 | 104447 | Stefano Morozzi | 11/2024 |
7292 | 2^346962+128917 | 104446 | Stefano Morozzi | 11/2024 |
7293 | 2^346956+110455 | 104445 | Stefano Morozzi | 11/2024 |
7294 | 2^346956+72711 | 104445 | Stefano Morozzi | 11/2024 |
7295 | 2^346954+178093 | 104444 | Stefano Morozzi | 11/2024 |
7296 | 2^346955+46205 | 104444 | Stefano Morozzi | 11/2024 |
7297 | 2^346954+186043 | 104444 | Stefano Morozzi | 11/2024 |
7298 | 2^346949+140865 | 104443 | Stefano Morozzi | 11/2024 |
7299 | 2^346950+79857 | 104443 | Stefano Morozzi | 11/2024 |
7300 | 2^346951+161939 | 104443 | Stefano Morozzi | 11/2024 |
7301 | 2^346950+143647 | 104443 | Stefano Morozzi | 11/2024 |
7302 | 2^346950+103369 | 104443 | Stefano Morozzi | 11/2024 |
7303 | 2^346952+128895 | 104443 | Stefano Morozzi | 11/2024 |
7304 | 2^346946+106593 | 104442 | Stefano Morozzi | 11/2024 |
7305 | 2^346947+63431 | 104442 | Stefano Morozzi | 11/2024 |
7306 | 2^346947+75735 | 104442 | Stefano Morozzi | 11/2024 |
7307 | 2^346948+135547 | 104442 | Stefano Morozzi | 11/2024 |
7308 | 2^346944+20295 | 104441 | Stefano Morozzi | 11/2024 |
7309 | 2^346944+93783 | 104441 | Stefano Morozzi | 11/2024 |
7310 | 2^346939+116879 | 104440 | Stefano Morozzi | 11/2024 |
7311 | 2^346939+138489 | 104440 | Stefano Morozzi | 11/2024 |
7312 | 2^346940+40675 | 104440 | Stefano Morozzi | 11/2024 |
7313 | 2^346942+108495 | 104440 | Stefano Morozzi | 11/2024 |
7314 | 2^346942+137535 | 104440 | Stefano Morozzi | 11/2024 |
7315 | 2^346936+78235 | 104439 | Stefano Morozzi | 11/2024 |
7316 | 2^346936+156271 | 104439 | Stefano Morozzi | 11/2024 |
7317 | 2^346937+180909 | 104439 | Stefano Morozzi | 11/2024 |
7318 | 2^346938+159885 | 104439 | Stefano Morozzi | 11/2024 |
7319 | 2^346933+7865 | 104438 | Stefano Morozzi | 11/2024 |
7320 | 2^346933+119759 | 104438 | Stefano Morozzi | 11/2024 |
7321 | 2^346934+187797 | 104438 | Stefano Morozzi | 11/2024 |
7322 | 2^346935+198629 | 104438 | Stefano Morozzi | 11/2024 |
7323 | 2^346929+85449 | 104437 | Stefano Morozzi | 11/2024 |
7324 | 2^346929+155487 | 104437 | Stefano Morozzi | 11/2024 |
7325 | 2^346931+60719 | 104437 | Stefano Morozzi | 11/2024 |
7326 | 2^346932+49215 | 104437 | Stefano Morozzi | 11/2024 |
7327 | 2^346927+65709 | 104436 | Stefano Morozzi | 11/2024 |
7328 | 2^346928+126963 | 104436 | Stefano Morozzi | 11/2024 |
7329 | 2^346928+143721 | 104436 | Stefano Morozzi | 11/2024 |
7334 | 2^346923-19585 | 104435 | Enzo Doria | 05/2013 |
7330 | 2^346923+73001 | 104435 | Stefano Morozzi | 11/2024 |
7331 | 2^346924+28671 | 104435 | Stefano Morozzi | 11/2024 |
