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 (> 30000) |
Who ? |
When ? |
6251 | (4*10^71498+173)/3 | 71499 | Robert Price | 01/2017 |
6252 | 3^149848+110 | 71496 | Lelio R Paula | 11/2014 |
6253 | 2^237498+513 | 71495 | Lelio R Paula | 05/2012 |
6254 | 2^237485+107 | 71491 | Lelio R Paula | 02/2012 |
6255 | (2^237465+9)/2419 | 71481 | Lelio R Paula | 05/2012 |
6256 | 2^237439-112237 | 71477 | Enzo Doria | 06/2014 |
6257 | 2^237407-9787 | 71467 | Lelio R Paula | 11/2009 |
6258 | 2^237383+72953 | 71460 | Enzo Doria | 04/2016 |
6259 | 82^37337-81^37337 | 71457 | Robert Price | 01/2015 |
6260 | (1017*2^237313-1)/19 | 71441 | Lelio R Paula | 04/2015 |
6261 | 2^237311+191 | 71438 | Lelio R Paula | 02/2012 |
6262 | 2^237280-59 | 71429 | Lelio R Paula | 02/2012 |
6263 | 11^68564-98 | 71403 | Lelio R Paula | 01/2015 |
6264 | 2^237173+74801 | 71397 | Enzo Doria | 04/2016 |
6265 | 15^60697+56 | 71386 | Lelio R Paula | 01/2015 |
6266 | 2^237118+177 | 71380 | Lelio R Paula | 02/2012 |
6267 | 2^237110+69 | 71378 | Lelio R Paula | 02/2012 |
6268 | 15^60690-58 | 71377 | Lelio R Paula | 01/2015 |
6269 | (5*2^237125-1)/599851191 | 71374 | Lelio R Paula | 01/2014 |
6270 | (3^149567+2)/539 | 71359 | Lelio R Paula | 06/2012 |
6271 | (5*10^71357-143)/3 | 71358 | Robert Price | 04/2016 |
6272 | 2^237039-114621 | 71356 | Enzo Doria | 05/2015 |
6273 | 12^66116-37 | 71352 | Lelio R Paula | 02/2015 |
6274 | (3^149497+2^149497)/5 | 71328 | Jean-Louis Charton | 10/2010 |
6275 | 2^236941-66945 | 71327 | Lelio R Paula | 05/2012 |
6276 | 2^236911-1147 | 71318 | Yves Minet | 10/2009 |
6277 | 65^39337+42 | 71315 | Lelio R Paula | 01/2016 |
6278 | 6*10^71299+7 | 71300 | Dmitry Domanov | 11/2010 |
6279 | (25*2^236843+1)/3753 | 71295 | Lelio R Paula | 06/2012 |
6280 | 10^71291+15187 | 71292 | Patrick De Geest | 03/2016 |
6282 | 10^71291-5587309119 | 71291 | Robert Price | 03/2015 |
6281 | 10^71291-273581 | 71291 | Patrick De Geest | 03/2016 |
6283 | -numer(bernoulli(22808)/22808) | 71290 | T. D. Noe | 09/2005 |
6284 | (2^236738+9)/13 | 71265 | Lelio R Paula | 05/2012 |
6285 | 5^101949+42 | 71260 | Lelio R Paula | 07/2014 |
6286 | 5*10^71237+9 | 71238 | Dmitry Domanov | 11/2010 |
6287 | 2^236634-16025 | 71234 | Enzo Doria | 04/2013 |
6288 | 71^38478+70 | 71233 | Norbert Schneider | 12/2014 |
6289 | 9*7^84280+8 | 71226 | Lelio R Paula | 10/2014 |
6290 | (10^71223+59)/3 | 71223 | Serge Batalov | 12/2014 |
6291 | (15185*2^236569-1)/453 | 71216 | Lelio R Paula | 04/2015 |
6292 | 51829#+(216091#)/(51829#) | 71208 | Makoto Morimoto | 03/2016 |
6293 | 2^236528-173 | 71203 | Lelio R Paula | 02/2012 |
6294 | 3*2^236511-5 | 71198 | Lelio R Paula | 04/2014 |
6295 | 2^236477-99 | 71187 | Lelio R Paula | 02/2012 |
6296 | 11^68356-2130 | 71186 | Enzo Doria | 12/2012 |
6297 | 11^68355-3120 | 71185 | Enzo Doria | 12/2012 |
6298 | 36^45737-35^45737 | 71181 | Robert Price | 10/2012 |
6299 | (3^149183-lucasV(1,3,149183)+1)/3 | 71178 | Paul Vanderveen | 12/2017 |
