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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Rank |
Probable prime |
Digits (> 50000) |
Who ? |
When ? |
9261 | 25206!+p(4114) | 100001 | Henri Lifchitz | 09/2005 |
9262 | 25206!-p(5447) | 100001 | Henri Lifchitz | 10/2005 |
9263 | 25206!-p(12402) | 100001 | Henri Lifchitz | 04/2006 |
9264 | 25206!-p(16290) | 100001 | Henri Lifchitz | 09/2006 |
9265 | 25206!-p(19647) | 100001 | Henri Lifchitz | 02/2007 |
9266 | 2^332194+11473 | 100001 | Henri Lifchitz | 03/2007 |
9256 | 10^100000+342909 | 100001 | Milton L. Brown | 12/2007 |
9257 | 10^100000+346579 | 100001 | Robert Price | 04/2012 |
9258 | 10^100000+829767 | 100001 | Robert Price | 05/2012 |
9259 | 10^100000+871899 | 100001 | Robert Price | 05/2012 |
9260 | 10^100000+1475997 | 100001 | Robert Price | 07/2012 |
9251 | 10^100000+2483527 | 100001 | Robert Price | 12/2012 |
9252 | 10^100000+2503087 | 100001 | Robert Price | 12/2012 |
9253 | 10^100000+2686179 | 100001 | Robert Price | 12/2012 |
9254 | 10^100000+2688933 | 100001 | Robert Price | 12/2012 |
9255 | 10^100000+3667159 | 100001 | Robert Price | 08/2013 |
9267 | 10^99999+309403 | 100000 | Daniel Heuer | 01/2004 |
9268 | 10^100000-260199 | 100000 | Patrick De Geest | 01/2010 |
9269 | 2^332192+10192681 | 100000 | Sujan Das | 06/2022 |
9270 | 1610172603059^8192+1610172602878^8192 | 100000 | Youcef Lemsafer | 01/2023 |
9272 | 10^99999-59511 | 99999 | Patrick De Geest | 07/2009 |
9271 | 10^99998+235437 | 99999 | Patrick De Geest | 02/2020 |
9273 | 10^99998-286587 | 99998 | Patrick De Geest | 02/2020 |
9274 | 10^99997+72297 | 99998 | Patrick De Geest | 02/2020 |
9275 | 10^99997-402627 | 99997 | Patrick De Geest | 02/2020 |
9276 | 10^99996+279853 | 99997 | Patrick De Geest | 02/2020 |
9277 | 10^99997-500000001 | 99997 | Robert Price | 12/2020 |
9278 | 10^99996-94961 | 99996 | Patrick De Geest | 02/2020 |
9279 | 10^99995+54633 | 99996 | Patrick De Geest | 02/2020 |
9280 | 10^99995-101429 | 99995 | Patrick De Geest | 02/2020 |
9281 | 10^99994+117271 | 99995 | Patrick De Geest | 02/2020 |
9282 | 10^99994-452289 | 99994 | Patrick De Geest | 02/2020 |
9283 | 10^99993+371311 | 99994 | Patrick De Geest | 02/2020 |
9284 | 10^99993-186491 | 99993 | Patrick De Geest | 02/2020 |
9285 | 10^99992+17431 | 99993 | Patrick De Geest | 02/2020 |
9286 | 10^99992-28607 | 99992 | Patrick De Geest | 02/2020 |
9287 | 10^99991+125391 | 99992 | Patrick De Geest | 02/2020 |
9288 | 10^99991-204573 | 99991 | Patrick De Geest | 02/2020 |
9289 | 10^99990+13899 | 99991 | Patrick De Geest | 02/2020 |
