Why get into GIMPS?

[ThomRuley]

Yesterday I was telling someone about GIMPS, and the question came up, "why are you doing this?" I explained that this had been the realization of a childhood dream to look for large prime numbers because they had always fascinated me. Then I thought, why not start a thread asking why others got into GIMPS?

So the question is, why did you start in GIMPS?

[Prime Monster]

http://ws9.jobnegotiator.com/html/whydc.html :D

heretic

[trif]

I like factoring. To me it is the fascination with a distribution that is utterly deterministic and yet seemingly so random.

[Gary Edstrom]

In my case, it was because I enjoy problems that are easy to state, but difficult to solve. The concept of prime numbers is so simple that even people with extremely limited math knowledge can understand what a prime number is. Yet proving that a large number is prime proves extremely computation intensive.

Other problems that I enjoy playing with include:
1. 3N+1 (Collatz) problem
2. Fermat's Last Theorem (While FMT has been proved, it's proof requires a high level of number theory that most of us don't have. It would be nice to find a simpler proof.
3. The 4 Color Theory (Once again, it has been proved, but it's proof requires the aid of a computer to attempt to 4-color numerous subtypes. Once again, it would be nice to find a simpler proof.

[eepiccolo]

Some people's stories are here: http://www.mersenneforum.org/viewtopic.php?t=516

[ET_]

3N+1 (Collatz) problem

Did you also work with Eric Roosendaal project? :-)

Luigi

[Gary Edstrom]

Originally Posted by ET_

Did you also work with Eric Roosendaal project? :-)

Luigi

No, I simply play around with new approaches to the problem, hoping that maybe I will stumble onto something useful. I realize that all of the obvious approaches have been tried many times before, so I am looking for odd ways in which to restate the problem that may lead to some insite on the solution.

[ET_]

So you may be interested in those links...

http://personal.computrain.nl/eric/wondrous/
http://www.cecm.sfu.ca/organics/papers/lagarias/
http://www.ieeta.pt/~tos/3x+1.html
http://mathworld.wolfram.com/CollatzProblem.html
http://www.cecm.sfu.ca/organics/papers/lagarias/paper/html/superLagarias.html

Sorry for the half-topic... :D

Luigi

[Orgasmic Troll]

Okay, there seems to be some knowledge here about the 3x+1 problem, and I was wondering if someone had some insight for some things I've observed.

If you make a tree starting with 1 and then branch off to the numbers that would iterate to the number at the top (i.e. 1 --> 2 --> 4 --> 8 --> 16 --> 32, 15 --> 64,10 --> (128,21) , (20,3) --> etc. ) why are the left and right branches off of 16 identical in structure? why do numbers that are one off end up next to each other if you write each generation on the same line (for example, 341 and 340 are next to each other, 53 and 52, 1365 and 1364, 213 and 212 are also next to each other)

There's a picture of this tree somewhere, if I can find the link, I'll post it, but if you've worked on the problem and followed a similar train of thought, I think you'll understand what I'm talking about

[ET_]

If you make a tree starting with 1 and then branch off to the numbers that would iterate to the number at the top (i.e. 1 --> 2 --> 4 --> 8 --> 16 --> 32, 15 --> 64,10 --> (128,21) , (20,3) --> etc. ) why are the left and right branches off of 16 identical in structure?

Are you referring to this?

http://www-personal.ksu.edu/~kconrow/gentrees.html

Luigi

[Orgasmic Troll]

Something like that :) without stripping the even integers though