May that those who are better qualified to correct
my assumptions, but here's my take...
Number Theory. Facinating field of
study. Many seemingly unrelated ideas show interconnectedness.
Example; take the series 1/(n-squared) where n goes from 1 to infinity; sum all
the terms together and you get the value (pi-squared)/6. How does the
summation of the inverse of all squares relate to the ratio of a
circle's circumference to its diameter?!
How about another value that shows up all the time?
- e the logarithmic constant.
The distribution of primes across the natural
number line has a logarithmic form. So we have a way of closely
estimating the nth prime P[n} but "close" just doesn't cut it does it? The
fact is, as simple the concept of a prime is, we cannot say what the nth prime
is. Nor can we say if P[n] is prime, what is P[n+1]? We
know there are twin primes, but we don't know if there are an endless number of
them. We know there are Mersenne primes, but we don't know if
there are an endless number of them either.
The way I see it. If we can find rhyme or
reason to the exact nature of Mersenne primes (hopefully acquiring more
data points will spur a new line of thought), that may help with the nature of
primes in general. And that will undoubtedly have an impact across many
current Number Theory dilemmas. Results from that would quite
possibly become the glue to a Unified Theory.
If you can't find the answer to a whole problem,
break it down and try solving some of the pieces. If you solve a piece of
the problem, the larger problem becomes easier. That's the way I
think of GIMPS.
aka DigitalConcepts
----- Original Message -----
|
- Re[2]: Mersenne: Dissed again mersenne
- Re: Mersenne: Dissed again Del S. Brand
- Re: Mersenne: Dissed again Jeff Woods
- Re: Mersenne: Dissed again spike66
- Re: Mersenne: Dissed again Justin Valcourt
- Re: Mersenne: Dissed again Jeff Woods
- Re: Mersenne: Dissed again Herman De Wael
- Re: Mersenne: Dissed again Daidalos
- Re: Mersenne: Dissed again spike66
- RE: Mersenne: Dissed again Aaron Blosser
- Re: Mersenne: Dissed again C. Garrison
- Re: Mersenne: Dissed again Jason Papadopoulos
- RE: Mersenne: Dissed again Paul Leyland
- Re: Mersenne: Dissed again ModularTao
- Re: Mersenne: Dissed again Richard Woods
- Re: Mersenne: Dissed again Gareth Randall