One thing that strikes me after following @metanumbers is how many large numbers have just two factors. I had this intuition that most large numbers have several factors, but that seems generally not true.
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If that were true then particularly large prime numbers would be either non existant or rare enough we could just document them all. The distance between primes is larger for larger numbers but this distance grows at a slower rate than the size of the numbers
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The Relationship is roughly logarithmic to be specific. The rate at which primes are seen decreases at a rate of inverse of the natural logarithm, roughly speaking.
