I mostly agree with what you say

Quote:

Originally Posted by

**ark600** Good luck with this one friend. :)

The only thing I would comment on is your comment about the string of eight 4's in a row being notable.

I don't think it is too notable; as you said *"no matter how far you go"*- there is a long way to go and you may notice many patterns which may or may not be of significance.

However I have found from experience that it is unusual to get a string of primes greater than four (however again there are different strings depending on exactly what you're looking at).

I'm aware of Euler's prime generating polynomial, http://mathworld.wolfram.com/images/...dEquation1.gif, and Wolfram has more to say on this. I think my comment about the sequence gradually increasing, especially the second sequence, is the most interesting part to my post because it seems to be linearly increasing (lacking a home computer, I'm unable to plot this out on a graph to see what happens as the sequence is extended further).

I don't know how deeply prime numbers have been explored. Other things come to mind. Regarding what I've posted, I do believe that both sequences are tending to infinity and I'm awaiting for someone to solve the puzzle.