 mersenneforum.org Factors for the differences between Mersenne numbers
 Register FAQ Search Today's Posts Mark Forums Read 2020-10-14, 19:32 #1 a nicol   Nov 2016 52 Posts Factors for the differences between Mersenne numbers It seems the differences between all Mersenne numbers have factors via: a1 = Mersenne exponent a2 = next Mersenne exponent b = (a2-a1)/2 (2^a1 * 3) * ((4^b - 1)/3) For example: (2^26-1) - (2^12-1) = 67104768 (2^12 * 3) * ((4^7 - 1)/3) = 12288 * 5461 = 67104768 If ((4^b - 1)/3) mod 3 is not 0, these factors are in lowest terms ratio. When ((4^b - 1)/3) mod 3 = 0, the lowest terms can be found by: (2^a1):((4^b - 1)/9) Is this always the case? Some factors for the first differences of Mersenne primes - http://oeis.org/A139231 24 * 1 = 24 96 * 1 = 96 384 * 21 = 8064 24576 * 5 = 122880 393216 * 1 = 393216 1572864 * 1365 = 2146959360 6442450944 * 357913941 = 2305843007066210304 6917529027641081856 * 89478485 = 618970017336847128235868160 1856910058928070412348686336 * 87381 = 162258657859193720701440560726016   2020-10-15, 09:53 #2 LaurV Romulan Interpreter   Jun 2011 Thailand 217018 Posts Think about how mersenne numbers are represented in binary, and what's happen if you subtract one from another. hint: you get a mersenne number with an even exponent, multiplied by a power of two.  Thread Tools Show Printable Version Email this Page Similar Threads Thread Thread Starter Forum Replies Last Post bhelmes Miscellaneous Math 8 2020-09-14 17:36 siegert81 Math 23 2014-03-18 11:50 devarajkandadai Miscellaneous Math 6 2006-01-04 22:44 asdf Math 17 2004-07-24 14:00 Fusion_power Math 13 2003-10-28 20:52

All times are UTC. The time now is 14:40.

Sat Jan 23 14:40:48 UTC 2021 up 51 days, 10:52, 0 users, load averages: 2.27, 2.35, 2.60