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 | 19^80560-68 | 103017 | Lelio R Paula | 10/2016 |
7252 | 2^342209+76607 | 103016 | Enzo Doria | 05/2016 |
7254 | 328^40945+40945^328 | 103013 | Norbert Schneider | 12/2014 |
7253 | 12^95454-91 | 103013 | Lelio R Paula | 10/2016 |
7255 | 25833^9716+9716^25833 | 103009 | Hans Havermann | 01/2019 |
7256 | (893*10^103004+7)/9 | 103006 | Robert Price | 06/2021 |
7257 | (1475^32503-1)/1474 | 102993 | Serge Batalov | 06/2022 |
7258 | 65^56809-64^56809 | 102990 | Robert Price | 08/2013 |
7259 | 5^147338-6 | 102985 | Lelio R Paula | 11/2014 |
7260 | 2^342084-112739 | 102978 | Enzo Doria | 06/2014 |
7261 | 9*6^132330+7 | 102974 | Lelio R Paula | 11/2014 |
7262 | 2^342034-16737 | 102963 | Enzo Doria | 05/2013 |
7263 | (9787*2^342011-1)/25 | 102959 | Lelio R Paula | 05/2015 |
7264 | (3^215802-5)/124343756 | 102956 | Lelio R Paula | 12/2013 |
7265 | 2^341991-17421 | 102950 | Enzo Doria | 05/2013 |
7266 | 2^341969-112225 | 102943 | Enzo Doria | 06/2014 |
7267 | (9787*2^341864-1)/3 | 102915 | Lelio R Paula | 05/2015 |
7268 | 2^341859+1869413 | 102910 | Enzo Doria | 05/2016 |
7269 | 10^102909+61 | 102910 | Lelio R Paula | 11/2016 |
7270 | 10^102909-67049 | 102909 | Patrick De Geest | 12/2016 |
7271 | 23814^20935+20935^23814 | 102898 | Hans Havermann | 02/2019 |
7272 | 28345^4264+4264^28345 | 102888 | Hans Havermann | 02/2019 |
7273 | 25665^10204+10204^25665 | 102886 | Hans Havermann | 02/2019 |
7274 | 26288^8181+8181^26288 | 102860 | Hans Havermann | 02/2019 |
7275 | 2^341659+1836773 | 102850 | Enzo Doria | 03/2016 |
7276 | 2^341608-110639 | 102835 | Enzo Doria | 05/2014 |
7277 | 10^102824+49 | 102825 | Lelio R Paula | 11/2016 |
7278 | 10^102824-168011 | 102824 | Patrick De Geest | 12/2016 |
7279 | (156^46877-1)/155 | 102805 | Anonymous | 06/2024 |
7280 | 11^98708-8 | 102794 | Lelio R Paula | 10/2016 |
7281 | 2^341466+4429 | 102792 | Lelio R Paula | 09/2011 |
7282 | 2^341460-107 | 102790 | Lelio R Paula | 08/2011 |
7283 | (2^341388+47)/21014943 | 102761 | Lelio R Paula | 12/2013 |
7284 | 2^341355+21 | 102759 | Lelio R Paula | 08/2011 |
7285 | 2^341319+224885 | 102748 | Enzo Doria | 07/2024 |
7286 | (6496^26947-1)/6495 | 102736 | Serge Batalov | 06/2022 |
7287 | 2^341246+40755 | 102726 | Lelio R Paula | 11/2016 |
7288 | (2^341256-5)/991699 | 102723 | Lelio R Paula | 12/2013 |
7289 | 7^121547+78 | 102720 | Lelio R Paula | 10/2016 |
7290 | 2^341223-461197 | 102719 | Enzo Doria | 06/2015 |
7291 | 27838^4893+4893^27838 | 102711 | Hans Havermann | 03/2019 |
