Actually, I was wondering if there was a way to predict the lines without knowing the primes in question... an approximation, at the very least.

I was thinking that the PNT could provide 2 values which you could use to output 2 lines (the % of ∞), then you could potentially predict a high and low limit range for both factors of the product of 2 primes, P. By choosing the smallest range, you'd be able to optimize factorization of large numbers. Depending on the (P) in question, it might speed things up considerably. Knowledge of the ranges would also, I believe, allow further optimizations based on other number theory concepts, although I don't know of any specifically...

I'm working with Python, currently... is there a specific programming language that is designed for math, or a package thats not as expensive as Mathematica? Pythons great for simple things, but not as optimized as I'd like it to be, and C is a pain in the butt for me.

Danny Fleming <

bsmath2000@...> wrote: If I am understanding correctly, all you have to do is take each prime and do the following:

3-9-15-... (3+2*3n), 5-15-25-... (5+2*5n), the general formula is p+2*pn. The even numbers

are all factors of the only even prime 2 (2-4-6-8-...).

Sincerely yours,

Danny Karl Fleming

Alec Smart <

pvp4tw@...> wrote:

Ahh, good catch. Yeah, my numbers were off... I'm kind of interested in what the graphs look like, because I've never encountered another series of numbers that look like the trail of a bouncing ball. I'm trying to figure out the significance of the bounces :)

If the lines change in some predictable manner, which I think they do, then couldn't you describe a function that takes X as the Xth prime number and outputs the numbers in it's line, without knowing the Xth prime number to begin with? Unless you have to know all primes preceding X.

E.G. output the graph for 7 by taking 4 as the argument?

I've found that by tweaking the graph for a prime, it intersects all primes greater than itself at the point where X is equal to the product of the two. For 7 and 13, it intersects at 91. If you didn't have to know the prime itself, then solving for prime factors would be simplified just by knowing the point of intersection.

Anyway, I appreciate all the comments, I'm beginning to see some of the difficult oddities in prime numbers.

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