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
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See the Latest PRPs
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Rank |
Probable prime |
Digits (> 50000) |
Who ? |
When ? |
8355 | 25206!+p(4114) | 100001 | Henri Lifchitz | 09/2005 |
8356 | 25206!-p(5447) | 100001 | Henri Lifchitz | 10/2005 |
8357 | 25206!-p(12402) | 100001 | Henri Lifchitz | 04/2006 |
8358 | 25206!-p(16290) | 100001 | Henri Lifchitz | 09/2006 |
8359 | 25206!-p(19647) | 100001 | Henri Lifchitz | 02/2007 |
8360 | 2^332194+11473 | 100001 | Henri Lifchitz | 03/2007 |
8350 | 10^100000+342909 | 100001 | Milton L. Brown | 12/2007 |
8351 | 10^100000+346579 | 100001 | Robert Price | 04/2012 |
8352 | 10^100000+829767 | 100001 | Robert Price | 05/2012 |
8353 | 10^100000+871899 | 100001 | Robert Price | 05/2012 |
8354 | 10^100000+1475997 | 100001 | Robert Price | 07/2012 |
8343 | 10^100000+1751769 | 100001 | Robert Price | 08/2012 |
8344 | 10^100000+2155489 | 100001 | Robert Price | 10/2012 |
8345 | 10^100000+2483527 | 100001 | Robert Price | 12/2012 |
8346 | 10^100000+2503087 | 100001 | Robert Price | 12/2012 |
8347 | 10^100000+2686179 | 100001 | Robert Price | 12/2012 |
8348 | 10^100000+2688933 | 100001 | Robert Price | 12/2012 |
8349 | 10^100000+3667159 | 100001 | Robert Price | 08/2013 |
8323 | 10^100000+15136771 | 100001 | Robert Price | 09/2019 |
8324 | 10^100000+15219873 | 100001 | Robert Price | 10/2019 |
8325 | 10^100000+15274039 | 100001 | Robert Price | 10/2019 |
8326 | 10^100000+15394069 | 100001 | Robert Price | 10/2019 |
8327 | 10^100000+15547119 | 100001 | Robert Price | 10/2019 |
8328 | 10^100000+15932923 | 100001 | Robert Price | 11/2019 |
8329 | 10^100000+16345467 | 100001 | Robert Price | 12/2019 |
8330 | 10^100000+16672143 | 100001 | Robert Price | 01/2020 |
8331 | 10^100000+16731939 | 100001 | Robert Price | 02/2020 |
8332 | 10^100000+16907049 | 100001 | Robert Price | 03/2020 |
8333 | 10^100000+17652523 | 100001 | Robert Price | 05/2020 |
8334 | 10^100000+18047167 | 100001 | Robert Price | 05/2020 |
8335 | 10^100000+18471819 | 100001 | Robert Price | 06/2020 |
8336 | 10^100000+18494793 | 100001 | Robert Price | 07/2020 |
8337 | 10^100000+18762609 | 100001 | Robert Price | 07/2020 |
8338 | 10^100000+19204141 | 100001 | Robert Price | 08/2020 |
8339 | 10^100000+19349793 | 100001 | Robert Price | 08/2020 |
8340 | 10^100000+19495699 | 100001 | Robert Price | 09/2020 |
8341 | 10^100000+19668927 | 100001 | Robert Price | 09/2020 |
8342 | 10^100000+19704313 | 100001 | Robert Price | 09/2020 |
8292 | 10^100000+19956229 | 100001 | Robert Price | 09/2020 |
8293 | 10^100000+3*(10^37093-1)/9*10^31454+1 | 100001 | Makoto Morimoto | 09/2020 |
8294 | 10^100000+4*(10^36149-1)/9*10^31926+1 | 100001 | Makoto Morimoto | 09/2020 |
8295 | 10^100000+6*(10^41029-1)/9*10^29486+1 | 100001 | Makoto Morimoto | 09/2020 |
8296 | 10^100000+7*(10^55505-1)/9*10^22248+1 | 100001 | Makoto Morimoto | 09/2020 |
8297 | 10^100000+20234607 | 100001 | Robert Price | 10/2020 |
8298 | 10^100000+20752303 | 100001 | Robert Price | 11/2020 |
8299 | 10^100000+20774041 | 100001 | Robert Price | 11/2020 |