7293 | 2^341190-20577 | 102709 | Enzo Doria | 06/2013 |
7292 | (27*2^341212+1)/84674449 | 102709 | Lelio R Paula | 12/2013 |
7294 | (25*10^102698+77)/3 | 102699 | Robert Price | 09/2022 |
7295 | 6^131976-65 | 102698 | Lelio R Paula | 10/2016 |
7296 | 2^341134+2533 | 102692 | Henri Lifchitz | 09/2005 |
7297 | 13^92184-54 | 102688 | Lelio R Paula | 10/2016 |
7298 | 2^341116-20873 | 102687 | Enzo Doria | 06/2013 |
7299 | 2^341094-19953 | 102680 | Enzo Doria | 06/2013 |
7300 | 23761^20950+20950^23761 | 102676 | Hans Havermann | 03/2019 |
7302 | 2^341053+129 | 102668 | Lelio R Paula | 08/2011 |
7301 | (4724^27943-1)/4723 | 102668 | Serge Batalov | 06/2022 |
7304 | (31*2^341006-1)/3 | 102655 | Lelio R Paula | 03/2014 |
7303 | 7^121471+94 | 102655 | Lelio R Paula | 10/2016 |
7306 | 2^341004-173 | 102653 | Lelio R Paula | 08/2011 |
7305 | 20^78901+3 | 102653 | Lelio R Paula | 10/2016 |
7307 | (2^341001+1674)/2 | 102652 | Stefano Morozzi | 09/2020 |
7308 | 5^146853-52 | 102646 | Lelio R Paula | 10/2016 |
7309 | 2^340969-216931 | 102642 | Enzo Doria | 05/2014 |
7310 | 122^49196+121 | 102641 | Norbert Schneider | 10/2018 |
7311 | 2^340952+1870021 | 102637 | Enzo Doria | 05/2016 |
7312 | 5*2^340940-3 | 102634 | Lelio R Paula | 08/2014 |
7313 | (6^131891+1)/7 | 102631 | Paul Bourdelais | 01/2010 |
7314 | (11*10^102629-23)/3 | 102630 | Robert Price | 09/2021 |
7315 | 3^215094+5*2^215094 | 102626 | Jon Grantham | 08/2023 |
7316 | 25876^9239+9239^25876 | 102615 | Hans Havermann | 02/2019 |
7317 | (4*10^102612+83)/3 | 102613 | Robert Price | 02/2018 |
7318 | 75^54717+74 | 102598 | Norbert Schneider | 01/2015 |
7319 | (17*10^102597+13)/3 | 102598 | Robert Price | 01/2019 |
7320 | 2^340806-20393 | 102593 | Enzo Doria | 06/2013 |
7321 | (2^340790+5)/138267 | 102583 | Lelio R Paula | 12/2013 |
7322 | 6^131821+77 | 102577 | Lelio R Paula | 10/2016 |
7323 | (203*10^102561-11)/3 | 102563 | Robert Price | 12/2020 |
7324 | 2^340688-29 | 102558 | Henri Lifchitz | 05/2005 |
7325 | 2^340685-109101 | 102557 | Enzo Doria | 04/2014 |
7326 | 65^56567-64 | 102552 | Norbert Schneider | 11/2014 |
7327 | 26230^8121+8121^26230 | 102550 | Hans Havermann | 03/2019 |
7328 | (64*10^102547+161)/9 | 102548 | Robert Price | 08/2022 |
7329 | (8*10^102541+49)/3 | 102542 | Robert Price | 05/2020 |
7330 | (536*10^102533-23)/9 | 102535 | Robert Price | 02/2020 |
7331 | 2^340547-108897 | 102515 | Enzo Doria | 03/2014 |
7332 | (2^340536+778)/2 | 102512 | Stefano Morozzi | 09/2020 |
7333 | 25592^10119+10119^25592 | 102500 | Hans Havermann | 02/2019 |