7332 | 2^346924+58657 | 104435 | Stefano Morozzi | 11/2024 |
7333 | 2^346924+173475 | 104435 | Stefano Morozzi | 11/2024 |
7335 | 2^346921+59357 | 104434 | Stefano Morozzi | 11/2024 |
7336 | 2^346916+18183 | 104433 | Stefano Morozzi | 11/2024 |
7337 | 2^346914+44625 | 104432 | Stefano Morozzi | 11/2024 |
7338 | 2^346912+26343 | 104431 | Stefano Morozzi | 11/2024 |
7339 | 2^346912+42367 | 104431 | Stefano Morozzi | 11/2024 |
7340 | 2^346908+123705 | 104430 | Stefano Morozzi | 11/2024 |
7341 | 2^346899+194015 | 104428 | Stefano Morozzi | 11/2024 |
7342 | 2^346900+63393 | 104428 | Stefano Morozzi | 11/2024 |
7343 | 2^346901+106215 | 104428 | Stefano Morozzi | 11/2024 |
7344 | 2^346901+119309 | 104428 | Stefano Morozzi | 11/2024 |
7345 | 2^346902+62587 | 104428 | Stefano Morozzi | 11/2024 |
7346 | 2^346897+120207 | 104427 | Stefano Morozzi | 11/2024 |
7347 | 2^346897+121107 | 104427 | Stefano Morozzi | 11/2024 |
7348 | 2^346897+134289 | 104427 | Stefano Morozzi | 11/2024 |
7349 | 2^346898+57429 | 104427 | Stefano Morozzi | 11/2024 |
7350 | 2^346898+162267 | 104427 | Stefano Morozzi | 11/2024 |
7351 | 2^346890+148989 | 104425 | Stefano Morozzi | 11/2024 |
7352 | 2^346891+46313 | 104425 | Stefano Morozzi | 11/2024 |
7353 | 2^346892+121191 | 104425 | Stefano Morozzi | 11/2024 |
7354 | 2^346888+39211 | 104424 | Stefano Morozzi | 11/2024 |
7355 | 2^346883+100949 | 104423 | Stefano Morozzi | 11/2024 |
7356 | 2^346883+138341 | 104423 | Stefano Morozzi | 11/2024 |
7357 | 2^346885+78357 | 104423 | Stefano Morozzi | 11/2024 |
7358 | 2^346882+167169 | 104422 | Stefano Morozzi | 11/2024 |
7359 | 2^346877+43587 | 104421 | Stefano Morozzi | 11/2024 |
7360 | 2^346879+69983 | 104421 | Stefano Morozzi | 11/2024 |
7361 | 2^346875+24885 | 104420 | Stefano Morozzi | 11/2024 |
7362 | 2^346875+131835 | 104420 | Stefano Morozzi | 11/2024 |
7363 | 2^346875+161301 | 104420 | Stefano Morozzi | 11/2024 |
7364 | 2^346871+85491 | 104419 | Stefano Morozzi | 11/2024 |
7365 | 2^346866+135849 | 104418 | Stefano Morozzi | 11/2024 |
7366 | 2^346868+445 | 104418 | Stefano Morozzi | 11/2024 |
7367 | 2^346868+111637 | 104418 | Stefano Morozzi | 11/2024 |
7368 | 2^346864+104917 | 104417 | Stefano Morozzi | 11/2024 |
7370 | (11*2^346864-1)/175 | 104416 | Lelio R Paula | 03/2014 |
7369 | 2^346862+60109 | 104416 | Stefano Morozzi | 11/2024 |
7371 | 2^346857+43607 | 104415 | Stefano Morozzi | 11/2024 |
7372 | 2^346857+142719 | 104415 | Stefano Morozzi | 11/2024 |
7376 | 2^346854+346854^2+1 | 104414 | Robert Price | 06/2014 |
7373 | 2^346853+29051 | 104414 | Stefano Morozzi | 11/2024 |