8300 | 10^100000+20854741 | 100001 | Robert Price | 11/2020 |
8301 | 10^100000+20908917 | 100001 | Robert Price | 11/2020 |
8302 | 10^100000+20994793 | 100001 | Robert Price | 11/2020 |
8303 | 10^100000+21354249 | 100001 | Robert Price | 12/2020 |
8304 | 10^100000+21455559 | 100001 | Robert Price | 12/2020 |
8305 | 10^100000+21538873 | 100001 | Robert Price | 12/2020 |
8306 | 10^100000+21830901 | 100001 | Robert Price | 01/2021 |
8307 | 10^100000+21842629 | 100001 | Robert Price | 01/2021 |
8308 | 10^100000+21930861 | 100001 | Robert Price | 01/2021 |
8309 | 10^100000+22092943 | 100001 | Robert Price | 03/2021 |
8310 | 10^100000+22278417 | 100001 | Robert Price | 03/2021 |
8311 | 10^100000+22388581 | 100001 | Robert Price | 03/2021 |
8312 | 10^100000+22390933 | 100001 | Robert Price | 03/2021 |
8313 | 10^100000+22436169 | 100001 | Robert Price | 03/2021 |
8314 | 10^100000+22714557 | 100001 | Robert Price | 04/2021 |
8315 | 10^100000+22847671 | 100001 | Robert Price | 04/2021 |
8316 | 10^100000+23178567 | 100001 | Robert Price | 05/2021 |
8317 | 10^100000+23332003 | 100001 | Robert Price | 05/2021 |
8318 | 10^100000+23414571 | 100001 | Robert Price | 05/2021 |
8319 | 10^100000+23529979 | 100001 | Robert Price | 05/2021 |
8320 | 10^100000+23749243 | 100001 | Robert Price | 06/2021 |
8321 | 10^100000+23821771 | 100001 | Robert Price | 06/2021 |
8322 | 10^100000+24179307 | 100001 | Robert Price | 07/2021 |
8251 | 10^100000+30762711 | 100001 | Robert Price | 07/2022 |
8252 | 10^100000+30862057 | 100001 | Robert Price | 07/2022 |
8253 | 10^100000+30998953 | 100001 | Robert Price | 07/2022 |
8254 | 10^100000+31405203 | 100001 | Robert Price | 07/2022 |
8255 | 10^100000+40159119 | 100001 | Robert Price | 07/2022 |
8256 | 10^100000+40181863 | 100001 | Robert Price | 07/2022 |
8257 | 10^100000+40277131 | 100001 | Robert Price | 07/2022 |
8258 | 10^100000+40326061 | 100001 | Robert Price | 07/2022 |
8259 | 10^100000+40417411 | 100001 | Robert Price | 07/2022 |
8260 | 10^100000+50049909 | 100001 | Robert Price | 07/2022 |
8261 | 10^100000+50510163 | 100001 | Robert Price | 07/2022 |
8262 | 10^100000+50591583 | 100001 | Robert Price | 07/2022 |
8263 | 10^100000+50850357 | 100001 | Robert Price | 07/2022 |
8264 | 10^100000+50974641 | 100001 | Robert Price | 07/2022 |
8265 | 10^100000+51046671 | 100001 | Robert Price | 07/2022 |
8266 | 10^100000+51459657 | 100001 | Robert Price | 07/2022 |
8267 | 10^100000+70081471 | 100001 | Robert Price | 07/2022 |
8268 | 10^100000+70159557 | 100001 | Robert Price | 07/2022 |
8269 | 10^100000+70262479 | 100001 | Robert Price | 07/2022 |
8270 | 10^100000+70417521 | 100001 | Robert Price | 07/2022 |
8271 | 10^100000+70476531 | 100001 | Robert Price | 07/2022 |
8272 | 10^100000+70534627 | 100001 | Robert Price | 07/2022 |
8273 | 10^100000+70873077 | 100001 | Robert Price | 07/2022 |
8274 | 10^100000+71114643 | 100001 | Robert Price | 07/2022 |
8275 | 10^100000+71272539 | 100001 | Robert Price | 07/2022 |
8276 | 10^100000+80025337 | 100001 | Robert Price | 07/2022 |
8277 | 10^100000+71580817 | 100001 | Robert Price | 07/2022 |