7334 | (5*10^102492-23)/9 | 102492 | Serge Batalov | 11/2022 |
7335 | 7^121268+82 | 102484 | Lelio R Paula | 10/2016 |
7336 | (6883*2^340443-1)/162401 | 102483 | Lelio R Paula | 05/2015 |
7337 | 2^340434-5955 | 102481 | Lelio R Paula | 11/2016 |
7338 | (7*10^102480-19)/3 | 102481 | Robert Price | 10/2020 |
7339 | (2^340381+47)/7 | 102465 | Lelio R Paula | 12/2013 |
7340 | 111^50095+110 | 102461 | Norbert Schneider | 04/2017 |
7341 | 2^340291-20301 | 102438 | Enzo Doria | 06/2013 |
7342 | 12^94915+89 | 102431 | Lelio R Paula | 10/2016 |
7343 | (106*10^102422+17)/3 | 102424 | Robert Price | 04/2021 |
7344 | 24466^15349+15349^24466 | 102417 | Hans Havermann | 03/2019 |
7345 | 2^340212+111546435 | 102415 | Paul Bourdelais | 10/2021 |
7346 | 2^340208-20373 | 102413 | Enzo Doria | 06/2013 |
7347 | 6^131598-17273 | 102404 | Enzo Doria | 02/2013 |
7348 | (2^340132+1182)/2 | 102390 | Stefano Morozzi | 09/2020 |
7349 | (2^340133+1166)/2 | 102390 | Stefano Morozzi | 09/2020 |
7350 | 2^340115-21181 | 102385 | Enzo Doria | 06/2013 |
7351 | (55459*2^340090+1)/1591 | 102379 | Lelio R Paula | 07/2014 |
7352 | (2^340064+3630)/2 | 102370 | Stefano Morozzi | 09/2020 |
7353 | 9348*31^68638+13 | 102369 | Eric Chen | 04/2024 |
7354 | 89^52511-88^52511 | 102365 | Robert Price | 06/2015 |
7355 | 3^214539-112756 | 102362 | Enzo Doria | 07/2014 |
7356 | 23159^23450-23450^23159 | 102353 | Norbert Schneider | 12/2019 |
7357 | 2^340000-19877 | 102351 | Enzo Doria | 06/2013 |
7358 | 2^339990-114845 | 102348 | Enzo Doria | 05/2015 |
7359 | (3^214516-2)/51383 | 102346 | Lelio R Paula | 12/2013 |
7360 | 20^78661-99 | 102341 | Lelio R Paula | 09/2016 |
7362 | 2^339951-19585 | 102336 | Enzo Doria | 05/2013 |
7361 | (17*10^102335-167)/3 | 102336 | Robert Price | 05/2022 |
7363 | (13*2^339943+1)/45 | 102333 | Lelio R Paula | 12/2013 |
7364 | (236282#+121441)/(121441*25499429) | 102332 | Makoto Morimoto | 08/2020 |
7365 | 5*10^102323-91 | 102324 | Robert Price | 03/2021 |
7367 | 2^339889+29327 | 102317 | Yves Minet | 06/2010 |
7366 | (167*10^102315-17)/3 | 102317 | Robert Price | 03/2020 |
7368 | 26348^7641+7641^26348 | 102314 | Hans Havermann | 03/2019 |
7369 | Phi(239414,10)/6333218543 | 102303 | Makoto Kamada | 08/2019 |
7370 | 2^339834-109493 | 102301 | Enzo Doria | 04/2014 |
7371 | (16*10^102299-19)/3 | 102300 | Robert Price | 02/2019 |
7372 | (11^98221-5^98221)/6 | 102286 | Robert Price | 01/2013 |
7373 | 3^214365+1820 | 102279 | Lelio R Paula | 10/2016 |
7374 | 31978^1579+1579^31978 | 102278 | Hans Havermann | 03/2019 |
7375 | (89*10^102262-467)/9 | 102263 | Robert Price | 04/2022 |
