At 07:42 PM 1999/03/06 -0600, "Robert G. Wilson v, PhD ATP"
<[EMAIL PROTECTED]> wrote:
>
>
>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, ... , .
The above is a steadily increasing sequence, which could be used to advantage.
One could represent delta n for additional compression.
1,1,1,1,2,1,1,3,7,6,4,3,67,12,... has fewer bits.
Then put the message through something standard like Huffman or LZH.
The difficulty is that with each step the message becomes more obscure.
And the essence of a message is to communicate something.
Ken
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