8278 | 10^100000+80270349 | 100001 | Robert Price | 07/2022 |
8279 | 10^100000+29831551 | 100001 | Robert Price | 07/2022 |
8280 | 10^100000+29955417 | 100001 | Robert Price | 08/2022 |
8281 | 479072067*10^99992+1+2*1779 | 100001 | Matt Stath | 12/2022 |
8282 | 10^100000+90000000+851439 | 100001 | Robert Price | 04/2023 |
8283 | 10^100000+90000000+1088017 | 100001 | Robert Price | 04/2023 |
8284 | 10^100000+90000000+1288173 | 100001 | Robert Price | 04/2023 |
8285 | 10^100000+90000000+1324549 | 100001 | Robert Price | 04/2023 |
8286 | 10^100000+90000000+3643869 | 100001 | Robert Price | 04/2023 |
8287 | 10^100000+110000000+60221 | 100001 | Robert Price | 04/2023 |
8288 | 10^100000+110000000+373261 | 100001 | Robert Price | 04/2023 |
8289 | 10^100000+110000000+497513 | 100001 | Robert Price | 04/2023 |
8290 | 10^100000+120000000+33823 | 100001 | Robert Price | 04/2023 |
8291 | 10^100000+120000000+419053 | 100001 | Robert Price | 04/2023 |
8361 | 10^99999+309403 | 100000 | Daniel Heuer | 01/2004 |
8362 | 10^100000-260199 | 100000 | Patrick De Geest | 01/2010 |
8363 | 2^332192+10192681 | 100000 | Sujan Das | 06/2022 |
8364 | 1610172603059^8192+1610172602878^8192 | 100000 | Youcef Lemsafer | 01/2023 |
8366 | 10^99999-59511 | 99999 | Patrick De Geest | 07/2009 |
8365 | 10^99998+235437 | 99999 | Patrick De Geest | 02/2020 |
8367 | 10^99998-286587 | 99998 | Patrick De Geest | 02/2020 |
8368 | 10^99997+72297 | 99998 | Patrick De Geest | 02/2020 |
8369 | 10^99997-402627 | 99997 | Patrick De Geest | 02/2020 |
8370 | 10^99996+279853 | 99997 | Patrick De Geest | 02/2020 |
8371 | 10^99997-500000001 | 99997 | Robert Price | 12/2020 |
8372 | 10^99996-94961 | 99996 | Patrick De Geest | 02/2020 |
8373 | 10^99995+54633 | 99996 | Patrick De Geest | 02/2020 |
8374 | 10^99995-101429 | 99995 | Patrick De Geest | 02/2020 |
8375 | 10^99994+117271 | 99995 | Patrick De Geest | 02/2020 |
8376 | 10^99994-452289 | 99994 | Patrick De Geest | 02/2020 |
8377 | 10^99993+371311 | 99994 | Patrick De Geest | 02/2020 |
8378 | 10^99993-186491 | 99993 | Patrick De Geest | 02/2020 |
8379 | 10^99992+17431 | 99993 | Patrick De Geest | 02/2020 |
8380 | 10^99992-28607 | 99992 | Patrick De Geest | 02/2020 |
8381 | 10^99991+125391 | 99992 | Patrick De Geest | 02/2020 |
8382 | 10^99991-204573 | 99991 | Patrick De Geest | 02/2020 |
8383 | 10^99990+13899 | 99991 | Patrick De Geest | 02/2020 |
8384 | 10^99990-8111 | 99990 | Patrick De Geest | 02/2020 |
8385 | 2^332141-113073 | 99985 | Enzo Doria | 07/2014 |
8386 | (1610172603037^8192+1610172602919^8192)/17110948127473666 | 99983 | Youcef Lemsafer | 01/2023 |
8387 | 6*10^99979-79 | 99980 | Robert Price | 03/2022 |
8389 | (3^209561+2)/728101255 | 99978 | Lelio R Paula | 09/2013 |
8388 | 23827^15702+15702^23827 | 99978 | Hans Havermann | 04/2018 |
8390 | 2^332085+1865897 | 99968 | Enzo Doria | 03/2016 |
8391 | (9787*2^332070-1)/936402369 | 99959 | Lelio R Paula | 05/2015 |
8392 | 2^332023+191 | 99949 | Lelio R Paula | 02/2011 |
8393 | (6271^26321-1)/6270 | 99946 | Serge Batalov | 06/2022 |
8394 | 7*10^99944+27 | 99945 | Robert Price | 11/2020 |
8395 | 2^331938+71149 | 99924 | Enzo Doria | 04/2016 |
