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2022-04-06, 14:06   #320
Dr Sardonicus

Feb 2017
Nowhere

171D16 Posts

Quote:
 Originally Posted by kruoli 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 many-digit 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 Mp 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 2n - 1, or AFAIK for 2p - 1 with p prime, there is an upper bound for the number of terminal 1's. Three. The proof is easy.

(The Mersenne number 2888689 - 1 has 4 leading 1's and 3 terminal 1's. M888689 has a small factor q = 24*p + 1, and the cofactor is proven composite.)

Last fiddled with by Dr Sardonicus on 2022-04-06 at 19:47 Reason: As indicated