S U R F
C A L M
E X P O
T I N Y

Each of the above letters represents a positive integer smaller than 200. In some order they represent an arithmetic sequence. Overall, the grid as presented is a magic square, with each row, each column and each of the two large diagonals adding to the same value.

Also, each of the letters in P-R-I-M-E-S represents a prime number, and in themselves they also form an ascending arithmetic sequence, in the order P-R-I-M-E-S.

What is this magic square?

First find 6 primes under 200 that are in arithmetic progression.

Then find a magic square using numbers 1 through 16, where the positions marked by P, R, I, M, E and S are in arightmetic sequence, not necessarily without gaps, but in order.

Then find a linear relation between the prime sequence and the P-R-I-M-E-S sequence.