Numbers from the Green-Tao theorem

The Green-Tao theorem asserts that there are arithmetic progressions of prime numbers that are arbitrarily longB. Green, T. Tao, The primes contain arbitrarily long arithmetic progressions (2004, accessed 2020-11-10), and some of the common differences of these sequences can be large even if the sequence is short. For example, the smallest common difference of the first 19-term arithmetic sequence of prime numbers is \(2,166,703,103,992,332,274,919,550\)OEIS, sequence A061558 (Accessed 2020-11-10), or about 2 septillion using the short scale.
Even larger numbers come from a weak upper bound given by Terence Tao that the first arithmetic progression of length \(n\) of primes has all of its entries less than \(2^{2^{2^{2^{2^{2^{2^{100n}}}}}}}\)UCLA, Terence Tao: Structure and Randomness in the Prime Numbers (2009, accessed 2020-11-10) (E[2](100n)#7 using Hyper-E Notation).
==Approximations==
19-term sequence number:
Upper bound for entries in 100-long sequence:
==Sources==
Category:Prime numbers
Category:Tetration level
Category:Class 2