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I don't think this is right. There are certainly prime gaps that exceed 600. In fact, the higher you up (in the number line), the higher these prime gaps tend
by ipince 13y ago
I don't think this is right.
There are certainly prime gaps that exceed 600. In fact, the higher you up (in the number line), the higher these prime gaps tend to get.
http://en.wikipedia.org/wiki/Prime_gap http://en.wikipedia.org/wiki/Prime_gap
What's being said here is that despite of that, there will always be prime gaps smaller than 600. No matter how high you go, you can always find a pair of primes that are separated by less than 600. In other words, pick the biggest N you can ever dream of, and there will exist primes p1 and p2 such that they are both bigger than N and their difference is smaller than 600.
- lutusp 13y agoYes, you're right, and it's too late for me to either delete or edit my original post. :( In light of that, I think the discussion and work revolves around discovering the smallest gap as the numbers themselves become larger and tend toward infinity. Obviously the very smallest prime gap is that between 2 and 3, i.e. 1, and there are a great number of primes separated by 2, and the Twin Prime Conjecture asserts that there will always be occasional pairs of primes separated by 2 no matter how large the numbers themselves become. The present work is in part meant to put that conjecture on a more analytical footing. I would love to delete my original post.