9290 | 10^99990-8111 | 99990 | Patrick De Geest | 02/2020 |
9291 | 2^332141-113073 | 99985 | Enzo Doria | 07/2014 |
9292 | (1610172603037^8192+1610172602919^8192)/17110948127473666 | 99983 | Youcef Lemsafer | 01/2023 |
9293 | 6*10^99979-79 | 99980 | Robert Price | 03/2022 |
9295 | (3^209561+2)/728101255 | 99978 | Lelio R Paula | 09/2013 |
9294 | 23827^15702+15702^23827 | 99978 | Hans Havermann | 04/2018 |
9296 | 2^332085+1865897 | 99968 | Enzo Doria | 03/2016 |
9297 | (9787*2^332070-1)/936402369 | 99959 | Lelio R Paula | 05/2015 |
9298 | 2^332023+191 | 99949 | Lelio R Paula | 02/2011 |
9299 | (6271^26321-1)/6270 | 99946 | Serge Batalov | 06/2022 |
9300 | 7*10^99944+27 | 99945 | Robert Price | 11/2020 |
9301 | 3188^28523-28523^3188 | 99931 | Norbert Schneider | 06/2023 |
9302 | 2^331938+71149 | 99924 | Enzo Doria | 04/2016 |
9303 | 2^331932-78795 | 99922 | Lelio R Paula | 09/2016 |
9304 | 2^331921+771 | 99919 | Lelio R Paula | 01/2013 |
9305 | 7947^25618-25618^7947 | 99916 | Norbert Schneider | 08/2023 |
9306 | (3^209419-2)/5132755 | 99912 | Lelio R Paula | 09/2013 |
9307 | 2^331860-114989 | 99900 | Enzo Doria | 05/2015 |
9308 | 2^331746-11655 | 99866 | Lelio R Paula | 09/2016 |
9309 | 11^95891-28 | 99861 | Lelio R Paula | 08/2016 |
9310 | (2^331694-5)/11 | 99849 | Lelio R Paula | 10/2013 |
9311 | (3^209246+7)/64 | 99834 | Lelio R Paula | 09/2013 |
9312 | 25062^9617+9617^25062 | 99823 | Hans Havermann | 04/2018 |
9313 | 15^84866-52 | 99811 | Lelio R Paula | 08/2016 |
9314 | 13^89600+30 | 99810 | Lelio R Paula | 08/2016 |
9315 | 2^331527+100280245065 | 99800 | Paul Bourdelais | 10/2021 |
9316 | 22950^22309+22309^22950 | 99798 | Hans Havermann | 03/2018 |
9317 | 5^142772-38 | 99794 | Lelio R Paula | 08/2016 |
9318 | (7482^25759-1)/7481 | 99787 | Serge Batalov | 06/2022 |
9319 | (23*2^331459+1)/475 | 99778 | Lelio R Paula | 11/2013 |
9320 | 2^331416-331416+1 | 99767 | Robert Price | 10/2014 |
9321 | 2^331256-57 | 99718 | Lelio R Paula | 12/2012 |
9322 | 28192^3443+3443^28192 | 99714 | Hans Havermann | 03/2018 |
9323 | 2^331185+737 | 99697 | Lelio R Paula | 01/2013 |
9324 | (4*10^99693+149)/9 | 99693 | Robert Price | 03/2017 |
9325 | 2^331154+1880527 | 99688 | Enzo Doria | 10/2016 |
9327 | (19^77951+1)/20 | 99679 | Paul Bourdelais | 03/2010 |
9326 | 24354^12385+12385^24354 | 99679 | Hans Havermann | 03/2018 |
9328 | 2^331110+1870459 | 99675 | Enzo Doria | 05/2016 |
9329 | 5*2^331075+7 | 99665 | Lelio R Paula | 08/2014 |
9330 | 25776^7351+7351^25776 | 99659 | Hans Havermann | 02/2018 |