7374 | 2^346855+3549 | 104414 | Stefano Morozzi | 11/2024 |
7375 | 2^346855+194849 | 104414 | Stefano Morozzi | 11/2024 |
7377 | 2^346850+34423 | 104413 | Stefano Morozzi | 11/2024 |
7378 | 2^346851+95235 | 104413 | Stefano Morozzi | 11/2024 |
7379 | 2^346846+99883 | 104412 | Stefano Morozzi | 11/2024 |
7380 | 2^346846+146089 | 104412 | Stefano Morozzi | 11/2024 |
7381 | 2^346848+14577 | 104412 | Stefano Morozzi | 11/2024 |
7382 | 2^346848+38901 | 104412 | Stefano Morozzi | 11/2024 |
7383 | 2^346849+94107 | 104412 | Stefano Morozzi | 11/2024 |
7384 | 2^346843+112473 | 104411 | Stefano Morozzi | 11/2024 |
7385 | 2^346845+186035 | 104411 | Stefano Morozzi | 11/2024 |
7386 | 2^346841+146711 | 104410 | Stefano Morozzi | 11/2024 |
7387 | 2^346839+59931 | 104409 | Stefano Morozzi | 11/2024 |
7388 | 2^346834+11715 | 104408 | Lelio R Paula | 04/2015 |
7389 | 2^346830+73129 | 104407 | Stefano Morozzi | 11/2024 |
7390 | 2^346832+168607 | 104407 | Stefano Morozzi | 11/2024 |
7391 | 2^346832+179253 | 104407 | Stefano Morozzi | 11/2024 |
7392 | 2^346826+73969 | 104406 | Stefano Morozzi | 11/2024 |
7393 | 2^346827+122901 | 104406 | Stefano Morozzi | 11/2024 |
7394 | 2^346823+36191 | 104405 | Stefano Morozzi | 11/2024 |
7395 | 2^346823+185955 | 104405 | Stefano Morozzi | 11/2024 |
7396 | 2^346825+3297 | 104405 | Stefano Morozzi | 11/2024 |
7397 | 2^346822+74757 | 104404 | Stefano Morozzi | 11/2024 |
7398 | 2^346822+160495 | 104404 | Stefano Morozzi | 11/2024 |
7399 | 2^346816+146085 | 104403 | Stefano Morozzi | 11/2024 |
7400 | 2^346816+158707 | 104403 | Stefano Morozzi | 11/2024 |
7401 | 2^346818+26689 | 104403 | Stefano Morozzi | 11/2024 |
7402 | 2^346818+69805 | 104403 | Stefano Morozzi | 11/2024 |
7403 | 2^346818+83899 | 104403 | Stefano Morozzi | 11/2024 |
7404 | 2^346818+110299 | 104403 | Stefano Morozzi | 11/2024 |
7405 | 2^346818+182793 | 104403 | Stefano Morozzi | 11/2024 |
7406 | 2^346819+95351 | 104403 | Stefano Morozzi | 11/2024 |
7407 | 2^346814+136243 | 104402 | Stefano Morozzi | 11/2024 |
7408 | 2^346814+188649 | 104402 | Stefano Morozzi | 11/2024 |
7409 | 2^346810+106309 | 104401 | Stefano Morozzi | 11/2024 |
7410 | 2^346807+86769 | 104400 | Stefano Morozzi | 11/2024 |
7411 | 2^346808+114975 | 104400 | Stefano Morozzi | 11/2024 |
7412 | 2^346809+61035 | 104400 | Stefano Morozzi | 11/2024 |
7413 | 2^346803+10845 | 104399 | Stefano Morozzi | 11/2024 |
7414 | 2^346803+110705 | 104399 | Stefano Morozzi | 11/2024 |
7415 | 2^346804+134761 | 104399 | Stefano Morozzi | 11/2024 |
7416 | 2^346800+137791 | 104398 | Stefano Morozzi | 11/2024 |