7376 | (11*2^339705-1)/183 | 102261 | Lelio R Paula | 03/2014 |
7377 | 2^339694-16995 | 102259 | Lelio R Paula | 09/2016 |
7378 | (56*10^102255+691)/9 | 102256 | Robert Price | 05/2019 |
7379 | 122^49008+121 | 102249 | Norbert Schneider | 10/2018 |
7380 | (2^339652+3178)/2 | 102246 | Stefano Morozzi | 09/2020 |
7381 | 7^120985-38 | 102245 | Lelio R Paula | 10/2016 |
7382 | 10^102244+122961 | 102245 | Patrick De Geest | 12/2016 |
7383 | 10^102244-27 | 102244 | Lelio R Paula | 09/2016 |
7384 | 7^120982-62 | 102242 | Lelio R Paula | 10/2016 |
7385 | (2^339640+2670)/2 | 102242 | Stefano Morozzi | 09/2020 |
7386 | 4*6^131382-5 | 102236 | Lelio R Paula | 11/2014 |
7387 | (2^339607+3290)/2 | 102232 | Stefano Morozzi | 02/2021 |
7388 | 2^339586-1091 | 102226 | Yves Minet | 11/2012 |
7389 | 11^98161-3072000 | 102225 | Enzo Doria | 12/2012 |
7390 | 9*7^120961-4 | 102225 | Lelio R Paula | 11/2014 |
7391 | 5*3^214250+2 | 102224 | Serge Batalov | 10/2010 |
7392 | 12^94713-59 | 102213 | Lelio R Paula | 10/2016 |
7393 | 12^94705+89 | 102204 | Lelio R Paula | 10/2016 |
7394 | 2^339407-177 | 102172 | Lelio R Paula | 08/2011 |
7395 | 4*10^102163-57 | 102164 | Robert Price | 10/2018 |
7396 | 2^339355+65 | 102157 | Lelio R Paula | 07/2011 |
7397 | (28*10^102142-31)/3 | 102143 | Robert Price | 12/2019 |
7398 | (2^339323+47)/880715 | 102141 | Lelio R Paula | 12/2013 |
7399 | (2^339268+1758)/2 | 102130 | Stefano Morozzi | 09/2020 |
7400 | U(610865) | 102130 | Serge Batalov | 07/2024 |
7401 | s(178551) | 102122 | Robert Price | 05/2020 |
7402 | (797*10^102112-23)/9 | 102114 | Robert Price | 01/2022 |
7403 | (5*10^102107+7)/3 | 102108 | Tyler Busby | 02/2023 |
7404 | (2^339175+2790)/2 | 102102 | Stefano Morozzi | 02/2021 |
7406 | 2^339168+21 | 102100 | Lelio R Paula | 07/2011 |
7407 | 2^339167-108807 | 102100 | Enzo Doria | 03/2014 |
7405 | (2^339169+42)/2 | 102100 | Stefano Morozzi | 09/2020 |
7408 | 2^339156+163 | 102097 | Lelio R Paula | 08/2011 |
7409 | (2^339149+746)/2 | 102094 | Stefano Morozzi | 09/2020 |
7410 | (25*10^102076-67)/3 | 102077 | Robert Price | 06/2019 |
7411 | 2^339081-4543 | 102074 | Yves Minet | 03/2019 |
7412 | (3435^28867-1)/3434 | 102069 | Serge Batalov | 06/2022 |
7413 | 2*10^102062+77 | 102063 | Robert Price | 08/2020 |
7415 | 24327^15668+15668^24327 | 102053 | Hans Havermann | 02/2019 |
7414 | 10^102052+66793 | 102053 | Patrick De Geest | 09/2022 |
7416 | 10^102052-7000001 | 102052 | Robert Price | 06/2021 |
7417 | 10^102052-618623 | 102052 | Patrick De Geest | 09/2022 |
