Prime gaps see this and this.I have noticed that when adding positive integers to prime numbers, the result may or may not yield another prime number. There does not seem to be a pattern as to when an addition yields another prime. However, there is a set of numbers that does not appear to ever yield another prime when added to a prime.
I do not know how large this set is, and have so far not found any particular pattern within this set, but for numbers from 1 to 360 there are 109 numbers that, when added to any prime, do not yield another prime. I have verified this for the first 500,000 primes.
From this set, 50 are primes themselves and 59 are not.
Also, when mapped on a circle, 80% of these 109 numbers appear 180 degrees opposite of each other.
Has anyone else ever played around with this?