Okay. I found what I remembered. It is the Consequence Two of the Prime Number Theorem.

If I interpret this correctly, which is a big IF, then given that you know a prime and its position then the theorum provides a way of calculating a set of bounds within which the next prime will be located which reduces the search area considerably.

There are various refinements which reduce the search space further with the most recent being

In 1986 Te Riele showed there are more than 10180 successive integers x for which pi(x)>Li(x) between 6.62.10370 and 6.69.10370

However, what the hell the number? "6.62.10" is?, raised to any damn power, I haven't a clue :)

Examine what is said, not who speaks.
"Efficiency is intelligent laziness." -David Dunham
"Think for yourself!" - Abigail
Hooray!

In reply to Re: Finding the next larger prime. by BrowserUk
in thread Finding the next larger prime. by BrowserUk

Title:
Use:  <p> text here (a paragraph) </p>
and:  <code> code here </code>
to format your post, it's "PerlMonks-approved HTML":


  • Posts are HTML formatted. Put <p> </p> tags around your paragraphs. Put <code> </code> tags around your code and data!
  • Titles consisting of a single word are discouraged, and in most cases are disallowed outright.
  • Read Where should I post X? if you're not absolutely sure you're posting in the right place.
  • Please read these before you post! —
  • Posts may use any of the Perl Monks Approved HTML tags:
    a, abbr, b, big, blockquote, br, caption, center, col, colgroup, dd, del, details, div, dl, dt, em, font, h1, h2, h3, h4, h5, h6, hr, i, ins, li, ol, p, pre, readmore, small, span, spoiler, strike, strong, sub, summary, sup, table, tbody, td, tfoot, th, thead, tr, tt, u, ul, wbr
  • You may need to use entities for some characters, as follows. (Exception: Within code tags, you can put the characters literally.)
            For:     Use:
    & &amp;
    < &lt;
    > &gt;
    [ &#91;
    ] &#93;
  • Link using PerlMonks shortcuts! What shortcuts can I use for linking?
  • See Writeup Formatting Tips and other pages linked from there for more info.