It is true that 121857779 is a prime, but that is insignificant.
You have found another AP:
140980475961780677+121745694*23#*n for n=0..20
and 121745694 is not a prime. (It is 2 * 3 * 7^2 * 414101.)
Not sure if this is what you ask, but from the list of your AP finds, if you click on each line, you can see the primes that constitute the progression.
For an AP21, there are 21 primes in the progression, and they are positioned with uniform spacing on a number line.