Sylvester's sequence

Sylvester's sequence is a sequence defined as follows:

S1 = 1

Sn+1 = S1*S2 ... * Sn

The sequence is named after James Joseph Sylvester. It can be used to show that there are infinitely many prime numbers, since it is easy to see that no temrs of the sequence have any prime factors in common.

Sylvester's sequence begins 1, 2, 3, 7, 43, 1807, 3,263,443, 10,650,056,950,807... and it achieves hyper-exponential growth rates, comparable to f(x) = 22 x and similar to the fuga- prefix.