A friend of mine posed an interesting prime number theorem I have never seen before. He claims he thought this up on his own.
Suppose you take any prime number, then double it. Say, 2p.
Then, accordingly to his theory, you can add or subtract any integer 2 through 9 and get another prime number.
Say we take 1009, double it and get 2018. If we add 9 we get another prime.
Which is 2027. This is prime.
Can we prove or disprove in the general case and find an instance where it doesn't hold?.
Intuitively, one would think that it will break down after the numbers get so big.