6300 | 2^236432+25 | 71174 | Lelio R Paula | 02/2012 |
6301 | 5^101818-12806 | 71168 | Enzo Doria | 02/2013 |
6302 | (7*10^71166-457)/9 | 71166 | Robert Price | 09/2017 |
6303 | 65^39253+62 | 71163 | Lelio R Paula | 01/2016 |
6304 | 39^44718+38 | 71150 | Norbert Schneider | 05/2014 |
6305 | 2^236296-407 | 71133 | Yves Minet | 02/2012 |
6306 | 2^236286-117 | 71130 | Lelio R Paula | 02/2012 |
6307 | 2^236257-111193 | 71121 | Enzo Doria | 05/2014 |
6308 | 7^84149-36 | 71115 | Lelio R Paula | 08/2014 |
6309 | 2^236209-112123 | 71106 | Enzo Doria | 06/2014 |
6310 | 18^56644-4985 | 71104 | Enzo Doria | 03/2013 |
6311 | (46*10^71077+521)/9 | 71078 | Robert Price | 08/2017 |
6312 | 21^53753+2 | 71074 | Ray Chandler | 08/2011 |
6313 | (86*10^71068-311)/9 | 71069 | Robert Price | 10/2017 |
6314 | 2^236081-110923 | 71068 | Enzo Doria | 05/2014 |
6315 | (293*27^49642-1736)/13 | 71058 | Curtis Bright | 05/2015 |
6316 | 65^39192+22 | 71052 | Lelio R Paula | 01/2016 |
6317 | (439#+1)^397-439#^397 | 71038 | Mike Oakes | 11/2010 |
6318 | 7^84050-2 | 71031 | Lelio R Paula | 09/2013 |
6319 | 20^54558-23 | 70982 | Lelio R Paula | 01/2015 |
6320 | 2^235793-112555 | 70981 | Enzo Doria | 06/2014 |
6321 | 49936!3-3^49936 | 70981 | Robert Price | 08/2015 |
6322 | 2^235787-78795 | 70979 | Lelio R Paula | 05/2012 |
6323 | Perrin(581132) | 70970 | Eric W. Weisstein | 02/2011 |
6324 | 14^61913-97 | 70961 | Lelio R Paula | 01/2015 |
6325 | 2^235720+16321 | 70959 | Yves Minet | 03/2010 |
6326 | 2^235718+16095 | 70959 | Lelio R Paula | 05/2012 |
6327 | 163841#+349933 | 70957 | Nicolas PALAU | 11/2016 |
6328 | 2^235710+7 | 70956 | Lelio R Paula | 02/2012 |
6329 | (175^31627+1)/176 | 70939 | Eric Chen | 10/2017 |
6330 | 2^235635-112087 | 70934 | Enzo Doria | 06/2014 |
6332 | 2^235575-1965 | 70916 | Lelio R Paula | 05/2012 |
6331 | 6^91133+101 | 70916 | Lelio R Paula | 01/2015 |
6333 | (21181*2^235505+1)/3 | 70898 | Lelio R Paula | 06/2014 |
6334 | (14*10^70896+211)/9 | 70897 | Robert Price | 11/2017 |
6335 | 5^101425+84 | 70894 | Lelio R Paula | 07/2014 |
6336 | 177^31536+2 | 70893 | Lelio R Paula | 05/2013 |
6337 | 43*71^38292+4 | 70891 | Serge Batalov | 03/2016 |
6338 | (29*2^235506-1)/112029785 | 70888 | Lelio R Paula | 01/2014 |
6339 | 11^68045-1530 | 70862 | Enzo Doria | 12/2012 |
6340 | 5*10^70858+21 | 70859 | Robert Price | 01/2017 |
6342 | 2^235326+3 | 70841 | Donovan Johnson | 02/2006 |
6341 | 34523!2+4 | 70841 | Robert Price | 02/2015 |
6343 | (31*2^235307+1)/3 | 70836 | Lelio R Paula | 06/2012 |
6344 | 2^235308+135 | 70835 | Lelio R Paula | 02/2012 |
6345 | r(35414,90)*1000+911 | 70831 | Patrick De Geest | 07/2004 |
6346 | 2^235274+159 | 70825 | Lelio R Paula | 02/2012 |
6347 | 3^148409+70 | 70810 | Lelio R Paula | 11/2014 |
6348 | (19*10^70794+17)/9 | 70795 | Robert Price | 03/2015 |
6349 | 2^235108-232709 | 70775 | Paul Bourdelais | 03/2013 |
6350 | (2^235099-2^117550+1)/5 | 70772 | | 11/2006 |
6351 | 19^55325-6 | 70748 | Lelio R Paula | 08/2014 |
6352 | 257^29356+29356^257 | 70746 | Norbert Schneider | 10/2014 |
6353 | 22*10^70729+3 | 70731 | Robert Price | 10/2017 |
6354 | 2^234956+11715 | 70729 | Lelio R Paula | 05/2012 |
6355 | (7*10^70727-43)/9 | 70727 | Robert Price | 10/2014 |
6356 | 2^234890-30341 | 70709 | Enzo Doria | 11/2012 |
6357 | 17^57461+14 | 70703 | Lelio R Paula | 01/2015 |
6358 | (9179*2^234834-1)/5 | 70696 | Lelio R Paula | 04/2015 |
6359 | 2*10^70688+51 | 70689 | Robert Price | 10/2017 |
6360 | 123^33822-122 | 70685 | Norbert Schneider | 01/2015 |
6361 | 7*10^70680-99 | 70681 | Robert Price | 11/2017 |
6362 | (21*2^234772-1)/2095 | 70672 | Lelio R Paula | 01/2014 |
6363 | (29*2^234686-1)/21145 | 70645 | Lelio R Paula | 01/2014 |
6364 | (15*2^234688-1)/5278141 | 70643 | Lelio R Paula | 01/2014 |
6366 | 2^234655-67 | 70639 | Lelio R Paula | 02/2012 |
6365 | (79*10^70638-61)/9 | 70639 | Robert Price | 10/2015 |
6367 | 2^234652-173 | 70638 | Lelio R Paula | 02/2012 |
6368 | 2^234618-3645 | 70628 | Lelio R Paula | 05/2012 |
6369 | (2^234610-5)/19 | 70624 | Lelio R Paula | 05/2012 |
6370 | 4*5^101038+9 | 70624 | Lelio R Paula | 10/2014 |
6371 | 2^234603+71963 | 70623 | Enzo Doria | 04/2016 |
6372 | 2^234600-113129 | 70622 | Enzo Doria | 07/2014 |
6373 | 2^234586+9 | 70618 | Lelio R Paula | 02/2012 |
6374 | 3^148008+26 | 70618 | Robert Price | 11/2013 |
6375 | (7*10^70616-151)/9 | 70616 | Robert Price | 09/2017 |
6376 | 65^38947+32 | 70608 | Lelio R Paula | 01/2016 |
6377 | (2^234488-3)/11 | 70587 | Lelio R Paula | 05/2012 |
6378 | (3*2^234451+1)/35 | 70576 | Lelio R Paula | 08/2012 |
6379 | Phi(159495,10) | 70560 | Maksym Voznyy | 09/2015 |
6380 | 2^234383-4035 | 70557 | Lelio R Paula | 05/2012 |
6381 | 2^234315-111241 | 70536 | Enzo Doria | 05/2014 |
6382 | 14^61526+97 | 70517 | Lelio R Paula | 01/2015 |
6383 | (3*2^234170+1)/13 | 70492 | Lelio R Paula | 08/2012 |
6384 | 51^41281-50^41281 | 70491 | Robert Price | 02/2013 |
6385 | 2^234141-112123 | 70484 | Enzo Doria | 06/2014 |
6386 | 2^234139+12285 | 70483 | Lelio R Paula | 04/2012 |
6387 | 2^234133-3163 | 70482 | Yves Minet | 04/2009 |
6388 | 2^234115+83 | 70476 | Lelio R Paula | 02/2012 |
6389 | 2^234114-1595 | 70476 | Lelio R Paula | 05/2012 |
6390 | 24^51061-23^51061 | 70475 | Robert Price | 07/2012 |
6391 | 19471^16428-2 | 70467 | Faysal YAtim | 09/2005 |
6392 | 7^83381+12 | 70466 | Robert Price | 01/2014 |
6393 | 2^234067-111427 | 70462 | Enzo Doria | 05/2014 |
6394 | (266*10^70457+1)/3 | 70459 | Robert Price | 02/2016 |
6395 | (31*2^234041-1)/97 | 70453 | Lelio R Paula | 01/2014 |
6396 | 2^234026+12909 | 70449 | Lelio R Paula | 04/2012 |
6397 | 2^233965-19 | 70431 | Lelio R Paula | 02/2012 |
6398 | (5*2^233932-1)/179 | 70419 | Lelio R Paula | 01/2014 |
6399 | 2^233908-17109 | 70414 | Enzo Doria | 05/2013 |
6400 | 695^24772+24772^695 | 70402 | Norbert Schneider | 09/2016 |
6401 | 3*5^100719-2 | 70401 | Lelio R Paula | 10/2014 |
6402 | 2^233829-111355 | 70390 | Enzo Doria | 05/2014 |
6403 | (19775^16384+1)/2 | 70388 | Henri Lifchitz | 03/2007 |
6404 | 7*3^147519+8 | 70386 | Lelio R Paula | 04/2014 |
6405 | 141^32749-2 | 70385 | Lelio R Paula | 10/2017 |
6406 | 5*7^83265+2 | 70368 | Lelio R Paula | 10/2014 |
6407 | (23*10^70363+97)/3 | 70364 | Robert Price | 02/2017 |
6408 | (23*2^233749-1)/35325 | 70363 | Lelio R Paula | 01/2014 |
6409 | 5^100652-13916 | 70353 | Enzo Doria | 02/2013 |
6410 | 45^42555-2 | 70353 | Lelio R Paula | 08/2013 |
6411 | 2^233661-61 | 70339 | Lelio R Paula | 02/2012 |
6412 | 2^233523-112249 | 70298 | Enzo Doria | 06/2014 |
6413 | 5*3^147324-8 | 70293 | Lelio R Paula | 04/2014 |
6414 | 2^233488-13065 | 70287 | Enzo Doria | 11/2012 |
6415 | (3^147322+8)/42851 | 70286 | Lelio R Paula | 06/2012 |
6416 | (22*10^70259+161)/3 | 70260 | Robert Price | 02/2017 |
6417 | 2^233388+465 | 70257 | Lelio R Paula | 11/2012 |
6418 | 14^61299+59 | 70257 | Lelio R Paula | 01/2015 |
6419 | 2^233383+94065 | 70256 | Lelio R Paula | 04/2012 |
6420 | 49471!3-6561 | 70253 | Robert Price | 11/2015 |
6421 | 7^83121+6^(83121-1) | 70246 | Robert Price | 03/2016 |
6422 | (197*10^70241-11)/3 | 70243 | Robert Price | 10/2017 |
6423 | 23*10^70240-7 | 70242 | Robert Price | 03/2016 |
6424 | (71*10^70227-53)/9 | 70228 | Robert Price | 10/2015 |
6425 | (2^233247-9)/17 | 70214 | Lelio R Paula | 05/2012 |
6426 | (11^67421-2^67421)/9 | 70211 | Robert Price | 01/2013 |
6427 | (23*10^70209-41)/9 | 70210 | Robert Price | 03/2015 |
6428 | (29*10^70194-11)/9 | 70195 | Robert Price | 04/2015 |
6429 | 3^147109+196 | 70189 | Lelio R Paula | 05/2014 |
6430 | (34*10^70191-7)/9/3/40583/573047 | 70181 | Makoto Morimoto | 05/2016 |
6431 | 9^73538+8^(73538+1) | 70174 | Robert Price | 06/2016 |
6432 | 2*5^100391+7 | 70171 | Lelio R Paula | 10/2014 |
6433 | 99^35156-2 | 70159 | Lelio R Paula | 08/2013 |
6434 | (68*10^70148+7)/3 | 70150 | Robert Price | 03/2016 |
6435 | 11^67360-6030 | 70149 | Enzo Doria | 01/2013 |
6436 | (35*10^70130-377)/9 | 70131 | Robert Price | 12/2017 |
6437 | 49391!3+3^49391 | 70128 | Robert Price | 09/2015 |
6438 | (229*10^70122-1)/3 | 70124 | Robert Price | 12/2016 |
6439 | 7^82975-92 | 70123 | Lelio R Paula | 07/2014 |
6440 | 65^38670+58 | 70106 | Lelio R Paula | 01/2016 |
6441 | 105^34684+34684^105 | 70103 | Serge Batalov | 05/2014 |
6442 | 134^32955-133 | 70099 | Norbert Schneider | 03/2015 |
6444 | 2^232836-227903 | 70091 | Enzo Doria | 12/2012 |
6443 | 2^232837-1859173 | 70091 | Enzo Doria | 03/2016 |
6445 | 3*2^232820+5 | 70087 | Lelio R Paula | 04/2014 |
6447 | 2^232799+90195 | 70080 | Lelio R Paula | 02/2013 |
6446 | 2^232799-112237 | 70080 | Enzo Doria | 06/2014 |
6448 | 2^232759+262145 | 70068 | Lelio R Paula | 04/2012 |
6449 | 3*2^232750+7 | 70066 | Lelio R Paula | 04/2014 |
6450 | 12^64918-11 | 70059 | Lelio R Paula | 01/2015 |
6451 | 7^82899-12 | 70058 | Lelio R Paula | 09/2013 |
6452 | (22*10^70051-13)/9 | 70052 | Robert Price | 03/2015 |
6453 | (2^232685-7)/2514625 | 70039 | Lelio R Paula | 04/2012 |
6454 | 18^55786-5363 | 70027 | Enzo Doria | 03/2013 |
6455 | (2^(77537*3+1)+243)/7 | 70023 | Kevin Acres | 11/2013 |
6456 | 2^232602+169 | 70021 | Lelio R Paula | 02/2012 |
6457 | (137^32768+29^32768)/2 | 70016 | Jeppe Stig Nielsen | 04/2018 |
6458 | 2^232580+72133 | 70014 | Enzo Doria | 04/2016 |
6459 | 4*6^89958-7 | 70002 | Lelio R Paula | 09/2014 |
6460 | 10^70000+80487 | 70001 | Milton L. Brown | 05/2006 |
6461 | 10^69999+134857 | 70000 | Patrick De Geest | 02/2007 |
6466 | 10^70000-9273 | 70000 | Patrick De Geest | 08/2009 |
6462 | (79*10^69999-7)/9 | 70000 | Robert Price | 01/2015 |
6463 | ((2^43112609)/10^38420)%10^70000 | 70000 | Michael Vang | 10/2016 |
6464 | (2^756839/10^36014)%10^70000 | 70000 | Michael Vang | 12/2016 |
6465 | (2^74207281/10^32641)%10^70000 | 70000 | Michael Vang | 12/2016 |
6467 | 10^69999-88251 | 69999 | Patrick De Geest | 08/2009 |
6468 | 2^232507+1089 | 69992 | Lelio R Paula | 04/2012 |
6469 | (17*2^232445+1)/5 | 69974 | Lelio R Paula | 08/2012 |
6470 | (529^25693+1)/530 | 69972 | Richard Fischer | 12/2017 |
6471 | 7^82778+48 | 69956 | Lelio R Paula | 09/2013 |
6472 | 7*2^232381+3 | 69955 | Lelio R Paula | 04/2014 |
6473 | 2^232362-110541 | 69948 | Enzo Doria | 05/2014 |
6474 | 2^232326-112391 | 69938 | Enzo Doria | 06/2014 |
6475 | 3^146575+236 | 69935 | Lelio R Paula | 09/2013 |
6476 | 30^47341-29 | 69929 | Norbert Schneider | 02/2014 |
6477 | 5^100040-68 | 69925 | Lelio R Paula | 09/2013 |
6478 | (35*10^69866-593)/9 | 69867 | Robert Price | 08/2017 |
6479 | 2^232045-17295 | 69853 | Lelio R Paula | 04/2012 |
6480 | (2^231987+78557)/95 | 69834 | Lelio R Paula | 05/2012 |
6481 | 2^231955+74243 | 69826 | Yves Minet | 03/2011 |
6482 | 2^231946-15873 | 69823 | Enzo Doria | 04/2013 |
6483 | 18^55618+95 | 69816 | Lelio R Paula | 09/2013 |
6484 | 6^89712+5^(89712-1) | 69810 | Robert Price | 02/2016 |
6485 | 2^231870+135 | 69800 | Lelio R Paula | 02/2012 |
6486 | (23*2^231827-1)/4179 | 69785 | Lelio R Paula | 01/2014 |
6487 | 2^231778+54615 | 69773 | Lelio R Paula | 04/2012 |
6488 | (19*2^231780+1)/235 | 69772 | Lelio R Paula | 08/2012 |
6489 | 14^60866+27 | 69761 | Lelio R Paula | 09/2013 |
6490 | 13^62619-44 | 69755 | Lelio R Paula | 09/2013 |
6491 | (2^231715-509203)/35 | 69752 | Lelio R Paula | 05/2012 |
6492 | 2^231711-110467 | 69752 | Enzo Doria | 05/2014 |
6493 | (19^54547+18^54547)/37 | 69751 | Robert Price | 08/2013 |
6494 | (23*2^231697-1)/45 | 69748 | Lelio R Paula | 01/2014 |
6495 | 2^231696-1861499 | 69748 | Enzo Doria | 03/2016 |
6496 | 2^231684-147 | 69744 | Lelio R Paula | 02/2012 |
6497 | (23*2^231686-1)/1183 | 69743 | Lelio R Paula | 01/2014 |
6498 | 2^231591-477397 | 69716 | Paul Bourdelais | 03/2013 |
6499 | 11^66916-420 | 69686 | Enzo Doria | 08/2012 |
6500 | 5^99680-13706 | 69674 | Enzo Doria | 02/2013 |