Re: Mersenne: Dissed again

[C. Garrison]

May that those who are better qualified to correct my assumptions, but here's my take...   I look at GIMPS' finding of large primes as an avenue of advancing the concept of a Unified Theory for Mathematics - much like that which you hear about in Physics.   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 www.teamprimerib.com   ----- Original Message ----- From: Del S. Brand To: [EMAIL PROTECTED] Sent: Wednesday, October 23, 2002 3:14 AM Subject: Re: Mersenne: Dissed again I always get asked what is the purpose or use for such large prime numbers. Since I'm not a math geek, I don't know what to tell them.   Any ideas?   D.Brand