Primes in arithmetic progression with the first term and the common difference of minimum values.

Question

The primes that form the subject of this question are of the form
P = Pi + Δi (0, 1, 2, 3, Pi-1). So far, there are known only 7 sets of this type. They have the following first terms and common differences: Pi = {3, 5, 7, 11, 13, 17, 19} and Δi = {2, 6,150, 1536160080, 9918821194590, 341976204789992332560, 2166703103992332274919550} If one neglects the first two differences 2 and 6 as insignificant, and plots the function Ln Δi = f(Pi) one obtains a straight line. Since there aren't too many linear correlations linking directly the prime numbers to relevant quantities, it would be interesting to calculate the difference Δ23 pertaining to the prime Pi = 23, and see if the point corresponding to its logarithm is situated on the above line. Knowing that Δ23 is on the order of 10^32, and that all differences Δ(Pn) are multiple of the primorial P(n-1)#, can someone approximate the feasibility of computing Δ23 using: a) an ordinary computer, b) a very powerful one and c) a polymath type collaboration ?