Creating text files of exponents in standard notation

[cheesehead]

Originally Posted by Xyzzy

Is there anything special about the distribution of digits in the decimal expansion of a Mersenne prime, or is that a red herring? I know in binary form a Mersenne prime is all ones...

AFAIK no one's figured out any difference between Mersenne primes and Mersenne composites as far as their decimal expansions go. (And, of course, all Mersenne numbers 2^n-1 are strings of only 1-digits when written in binary form, regardless of whether 2^n-1 is prime or composite.)

There is at least one noticeable difference between the decimal expansions of Mersenne numbers (whether prime or composite) and the decimal expansions of other numbers in general. Because each Mersenne number is one less than a power-of-two, and powers'-of-two final decimal digits recur in a length-4 cycle of 2, 4, 8, 6, ..., the final decimal digits of Mersenne numbers also recur in a length-4 cycle of 1, 3, 7, 5, ... No Mersenne number has a final decimal digit of 0, 2, 4, 6, 8, or 9.

[Xyzzy]

http://www.isthe.com/chongo/tech/math/prime/mersenne.html