8396 | 2^331932-78795 | 99922 | Lelio R Paula | 09/2016 |
8397 | 2^331921+771 | 99919 | Lelio R Paula | 01/2013 |
8398 | (3^209419-2)/5132755 | 99912 | Lelio R Paula | 09/2013 |
8399 | 2^331860-114989 | 99900 | Enzo Doria | 05/2015 |
8400 | 2^331746-11655 | 99866 | Lelio R Paula | 09/2016 |
8401 | 11^95891-28 | 99861 | Lelio R Paula | 08/2016 |
8402 | (2^331694-5)/11 | 99849 | Lelio R Paula | 10/2013 |
8403 | (3^209246+7)/64 | 99834 | Lelio R Paula | 09/2013 |
8404 | 25062^9617+9617^25062 | 99823 | Hans Havermann | 04/2018 |
8405 | 15^84866-52 | 99811 | Lelio R Paula | 08/2016 |
8406 | 13^89600+30 | 99810 | Lelio R Paula | 08/2016 |
8407 | 2^331527+100280245065 | 99800 | Paul Bourdelais | 10/2021 |
8408 | 22950^22309+22309^22950 | 99798 | Hans Havermann | 03/2018 |
8409 | 5^142772-38 | 99794 | Lelio R Paula | 08/2016 |
8410 | (7482^25759-1)/7481 | 99787 | Serge Batalov | 06/2022 |
8411 | (23*2^331459+1)/475 | 99778 | Lelio R Paula | 11/2013 |
8412 | 2^331416-331416+1 | 99767 | Robert Price | 10/2014 |
8413 | 2^331256-57 | 99718 | Lelio R Paula | 12/2012 |
8414 | 28192^3443+3443^28192 | 99714 | Hans Havermann | 03/2018 |
8415 | 2^331185+737 | 99697 | Lelio R Paula | 01/2013 |
8416 | (4*10^99693+149)/9 | 99693 | Robert Price | 03/2017 |
8417 | 2^331154+1880527 | 99688 | Enzo Doria | 10/2016 |
8419 | (19^77951+1)/20 | 99679 | Paul Bourdelais | 03/2010 |
8418 | 24354^12385+12385^24354 | 99679 | Hans Havermann | 03/2018 |
8420 | 2^331110+1870459 | 99675 | Enzo Doria | 05/2016 |
8421 | 5*2^331075+7 | 99665 | Lelio R Paula | 08/2014 |
8422 | 25776^7351+7351^25776 | 99659 | Hans Havermann | 02/2018 |
8423 | (16*10^99656-31)/3 | 99657 | Robert Price | 03/2016 |
8424 | (6059^26347-1)/6058 | 99652 | Serge Batalov | 06/2022 |
8425 | (15544^23773-1)/15543 | 99642 | Serge Batalov | 06/2022 |
8427 | 2^330968+345 | 99632 | Lelio R Paula | 09/2016 |
8426 | (2^330969+690)/2 | 99632 | Stefano Morozzi | 09/2020 |
8429 | 2*5^142528-7 | 99624 | Lelio R Paula | 11/2014 |
8428 | 2^330942+77329 | 99624 | Enzo Doria | 05/2016 |
8430 | 14^86914-99 | 99615 | Lelio R Paula | 08/2016 |
8431 | (19*2^330902+1)/77 | 99611 | Lelio R Paula | 11/2013 |
8432 | 22971^21692+21692^22971 | 99610 | Hans Havermann | 03/2018 |
8433 | 2^330845+71687 | 99595 | Enzo Doria | 04/2016 |
8434 | (26667^22501-1)/26666 | 99585 | Serge Batalov | 06/2022 |
8435 | (23*2^330770+1)/3 | 99573 | Lelio R Paula | 11/2013 |
8436 | 24494^11613+11613^24494 | 99567 | Hans Havermann | 03/2018 |
8437 | 2^330735+8415 | 99562 | Lelio R Paula | 09/2016 |
8438 | 2^330720+74071 | 99557 | Enzo Doria | 04/2016 |
8439 | (10405^24781-1)/10404 | 99548 | Serge Batalov | 06/2022 |
8441 | 31^66738-2 | 99531 | Lelio R Paula | 09/2013 |
8440 | (9002^25171-1)/9001 | 99531 | Serge Batalov | 06/2022 |
8442 | (5023^26893-1)/5022 | 99527 | Serge Batalov | 06/2022 |
8443 | 7*3^208567+4 | 99513 | Lelio R Paula | 08/2014 |
8444 | (15881^23689-1)/15880 | 99511 | Serge Batalov | 06/2022 |
8445 | (13*10^99508+47)/3 | 99509 | Robert Price | 01/2017 |
8446 | 2^330553+779 | 99507 | Lelio R Paula | 01/2013 |
8447 | 15^84606-94 | 99505 | Lelio R Paula | 08/2016 |