9331 | (16*10^99656-31)/3 | 99657 | Robert Price | 03/2016 |
9332 | (6059^26347-1)/6058 | 99652 | Serge Batalov | 06/2022 |
9333 | (15544^23773-1)/15543 | 99642 | Serge Batalov | 06/2022 |
9335 | 2^330968+345 | 99632 | Lelio R Paula | 09/2016 |
9334 | (2^330969+690)/2 | 99632 | Stefano Morozzi | 09/2020 |
9337 | 2*5^142528-7 | 99624 | Lelio R Paula | 11/2014 |
9336 | 2^330942+77329 | 99624 | Enzo Doria | 05/2016 |
9338 | 14^86914-99 | 99615 | Lelio R Paula | 08/2016 |
9339 | (19*2^330902+1)/77 | 99611 | Lelio R Paula | 11/2013 |
9340 | 22971^21692+21692^22971 | 99610 | Hans Havermann | 03/2018 |
9341 | 2^330845+71687 | 99595 | Enzo Doria | 04/2016 |
9342 | (26667^22501-1)/26666 | 99585 | Serge Batalov | 06/2022 |
9343 | (23*2^330770+1)/3 | 99573 | Lelio R Paula | 11/2013 |
9344 | 24494^11613+11613^24494 | 99567 | Hans Havermann | 03/2018 |
9345 | 2^330735+8415 | 99562 | Lelio R Paula | 09/2016 |
9346 | 2^330720+74071 | 99557 | Enzo Doria | 04/2016 |
9347 | (10405^24781-1)/10404 | 99548 | Serge Batalov | 06/2022 |
9349 | 31^66738-2 | 99531 | Lelio R Paula | 09/2013 |
9348 | (9002^25171-1)/9001 | 99531 | Serge Batalov | 06/2022 |
9350 | (5023^26893-1)/5022 | 99527 | Serge Batalov | 06/2022 |
9351 | 7*3^208567+4 | 99513 | Lelio R Paula | 08/2014 |
9352 | (15881^23689-1)/15880 | 99511 | Serge Batalov | 06/2022 |
9353 | (13*10^99508+47)/3 | 99509 | Robert Price | 01/2017 |
9354 | 2^330553+779 | 99507 | Lelio R Paula | 01/2013 |
9355 | 15^84606-94 | 99505 | Lelio R Paula | 08/2016 |
9356 | (10^99497+173)/3 | 99497 | Robert Price | 05/2021 |
9357 | 9*10^99493-43 | 99494 | Robert Price | 09/2021 |
9358 | 6^127858+47 | 99493 | Lelio R Paula | 08/2016 |
9359 | 5^142337+48 | 99490 | Lelio R Paula | 08/2016 |
9360 | 7^117724-20 | 99489 | Lelio R Paula | 08/2016 |
9361 | (559^36209-1)/558 | 99479 | Serge Batalov | 06/2022 |
9362 | (13470^24091-1)/13469 | 99477 | Serge Batalov | 06/2022 |
9363 | (29*10^99474-17)/3 | 99475 | Erik Branger | 09/2014 |
9364 | (185*10^99466-11)/3 | 99468 | Robert Price | 10/2020 |
9365 | (2^330410+2038)/2 | 99464 | Stefano Morozzi | 09/2020 |
9366 | (9*2^330407-1)/7 | 99463 | Lelio R Paula | 03/2014 |
9367 | (516*32^66077-175)/31 | 99458 | Eric Chen | 04/2023 |
9368 | (2863^28771-1)/2862 | 99453 | Serge Batalov | 06/2022 |
9369 | (2^330373+2114)/2 | 99452 | Stefano Morozzi | 09/2020 |
9370 | (68*10^99441+7)/3 | 99443 | Robert Price | 03/2016 |
9371 | 10^99434+155571 | 99435 | Patrick De Geest | 04/2020 |
9372 | 10^99434-123456789 | 99434 | Robert Price | 02/2020 |
9373 | 10^99434-191237 | 99434 | Patrick De Geest | 04/2020 |