7417 | 2^346797+109589 | 104397 | Stefano Morozzi | 11/2024 |
7418 | 2^346798+91909 | 104397 | Stefano Morozzi | 11/2024 |
7419 | 2^346798+163029 | 104397 | Stefano Morozzi | 11/2024 |
7420 | 2^346793+62669 | 104396 | Stefano Morozzi | 11/2024 |
7421 | 2^346793+189081 | 104396 | Stefano Morozzi | 11/2024 |
7422 | 2^346794+109095 | 104396 | Stefano Morozzi | 11/2024 |
7423 | 2^346796+57285 | 104396 | Stefano Morozzi | 11/2024 |
7424 | 2^346791+184833 | 104395 | Stefano Morozzi | 11/2024 |
7425 | 2^346787+81005 | 104394 | Stefano Morozzi | 11/2024 |
7426 | 2^346787+81605 | 104394 | Stefano Morozzi | 11/2024 |
7427 | 2^346789+2015 | 104394 | Stefano Morozzi | 11/2024 |
7428 | 2^346789+19595 | 104394 | Stefano Morozzi | 11/2024 |
7429 | 2^346784+84771 | 104393 | Stefano Morozzi | 11/2024 |
7430 | 2^346784+124243 | 104393 | Stefano Morozzi | 11/2024 |
7431 | 2^346784+143707 | 104393 | Stefano Morozzi | 11/2024 |
7432 | 2^346786+66117 | 104393 | Stefano Morozzi | 11/2024 |
7433 | 2^346786+194725 | 104393 | Stefano Morozzi | 11/2024 |
7437 | 24276^19961+19961^24276 | 104392 | Hans Havermann | 09/2020 |
7434 | 2^346780+81517 | 104392 | Stefano Morozzi | 11/2024 |
7435 | 2^346780+121341 | 104392 | Stefano Morozzi | 11/2024 |
7436 | 2^346780+171943 | 104392 | Stefano Morozzi | 11/2024 |
7438 | 2^346777+28991 | 104391 | Stefano Morozzi | 11/2024 |
7439 | 2^346777+110021 | 104391 | Stefano Morozzi | 11/2024 |
7440 | 2^346778+53769 | 104391 | Stefano Morozzi | 11/2024 |
7441 | 2^346779+134115 | 104391 | Stefano Morozzi | 11/2024 |
7442 | 2^346779+172961 | 104391 | Stefano Morozzi | 11/2024 |
7443 | 2^346773+81797 | 104390 | Stefano Morozzi | 11/2024 |
7444 | 2^346774+164119 | 104390 | Stefano Morozzi | 11/2024 |
7445 | 2^346775+72063 | 104390 | Stefano Morozzi | 11/2024 |
7446 | 2^346775+197315 | 104390 | Stefano Morozzi | 11/2024 |
7447 | 2^346776+32233 | 104390 | Stefano Morozzi | 11/2024 |
7448 | 2^346776+187777 | 104390 | Stefano Morozzi | 11/2024 |
7449 | 2^346770+98719 | 104389 | Stefano Morozzi | 11/2024 |
7450 | 2^346770+110437 | 104389 | Stefano Morozzi | 11/2024 |
7451 | 2^346771+1205 | 104389 | Stefano Morozzi | 11/2024 |
7452 | 2^346771+3465 | 104389 | Stefano Morozzi | 11/2024 |
7453 | 2^346771+129543 | 104389 | Stefano Morozzi | 11/2024 |
7454 | 2^346772+41143 | 104389 | Stefano Morozzi | 11/2024 |
7455 | 2^346772+69865 | 104389 | Stefano Morozzi | 11/2024 |
7456 | 2^346767+168441 | 104388 | Stefano Morozzi | 11/2024 |
7457 | 2^346768+37897 | 104388 | Stefano Morozzi | 11/2024 |
7458 | 2^346768+80977 | 104388 | Stefano Morozzi | 11/2024 |