8448 | (10^99497+173)/3 | 99497 | Robert Price | 05/2021 |
8449 | 9*10^99493-43 | 99494 | Robert Price | 09/2021 |
8450 | 6^127858+47 | 99493 | Lelio R Paula | 08/2016 |
8451 | 5^142337+48 | 99490 | Lelio R Paula | 08/2016 |
8452 | 7^117724-20 | 99489 | Lelio R Paula | 08/2016 |
8453 | (559^36209-1)/558 | 99479 | Serge Batalov | 06/2022 |
8454 | (13470^24091-1)/13469 | 99477 | Serge Batalov | 06/2022 |
8455 | (29*10^99474-17)/3 | 99475 | Erik Branger | 09/2014 |
8456 | (185*10^99466-11)/3 | 99468 | Robert Price | 10/2020 |
8457 | (2^330410+2038)/2 | 99464 | Stefano Morozzi | 09/2020 |
8458 | (9*2^330407-1)/7 | 99463 | Lelio R Paula | 03/2014 |
8459 | (516*32^66077-175)/31 | 99458 | Eric Chen | 04/2023 |
8460 | (2863^28771-1)/2862 | 99453 | Serge Batalov | 06/2022 |
8461 | (2^330373+2114)/2 | 99452 | Stefano Morozzi | 09/2020 |
8462 | (68*10^99441+7)/3 | 99443 | Robert Price | 03/2016 |
8463 | 10^99434+155571 | 99435 | Patrick De Geest | 04/2020 |
8464 | 10^99434-123456789 | 99434 | Robert Price | 02/2020 |
8465 | 10^99434-191237 | 99434 | Patrick De Geest | 04/2020 |
8466 | 46^59791-45^59791 | 99418 | Jean-Louis Charton | 01/2013 |
8467 | 23839^14802+14802^23839 | 99417 | Hans Havermann | 02/2018 |
8468 | (2*10^99408+529)/9 | 99408 | Robert Price | 01/2017 |
8469 | (2^330216+3510)/2 | 99405 | Stefano Morozzi | 09/2020 |
8470 | 53^57646-2 | 99398 | Lelio R Paula | 09/2013 |
8471 | 2^330165+1870025 | 99390 | Enzo Doria | 05/2016 |
8472 | 7*10^99383+97 | 99384 | Robert Price | 09/2021 |
8473 | 2^330142-155 | 99383 | Lelio R Paula | 12/2012 |
8474 | 2^330088-115259 | 99367 | Enzo Doria | 06/2015 |
8475 | 24216^12671+12671^24216 | 99354 | Hans Havermann | 01/2018 |
8476 | Phi(200548,10)/3208769 | 99354 | Makoto Kamada | 04/2019 |
8477 | (746*10^99303+1)/9 | 99305 | Robert Price | 02/2017 |
8478 | 3^208107+40 | 99293 | Lelio R Paula | 08/2016 |
8479 | (3939^27617-1)/3938 | 99291 | Serge Batalov | 06/2022 |
8480 | (5*2^329833-1)/369 | 99288 | Lelio R Paula | 02/2014 |
8481 | 8*3^208093+5 | 99287 | Lelio R Paula | 08/2014 |
8482 | 5^142043+56 | 99284 | Lelio R Paula | 08/2016 |
8483 | (13*10^99282-157)/9 | 99283 | Robert Price | 05/2021 |
8484 | (10^99284+7)/53/67 | 99281 | Alfred Reich | 06/2021 |
8485 | 22*10^99275+7 | 99277 | Robert Price | 04/2016 |
8486 | 2^329778+1876189 | 99274 | Enzo Doria | 07/2016 |
8487 | (6580^25997-1)/6579 | 99259 | Serge Batalov | 06/2022 |
8488 | (2249^29611-1)/2248 | 99253 | Serge Batalov | 06/2022 |
8489 | (10^99239-13)/3 | 99239 | Robert Price | 02/2017 |
8490 | (1199^32233-1)/1198 | 99237 | Serge Batalov | 06/2022 |
8492 | 3^207987+62 | 99236 | Lelio R Paula | 08/2016 |
8491 | (62*10^99235+91)/9 | 99236 | Robert Price | 07/2021 |
8493 | 2^329638+49 | 99231 | Lelio R Paula | 12/2012 |
8494 | 7^117413-18 | 99226 | Lelio R Paula | 08/2016 |
8495 | 2^329586-458903 | 99216 | Enzo Doria | 04/2015 |
8496 | (6290^26119-1)/6289 | 99214 | Serge Batalov | 06/2022 |
8498 | 2^329553+101 | 99206 | Lelio R Paula | 12/2012 |
8497 | (21297^22921-1)/21296 | 99206 | Serge Batalov | 06/2022 |
8499 | 2^329551-112897 | 99205 | Enzo Doria | 06/2014 |
8500 | (3^207925+7)/50 | 99204 | Lelio R Paula | 09/2013 |