9374 | 46^59791-45^59791 | 99418 | Jean-Louis Charton | 01/2013 |
9375 | 23839^14802+14802^23839 | 99417 | Hans Havermann | 02/2018 |
9376 | (2*10^99408+529)/9 | 99408 | Robert Price | 01/2017 |
9377 | (2^330216+3510)/2 | 99405 | Stefano Morozzi | 09/2020 |
9378 | 53^57646-2 | 99398 | Lelio R Paula | 09/2013 |
9379 | 2^330165+1870025 | 99390 | Enzo Doria | 05/2016 |
9380 | 7*10^99383+97 | 99384 | Robert Price | 09/2021 |
9381 | 2^330142-155 | 99383 | Lelio R Paula | 12/2012 |
9382 | 2^330088-115259 | 99367 | Enzo Doria | 06/2015 |
9383 | 24216^12671+12671^24216 | 99354 | Hans Havermann | 01/2018 |
9384 | Phi(200548,10)/3208769 | 99354 | Makoto Kamada | 04/2019 |
9385 | (746*10^99303+1)/9 | 99305 | Robert Price | 02/2017 |
9386 | 3^208107+40 | 99293 | Lelio R Paula | 08/2016 |
9387 | 2^329843+211343 | 99293 | Enzo Doria | 08/2023 |
9388 | (3939^27617-1)/3938 | 99291 | Serge Batalov | 06/2022 |
9389 | (5*2^329833-1)/369 | 99288 | Lelio R Paula | 02/2014 |
9390 | 8*3^208093+5 | 99287 | Lelio R Paula | 08/2014 |
9391 | 5^142043+56 | 99284 | Lelio R Paula | 08/2016 |
9392 | (13*10^99282-157)/9 | 99283 | Robert Price | 05/2021 |
9393 | (10^99284+7)/53/67 | 99281 | Alfred Reich | 06/2021 |
9394 | 22*10^99275+7 | 99277 | Robert Price | 04/2016 |
9395 | 2^329778+1876189 | 99274 | Enzo Doria | 07/2016 |
9396 | (149557^19321-1)/(149557^139-1) | 99264 | Ryan Propper | 11/2023 |
9397 | (6580^25997-1)/6579 | 99259 | Serge Batalov | 06/2022 |
9398 | (2249^29611-1)/2248 | 99253 | Serge Batalov | 06/2022 |
9399 | (10^99239-13)/3 | 99239 | Robert Price | 02/2017 |
9400 | (1199^32233-1)/1198 | 99237 | Serge Batalov | 06/2022 |
9402 | 3^207987+62 | 99236 | Lelio R Paula | 08/2016 |
9401 | (62*10^99235+91)/9 | 99236 | Robert Price | 07/2021 |
9403 | 2^329638+49 | 99231 | Lelio R Paula | 12/2012 |
9404 | 7^117413-18 | 99226 | Lelio R Paula | 08/2016 |
9405 | 2^329586-458903 | 99216 | Enzo Doria | 04/2015 |
9406 | (6290^26119-1)/6289 | 99214 | Serge Batalov | 06/2022 |
9408 | 2^329553+101 | 99206 | Lelio R Paula | 12/2012 |
9407 | (21297^22921-1)/21296 | 99206 | Serge Batalov | 06/2022 |
9409 | 2^329551-112897 | 99205 | Enzo Doria | 06/2014 |
9410 | (3^207925+7)/50 | 99204 | Lelio R Paula | 09/2013 |
9411 | 6^127458-17993 | 99182 | Enzo Doria | 03/2013 |
9412 | 27197^4428+4428^27197 | 99166 | Hans Havermann | 10/2017 |
9413 | (46*10^99143-1)/9 | 99144 | Robert Price | 12/2014 |
9414 | (64*10^99135+161)/9 | 99136 | Robert Price | 08/2022 |
9415 | 7*10^99133+69 | 99134 | Robert Price | 10/2017 |
9416 | (21701^22861-1)/21700 | 99132 | Serge Batalov | 06/2022 |
