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Old 2011-03-04, 16:39   #14
sascha77
 
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Jan 2010
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Quote:
Originally Posted by R.D. Silverman View Post
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
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