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2011-03-04, 16:39   #14
sascha77

Jan 2010
germany

2×13 Posts

Quote:
 Originally Posted by R.D. Silverman Note that 34 = 2^1 + 2^5 and 34^255 = 34 mod 255. Enough said? Not enough? Note that 65 = 2^0 + 2^6 and 65^510 = 1 mod 511. Still not enough? 72 = 2^3 + 2^6 and 72^510 = 1 mod 511. I am sure that one could find additional counter-examples. There was no reason to believe that an integer with Hamming weight 2 could not be a false witness to Mersenne numbers.

OK. my fault. I forgotten to mention that mersenne Numbers are Numbers of the Form n = 2^{p}-1 with:
The variable p is prime !!!!!

If the mersenne number $n$ with $n=2^{p}-1$ is also prime then this
Mersenne Number is called Mersenne Prime.

Your example with mod 511 -> $511 -> 2^{9}-1$

9 is not prime. -> 511 is not a mersenne number.

And 255 = $2^{8}-1 .$

-> 8 is also not prime -> 255 is not a mersenne number

Last fiddled with by sascha77 on 2011-03-04 at 16:44