9417 | 18^78968-3065 | 99127 | Enzo Doria | 03/2013 |
9419 | 25927^6654+6654^25927 | 99122 | Hans Havermann | 10/2017 |
9418 | 87915!4+16 | 99122 | Robert Price | 09/2019 |
9420 | 2^329259+189 | 99117 | Lelio R Paula | 12/2012 |
9421 | 8*10^99113+39 | 99114 | Robert Price | 01/2017 |
9422 | 6^127364+77 | 99109 | Lelio R Paula | 08/2016 |
9423 | (82*10^99103+143)/9 | 99104 | Robert Price | 06/2021 |
9424 | (11414^24421-1)/11413 | 99083 | Serge Batalov | 06/2022 |
9425 | (2^329135+1110)/2 | 99080 | Stefano Morozzi | 09/2020 |
9426 | (22089^22807-1)/22088 | 99074 | Serge Batalov | 06/2022 |
9427 | (59*10^99069+391)/9 | 99070 | Robert Price | 03/2021 |
9428 | (797*10^99061-41)/9 | 99063 | Robert Price | 04/2022 |
9429 | 2^329058-287681 | 99057 | Harrison Mesh | 06/2022 |
9430 | 6^127285+13 | 99047 | Lelio R Paula | 08/2016 |
9431 | (228581#+235862)/(2^3*11*71*151) | 99044 | Makoto Morimoto | 10/2017 |
9432 | 2^329007+73283 | 99041 | Enzo Doria | 04/2016 |
9433 | (145413^19321-1)/(145413^139-1) | 99030 | Ryan Propper | 11/2023 |
9434 | 5*3^207543-8 | 99024 | Lelio R Paula | 08/2014 |
9435 | (2^328930+570)/2 | 99018 | Stefano Morozzi | 09/2020 |
9436 | 2^328885+149 | 99005 | Lelio R Paula | 12/2012 |
9438 | 23392^17075+17075^23392 | 99004 | Hans Havermann | 09/2017 |
9437 | (7424^25579-1)/7423 | 99004 | Serge Batalov | 06/2022 |
9439 | (2^328879-9)/119 | 99001 | Lelio R Paula | 10/2013 |
9440 | 5^141618+54 | 98987 | Lelio R Paula | 08/2016 |
9441 | 2^328824+24391 | 98986 | Enzo Doria | 10/2023 |
9442 | 8*10^98982+51 | 98983 | Robert Price | 05/2017 |
9443 | (21*2^328809-1)/7709 | 98979 | Lelio R Paula | 03/2014 |
9444 | 2^328794-2797601 | 98977 | Enzo Doria | 04/2016 |
9445 | (88331^20011-1)/88330 | 98972 | Serge Batalov | 06/2022 |
9446 | 6^127176+5 | 98963 | Lelio R Paula | 11/2014 |
9447 | 2*10^98961-21 | 98962 | Robert Price | 09/2020 |
9448 | 24262^11989+11989^24262 | 98960 | Hans Havermann | 09/2017 |
9449 | (60138^20707-1)/60137 | 98958 | Serge Batalov | 06/2022 |
9450 | 2^328700-109709 | 98949 | Enzo Doria | 04/2014 |
9451 | (2^328698+1810)/2 | 98948 | Stefano Morozzi | 01/2021 |
9452 | (1014^32917-1)/1013 | 98947 | Serge Batalov | 06/2022 |
9453 | 87771!4-128 | 98944 | Robert Price | 11/2019 |
9454 | (4576^27031-1)/4575 | 98943 | Serge Batalov | 06/2022 |
9455 | (2^328658+3042)/2 | 98936 | Stefano Morozzi | 09/2020 |
9456 | (1933^30103-1)/1932 | 98923 | Serge Batalov | 06/2022 |
9457 | 46711!2-2^46711 | 98916 | Robert Price | 09/2015 |
9458 | 9*7^117037+4 | 98909 | Lelio R Paula | 11/2014 |
9459 | 127^47012+126 | 98905 | Norbert Schneider | 01/2019 |
9460 | (93826^19891-1)/93825 | 98900 | Serge Batalov | 06/2022 |
9461 | (2^328525+1250)/2 | 98896 | Stefano Morozzi | 09/2020 |
9462 | (10^98890+149)/3 | 98890 | Serge Batalov | 12/2014 |
9463 | 22775^21978+21978^22775 | 98889 | Hans Havermann | 08/2017 |
9464 | 2^328497-216933 | 98888 | Enzo Doria | 05/2014 |
9465 | 2^328487+32769 | 98885 | Lelio R Paula | 08/2016 |
9466 | 3^207250-112358 | 98884 | Enzo Doria | 06/2014 |
9467 | 13^88754-90 | 98867 | Lelio R Paula | 08/2016 |
9468 | 2^328406+709 | 98861 | Lelio R Paula | 02/2013 |
9469 | 2*10^98860-21 | 98861 | Robert Price | 09/2020 |
9470 | (17*2^328413-1)/16173 | 98860 | Lelio R Paula | 03/2014 |
9471 | 7^116976+76 | 98857 | Lelio R Paula | 08/2016 |
9472 | (2^328378+2710)/2 | 98852 | Stefano Morozzi | 09/2020 |
9473 | (25411^22441-1)/25410 | 98849 | Serge Batalov | 06/2022 |
9474 | (18668^23143-1)/18667 | 98842 | Serge Batalov | 06/2022 |
9476 | 2^328335+1155 | 98839 | Lelio R Paula | 08/2016 |
9475 | 2^328333-349003 | 98839 | Harrison Mesh | 06/2022 |
9478 | (3*2^328311+1)/5 | 98832 | Lelio R Paula | 11/2013 |
9477 | 287^40210+40210^287 | 98832 | Norbert Schneider | 11/2014 |
9479 | (2^328284+9)/1325 | 98821 | Lelio R Paula | 10/2013 |
9480 | (21*2^328258+1)/2125 | 98814 | Lelio R Paula | 11/2013 |
9481 | (28623^22171-1)/28622 | 98806 | Serge Batalov | 06/2022 |
9482 | 24746^9825+9825^24746 | 98795 | Hans Havermann | 07/2020 |
9483 | 26620^5143+5143^26620 | 98793 | Hans Havermann | 07/2020 |
9484 | 65^54491+48 | 98788 | Lelio R Paula | 04/2016 |
9485 | 3^207042+98 | 98785 | Lelio R Paula | 08/2016 |
9486 | (2^328121+3110)/2 | 98774 | Stefano Morozzi | 09/2020 |
9487 | 10^98754+73383 | 98755 | Patrick De Geest | 02/2021 |
9490 | 3^206977-112756 | 98754 | Enzo Doria | 07/2014 |
9489 | 10^98754-40000000001 | 98754 | Robert Price | 09/2020 |
9488 | 10^98754-169343 | 98754 | Patrick De Geest | 02/2021 |
9491 | 7^116846-50 | 98747 | Lelio R Paula | 08/2016 |
9492 | (19152^23059-1)/19151 | 98740 | Serge Batalov | 06/2022 |
9493 | 23267^17512+17512^23267 | 98730 | Hans Havermann | 04/2020 |
9494 | 2^327967-28635 | 98728 | Lelio R Paula | 08/2016 |
9495 | 707^34642+34642^707 | 98710 | Norbert Schneider | 12/2017 |
9496 | (10771^24481-1)/10770 | 98710 | Serge Batalov | 06/2022 |
9497 | 6^126850-47 | 98709 | Lelio R Paula | 08/2016 |
9498 | (2^327886+2170)/2 | 98704 | Stefano Morozzi | 09/2020 |
9499 | (22*10^98697+47)/3 | 98698 | Robert Price | 06/2021 |
9500 | (139706^19321-1)/(139706^139-1) | 98696 | Ryan Propper | 11/2023 |