Ken Kriesel wrote:
>
> Stating the exponents rather than the base10 representation seems to
> me to be almost the ultimate in data compression. (2^521-1 has 157 digits;
> the advantage increases along with the exponent, uh, exponentially.)
>
2^p -1 is prime for the following ps: 2, 3, 5, 7, 13, 17, 19, 31, 61, 89, 107,
127, 521, 607, 1279, 2203, ..., 1257787, 2976221, 3021377, ... . But all of
these are primes. Two is the first prime, denoted as p(1), three is p(2), five
is p(3), etc. So therefore the best data compression is represent the Mersenne
primes is to denote the n, such that 2^p(n) -1 is prime for the following ns:
1, 2, 3, 4, 6, 7, 8, 11, 18, 24, 28, 31, 98, 111, 207, 328, 339, 455, 583, 602,
1196, 1226, 1357, 2254, 2435, 2591, 4624, 8384, 10489, 12331, 19292, 60745,
68301, 97017, 106991, 215208, 218239, ... , .
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