Smallest number at distance 3n from nearest prime.

[Dean Hickerson]

Mostly to Jonathan Post:

> The corrected 2nd formula, verbally, becomes:
> "Largest number less than OR EQUAL TO the mean of the smallest prime
> gap of size at least 6n.

Maybe I don't understand what you mean by the mean of the gap.  I'm
assuming that if p and q are consecutive primes then the mean of their
gap is (p+q)/2.  Except for the gap from 2 to 3, that's always an
integer, so the largest integer less than or equal to the mean is equal
to the mean.  But unless the smallest prime gap of size at least 6n has
size exactly 6n, that won't be equal to the smallest number at distance
3n from the nearest prime.

For example, the first prime gap of size at least 60 actually has size 72,
from p to p+72, where p=31397.  The smallest number at distance 30 from
the nearest prime is p+30, but the mean of the gap is p+36.

Dean Hickerson
dean at math.ucdavis.edu