I mostly agree with what you say
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).
Originally Posted by ark600
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.