Re: Am I a crank?


skialps10@xxxxxxxxx wrote:

I like to think I came up with a fairly unique way of modeling the
Goldbach Conjecture and was thinking of programming it up to see if I
could find any patterns. I simply don't have the background to know of
any lemmas to make the job easier and don't plan on using calculus. In
the exceptionally unlikely event that I found some pattern I was
planning on formalizing it.

Does this sound crank-like?

Mathematicians can't reasonably claim that it is "crank-like", because
it is the kind of thing they do themselves.

Here's something I think you ought to think about:

Goldbach's conjecture is very likely to be true for simple
probabilistic reasons. There are lots of prime numbers, and for a large
even integer, probabilistic reasoning suggests that it is very likely
that some pair of prime numbers will add up to that even number. The
key to such an argument is to interpret the Prime Number Theorem as a
probabilistic assertion, telling us that the "probability" that a
randomly picked integer of size N will be prime is 1/log(N). Then
combined with the fact that Goldbach's conjecture has actually been
tested for all even integers up to about 10^18, we are led to conclude
that the conjecture is true with a probability of about 1-10^(-4000).

It could be argued that since the mathematics community does expend a
great deal of energy in the search for formal proofs of conjectures
having ridiculously high probabilities of being true, and often turns a
blind eye to the probabilistic arguments, the mathematics community
itself engages in crank-like behavior.

.

Relevant Pages

  • Re: Evidence for Big Leaps?
    ... single nucleotide mutation can be expressed, ... probability calculation leads to an erroneous conclusion. ... RM conjecture, an additional constraint on the final ... substratum) of the IA algorithms. ...
    (talk.origins)
  • Re: Computability
    ... I am sorry if my difficulties with exposition led you to believe ... And the conjecture _is_ interesting. ... probability and that that order will be the order of exposition next ... client cognitions in a pattern of correalations like "when client ...
    (sci.math)
  • Re: x^n + y^n (mod p)
    ... the probability that ... conjecture is false is the infinite product ... hence the infinite product is 0. ... number theory is full of innocent-looking problems that turn out ...
    (sci.math)
  • Re: x^n + y^n (mod p)
    ... the probability that ... conjecture is false is the infinite product ... hence the infinite product is 0. ... For each positive integer n, and all sufficiently large primes p ...
    (sci.math)