Quote:
Originally Posted by enzocreti
19 (a twin) is the smallest prime such that between it and the closest square surrounding it (16) there is a prime 17.
Another example is 41...between 41 and 36 there is 37. (36 is the closest square surrounding 41, being 7^2 further away than 6^2).
89 is the first non twin prime with this property, any Others?

The squares get sparse much faster than the primes, so once you get out of the very small numbers, there are going to many primes between adjacent squares. There are 23 primes between (100)^2 and (101)^2, still small numbers.