7418 | 2^339000-175635 | 102050 | Stefano Morozzi | 12/2021 |
7419 | 2^339000-151667 | 102050 | Stefano Morozzi | 12/2021 |
7420 | 2^338999+79289 | 102049 | Stefano Morozzi | 01/2022 |
7421 | 2^338998-63897 | 102049 | Stefano Morozzi | 12/2022 |
7422 | 2^338997+99659 | 102049 | Stefano Morozzi | 02/2023 |
7423 | 2^338994+188757 | 102048 | Stefano Morozzi | 05/2022 |
7424 | 2^338995+70785 | 102048 | Stefano Morozzi | 11/2022 |
7425 | 2^338994-12183 | 102048 | Stefano Morozzi | 12/2022 |
7426 | 2^338992+181591 | 102047 | Stefano Morozzi | 01/2022 |
7427 | 2^338992+136171 | 102047 | Stefano Morozzi | 03/2022 |
7428 | 2^338991-109435 | 102047 | Stefano Morozzi | 04/2022 |
7429 | 2^338991+193611 | 102047 | Stefano Morozzi | 09/2022 |
7430 | 2^338988-134619 | 102046 | Stefano Morozzi | 04/2022 |
7431 | 2^338987-62557 | 102046 | Stefano Morozzi | 12/2022 |
7432 | 2^338986-60141 | 102045 | Stefano Morozzi | 06/2022 |
7433 | 2^338986+98209 | 102045 | Stefano Morozzi | 11/2022 |
7434 | 2^338981+106391 | 102044 | Stefano Morozzi | 01/2022 |
7435 | 2^338982+34069 | 102044 | Stefano Morozzi | 03/2022 |
7436 | 2^338982-58781 | 102044 | Stefano Morozzi | 04/2022 |
7437 | 2^338980+70833 | 102044 | Stefano Morozzi | 11/2022 |
7438 | 2^338982-92111 | 102044 | Stefano Morozzi | 02/2023 |
7439 | 2^338977+83007 | 102043 | Stefano Morozzi | 02/2022 |
7440 | 2^338979-83601 | 102043 | Stefano Morozzi | 04/2022 |
7441 | 2^338975+28355 | 102042 | Stefano Morozzi | 01/2022 |
7442 | 2^338973+134619 | 102042 | Stefano Morozzi | 03/2022 |
7443 | 2^338974+183777 | 102042 | Stefano Morozzi | 03/2022 |
7444 | 2^338975+69293 | 102042 | Stefano Morozzi | 09/2022 |
7452 | 25080^11711+11711^25080 | 102041 | Hans Havermann | 02/2019 |
7445 | 2^338972+152343 | 102041 | Stefano Morozzi | 12/2021 |
7446 | 2^338972-180623 | 102041 | Stefano Morozzi | 02/2022 |
7447 | 2^338972+84441 | 102041 | Stefano Morozzi | 03/2022 |
7448 | 2^338971+64875 | 102041 | Stefano Morozzi | 05/2022 |
7449 | 2^338971+44985 | 102041 | Stefano Morozzi | 11/2022 |
7450 | 2^338971+145065 | 102041 | Stefano Morozzi | 11/2022 |
7451 | 2^338972-16635 | 102041 | Stefano Morozzi | 01/2023 |
7453 | 2^338968+53461 | 102040 | Stefano Morozzi | 01/2022 |
7454 | 2^338969+160175 | 102040 | Stefano Morozzi | 03/2022 |
7455 | 2^338967+13409 | 102040 | Stefano Morozzi | 04/2022 |
7456 | 2^338969+67635 | 102040 | Stefano Morozzi | 09/2022 |
7457 | 2^338969-15913 | 102040 | Stefano Morozzi | 01/2023 |
7458 | 2^338963-127455 | 102039 | Stefano Morozzi | 12/2021 |
7459 | 2^338963+132195 | 102039 | Stefano Morozzi | 02/2022 |
