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Forum: Miscellaneous Math 2021-08-09, 03:44
Replies: 13
Views: 1,329
Posted By Dobri
The even perfect numbers (2^(p-1))(2^p - 1) end...

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...
Forum: Miscellaneous Math 2021-08-07, 20:47
Replies: 13
Views: 1,329
Posted By Dobri
It was four o'clock in the afternoon and the...

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...
Forum: Miscellaneous Math 2021-08-07, 15:54
Replies: 13
Views: 1,329
Posted By Dobri
This actually is valid for ALL odd positive...

This actually is valid for ALL odd positive integers (both non-prime and prime).

For all odd integers p = 4k + 1, the first digit of 2^p in the base-16 numeral system is 2.
For instance, 9 = 3x3...
Forum: Miscellaneous Math 2021-08-07, 13:34
Replies: 13
Views: 1,329
Posted By Dobri
Note that this is valid for ALL odd prime...

Note that this is valid for ALL odd prime exponents but not just the Mersenne prime exponents.
For all odd primes p = 4k + 1, the first digit of 2^p in the base-16 numeral system is 2.
For all odd...
Forum: Miscellaneous Math 2021-08-07, 06:45
Replies: 13
Views: 1,329
Posted By Dobri
ADD116 = 4449710 One can use Wolfram...

ADD116 = 4449710

One can use Wolfram language (BaseForm[2^44497, 16]) to show the entire result (2000000000000...000000000000) in the base-16 numeral system. The first digit in this case is 2...
Forum: Miscellaneous Math 2021-08-07, 05:05
Replies: 13
Views: 1,329
Posted By Dobri
Yes, the first digit of 2^MersennePrimeExponent...

Yes, the first digit of 2^MersennePrimeExponent in the base-16 numeral system is always 2 or 8 except for M(1) which is 2^2 = 4.
This is of no value for narrowing the search for Mersenne primes...
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