In an arithmetic progression of form An + B, a prime p which does not divide the common difference A, will divide every p-th term of the progression.
For example, in any progression of form 60n + B, no matter what B is, every seventh term is divisible by the prime 7. That is because 7 does not divide 60. So if you want an AP that is greater than 7 in length (or just greater than 6 if no term of the AP equals 7 itself), you want a coefficient A which is divisible by 7.
If you want an AP of length 23, 24, 25, 26, 27, or 28, then the A in the formula An + B must be divisible by all the primes 2, 3, 5, 7, 11, 13, 17, 19, and 23.
This explains the 23# you see.
When, in the future, someone searches for an AP29 (and one not starting from the term 29, so B≠29), they would need to substitute 23# with 29#.