As afinal observation, we can exploit factorials, which by design have many factors, in order to prove that no arithmetic sequence ofnumbers, that is to say one of the form a, a+b, a+2b, a+3b,…can consist only ofprimes as it is possible to show that the gap between successive primes can be arbitrarily large while the common difference between consecutive members of the previous sequence is fixed at b. To see this,consider the sequence ofn consecutive integers: