Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Binary 2^n - 1 divisibility

  1. Mar 31, 2010 #1
    Dear All,
    I have to test if a binary number is divisible to
    2^n - 1 where n is even.
    Is there a test available for binary numbers like to test a divisibility by 3.
    Thanks in advance...
     
  2. jcsd
  3. Mar 31, 2010 #2
    You are talking about what, in general, is studied as Mersenne primes. Even powers are generally not prime. That's not hard to show.
     
    Last edited: Mar 31, 2010
  4. Mar 31, 2010 #3

    CRGreathouse

    User Avatar
    Science Advisor
    Homework Helper

    The sum of the base 2^n digits is divisible by 2^n-1 iff the number is, so you could use that. But I'm not sure how much of a speedup that gives.
     
  5. Mar 31, 2010 #4

    CRGreathouse

    User Avatar
    Science Advisor
    Homework Helper

    I interpreted the question as "how can I tell if N is divisible by 2^n-1" rather than "how can I tell if N divides 2^n-1".
     
  6. Mar 31, 2010 #5
    in my case n is even, not odd or prime
     
  7. Apr 1, 2010 #6
    Testing if a binary number is divisible by three is like testing if a number base 10 is divisible by 11. Alternately subtract than add the bits together and if your answer is divisable by three than the whole string was divisable by three.

    1100101 1-1+0-0+1-0+1=2 not divisible by 3
    1100110 1-1+0-0+1-1+0=0 divisible by three.
     
  8. Apr 1, 2010 #7

    CRGreathouse

    User Avatar
    Science Advisor
    Homework Helper

    3 is a funny number, since it's 2^1 + 1 and 2^2 - 1. You can use either type of test: add digits in blocks of two, or alternately add and subtract digits.

    10101011 = 10+10+10+11 = 1001 = 10 + 01 = 11 = 0 (mod 3)
    10101011 -> 1-0+1-0+1-0+1-1 = 11 = 0 (mod 3)

    The first preserves residues (not just divisibility) mod 3; the second works with smaller numbers (though twice as many).
     
  9. Apr 1, 2010 #8
    You can test if a number base 4 is a multiple of three the way you test if a number base ten is a multiple of nine. I saw your earlier post and decided to add some additional information. I don't know which approach , if either, gives you any calculating speed up.
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook