# # Numbers of shape: 41^(2^8) + b^(2^8) with 1 <= b < 41 # Filename: http://www.AlfredReich.com/GF.41.8.txt # Editor: Alfred Reich (zehnp@gmx.de) # Date: April 4, 2011 # Status: 30 composites # # Notes: There are 40 numbers, each number has 413 digits. # # Numbers of shape a^(2^m) + b^(2^m) with 1 <= b < a and gcd(a,b) = 1 are called Generalized Fermat Numbers and denoted by GF(a,b,m), # compare Hans Riesel, Prime Numbers and Computer Methods for Factorizations, 1994, 2nd ed, Birkhäuser, pp102 # and Wilfrid Keller, http://www.rrz.uni-hamburg.de/RRZ/W.Keller/GFNfacs.html. # 1 2 59393 11276801 1012779179521 77776979977487873 c372 2 86138369 5385742849 4260822277633 208429203225601 c369 3 2 629497411462788536753683936990888719361 c374 4 324114436164097 305664398995811023873 7150355536299387198984193 p354 5 2 9779201 516161655052801 2468450704565249 16992586925817479681 c357 6 226817 206617601 142667451247780258351065364866049 c368 7 2 74576897 p405 8 10753 c409 9 2 247411188765052407546620417 c387 10 4318466561 c404 11 2 7681 1892353 108828033431173357057 95767670432855016772609 95436790999230386710975489 c334 12 878593 p407 13 2 200888922396394801422489089 c387 14 325306383361 79111113014878157278721 p379 15 2 301057 2304256634881 261934572257683059322949633 c369 16 380929 2810369 65768618497 c391 17 2 184321 9407350234902017 32388590272298497 c375 18 138455873567852812273153 438718722008579410945537 p367 19 2 c413 20 18433 629249 c403 21 2 58369 35062029878321903468881409 1748763425877856840280582657 c356 22 2453736449 129991863475188542186962433 p378 23 2 2221121336321 c401 24 2689537 9409537 2091302909615592711027915305473 p370 25 2 c413 26 c413 27 2 11777 4992335766529 1951108443961589249 7450073824071074492712961 c353 28 1341797710693958466049 c392 29 2 c413 30 32281548289 c403 31 2 c413 32 380417 p408 33 2 9390456833 3963674521086587218433 47626820307938691671680001 c356 34 5276005877474111489 2428077765469564288001 c373 35 2 3686923099649 32921746284054353622529 c378 36 7681 2352087165684271813340161 p385 37 2 c413 38 1402322392520015983943087617 c386 39 2 c413 40 11777 46939956319379292161 p390