mersenneforum.org Are all MP# produced by logarithmic numbers beginning with 2 or 8 in ASCII?
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2021-08-07, 20:47   #12
Dobri

"刀-比-日"
May 2018

13·19 Posts

Quote:
 Originally Posted by Dr Sardonicus 'Twas brillig, and the slithy toves did gyre and gimbal in the wabe...
It was four o'clock in the afternoon and the slimy, smooth and active badgers did go round and round scratching like a dog and made holes like a gimlet in the grass plot around a sundial on the side of a hill being soaked by rain.

2021-08-09, 03:44   #13
Dobri

"刀-比-日"
May 2018

13·19 Posts

Quote:
 Originally Posted by WilliamJohnCox Might there be some relationship to the fact that in base 10, some perfect numbers end in 6s and others in 8s.
The even perfect numbers (2^(p-1))(2^p - 1) end in:
6, for the even Mersenne prime exponent p = 2, as 2x3=6;
6, for odd Mersenne prime exponents p = 4k + 1, k>0; and
8, for odd Mersenne prime exponents p = 4k + 3, k>=0.
It can be deduced from the observation that every even perfect number is represented in the base-2 numeral system as p ones followed by p-1 zeros.

 2021-08-12, 14:38 #14 WilliamJohnCox   Aug 2021 2 Posts Thank You Thanks to all for your courteous and helpful comments. ~wm

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