Quote:
Originally Posted by kruoli
<snip>
Edit, clarification: By 1…1, I do not mean only ones. It should be understood as starting with a one, other digits, and ending with a one.

For possible future reference, giving the first two (or more) most significant digits and the last two (or more) digits of a manydigit number is common practice. Sometimes the number of intervening digits is also given.
In the present instance, 14...91 or 14... (24862044 digits) ...91 would be much clearer.
The most significant digits of M
_{p} are determined by the fractional part of p*log(2)/log(10).
EDIT: Although there is no upper bound on the number of leading 1's in a Mersenne number 2
^{n}  1, or AFAIK for 2
^{p}  1 with p prime, there
is an upper bound for the number of terminal 1's. Three. The proof is easy.
(The Mersenne number 2
^{888689}  1 has 4 leading 1's and 3 terminal 1's. M
_{888689} has a small factor q = 24*p + 1, and the cofactor is proven composite.)