7460 | 2^338966+137919 | 102039 | Stefano Morozzi | 04/2022 |
7461 | 2^338963-87529 | 102039 | Stefano Morozzi | 12/2022 |
7462 | 2^338963-116859 | 102039 | Stefano Morozzi | 02/2023 |
7469 | (2^338982-7)/1754517 | 102038 | Lelio R Paula | 12/2013 |
7463 | 2^338960+53935 | 102038 | Stefano Morozzi | 01/2022 |
7464 | 2^338962+83157 | 102038 | Stefano Morozzi | 02/2022 |
7465 | 2^338961+12341 | 102038 | Stefano Morozzi | 04/2022 |
7466 | 2^338960+63933 | 102038 | Stefano Morozzi | 05/2022 |
7467 | 2^338960+170791 | 102038 | Stefano Morozzi | 11/2022 |
7468 | 2^338962+21679 | 102038 | Stefano Morozzi | 11/2022 |
7470 | 2^338959-30919 | 102037 | Stefano Morozzi | 02/2022 |
7471 | 2^338959+164769 | 102037 | Stefano Morozzi | 05/2022 |
7472 | 2^338958-43161 | 102037 | Stefano Morozzi | 02/2023 |
7473 | 2^338954-177003 | 102036 | Stefano Morozzi | 12/2021 |
7474 | 2^338954+154207 | 102036 | Stefano Morozzi | 01/2022 |
7475 | 2^338956+182493 | 102036 | Stefano Morozzi | 02/2022 |
7476 | 2^338954+162715 | 102036 | Stefano Morozzi | 04/2022 |
7477 | 2^338955-158241 | 102036 | Stefano Morozzi | 04/2022 |
7478 | 2^338956-33395 | 102036 | Stefano Morozzi | 04/2022 |
7479 | 2^338954+190915 | 102036 | Stefano Morozzi | 06/2022 |
7480 | 2^338955+41643 | 102036 | Stefano Morozzi | 09/2022 |
7481 | 2^338954+194427 | 102036 | Stefano Morozzi | 09/2022 |
7482 | 2^338956+117967 | 102036 | Stefano Morozzi | 09/2022 |
7483 | 2^338956+195495 | 102036 | Stefano Morozzi | 11/2022 |
7484 | 2^338954-186371 | 102036 | Stefano Morozzi | 12/2022 |
7485 | 2^338950+175077 | 102035 | Stefano Morozzi | 12/2021 |
7486 | 2^338951-51687 | 102035 | Stefano Morozzi | 12/2021 |
7487 | 2^338951+66123 | 102035 | Stefano Morozzi | 06/2022 |
7488 | 2^338950+19317 | 102035 | Stefano Morozzi | 09/2022 |
7489 | 2^338951-161479 | 102035 | Stefano Morozzi | 12/2022 |
7490 | 2^338950-66335 | 102035 | Stefano Morozzi | 01/2023 |
7491 | 2^338951-41611 | 102035 | Stefano Morozzi | 02/2023 |
7492 | 2^338952-142887 | 102035 | Stefano Morozzi | 02/2023 |
7493 | 2^338949+85449 | 102034 | Stefano Morozzi | 03/2022 |
7494 | 2^338949-184585 | 102034 | Stefano Morozzi | 04/2022 |
7495 | 2^338949-88555 | 102034 | Stefano Morozzi | 12/2022 |
7496 | 2^338948+49393 | 102034 | Stefano Morozzi | 02/2023 |
7497 | 2^338949-17601 | 102034 | Stefano Morozzi | 02/2023 |
7498 | 2^338943+127103 | 102033 | Stefano Morozzi | 12/2021 |
7499 | 2^338944-84003 | 102033 | Stefano Morozzi | 04/2022 |
7500 | 2^338945+138605 | 102033 | Stefano Morozzi | 05/2022 |