Prime Number Gaps

(Image credits: https://commons.wikimedia.org/wiki/User:David_Eppstein/Gallery)

An interesting topic is the gap between prime numbers. A prior posts discussed twin primes (those with a gap of 2). As we review the list of prime numbers, the first few gaps are mundane. The minimum gap is between 2 and 3. Since all prime numbers > 2 are odd, all subsequent gaps are at least 2. Progressing through the list of prime numbers below 100, most gaps are 2, 4 or 6. Just as we near 100, the gap between the primes 97 and 89 is 8. This observation invites the question of just how high this gap can become. 

A spreadsheet with the first 1229 primes is linked here.

The gaps continue to increase and the largest gap in the first 1229 primes is 36 and occurs occurs between 9551 and 9587.

A Mathematica program to generate the first 1000 prime gaps is:

Table[Prime[n+1]-Prime[n],{n,1000}]