7459 | 2^346769+158745 | 104388 | Stefano Morozzi | 11/2024 |
7465 | 79^55009+78 | 104387 | Norbert Schneider | 02/2015 |
7460 | 2^346763+14723 | 104387 | Stefano Morozzi | 11/2024 |
7461 | 2^346763+90743 | 104387 | Stefano Morozzi | 11/2024 |
7462 | 2^346764+95503 | 104387 | Stefano Morozzi | 11/2024 |
7463 | 2^346766+31645 | 104387 | Stefano Morozzi | 11/2024 |
7464 | 2^346766+51115 | 104387 | Stefano Morozzi | 11/2024 |
7466 | 2^346760+90225 | 104386 | Stefano Morozzi | 11/2024 |
7467 | 2^346762+31825 | 104386 | Stefano Morozzi | 11/2024 |
7468 | 2^346762+192817 | 104386 | Stefano Morozzi | 11/2024 |
7469 | 2^346757+97691 | 104385 | Stefano Morozzi | 11/2024 |
7470 | 2^346758+111415 | 104385 | Stefano Morozzi | 11/2024 |
7471 | 2^346759+86331 | 104385 | Stefano Morozzi | 11/2024 |
7472 | 2^346755+22085 | 104384 | Stefano Morozzi | 11/2024 |
7473 | 2^346750+140967 | 104383 | Stefano Morozzi | 11/2024 |
7474 | 2^346751+48515 | 104383 | Stefano Morozzi | 11/2024 |
7475 | 2^346751+74481 | 104383 | Stefano Morozzi | 11/2024 |
7476 | 2^346752+103497 | 104383 | Stefano Morozzi | 11/2024 |
7477 | 2^346747+4589 | 104382 | Stefano Morozzi | 11/2024 |
7478 | 2^346747+29969 | 104382 | Stefano Morozzi | 11/2024 |
7479 | 2^346747+130973 | 104382 | Stefano Morozzi | 11/2024 |
7480 | 2^346748+184387 | 104382 | Stefano Morozzi | 11/2024 |
7481 | 2^346743+39545 | 104381 | Stefano Morozzi | 11/2024 |
7482 | 2^346743+61335 | 104381 | Stefano Morozzi | 11/2024 |
7483 | 2^346746+99025 | 104381 | Stefano Morozzi | 11/2024 |
7484 | 2^346737+39431 | 104379 | Stefano Morozzi | 11/2024 |
7485 | 2^346733+96437 | 104378 | Stefano Morozzi | 11/2024 |
7486 | 2^346736+83025 | 104378 | Stefano Morozzi | 11/2024 |
7487 | 2^346736+196405 | 104378 | Stefano Morozzi | 11/2024 |
7488 | 2^346732+72685 | 104377 | Stefano Morozzi | 11/2024 |
7489 | 2^346727+86903 | 104376 | Stefano Morozzi | 11/2024 |
7490 | 2^346727+89829 | 104376 | Stefano Morozzi | 11/2024 |
7491 | 2^346729+199319 | 104376 | Stefano Morozzi | 11/2024 |
7492 | 2^346723+73521 | 104375 | Stefano Morozzi | 11/2024 |
7493 | 2^346724+91177 | 104375 | Stefano Morozzi | 11/2024 |
7494 | 2^346726+191527 | 104375 | Stefano Morozzi | 11/2024 |
7495 | 2^346720+235 | 104374 | Stefano Morozzi | 11/2024 |
7496 | 2^346720+189435 | 104374 | Stefano Morozzi | 11/2024 |
7497 | 2^346718+124833 | 104373 | Stefano Morozzi | 11/2024 |
7498 | 2^346718+127029 | 104373 | Stefano Morozzi | 11/2024 |
7499 | 2^346719+129291 | 104373 | Stefano Morozzi | 11/2024 |
7500 | 2^346719+183033 | 104373 | Stefano Morozzi | 11/2024 |