$e |- ( ph -> N e. ( ZZ>= ` ; ; ; ; 1 0 0 0 0 ) ) $. $e |- ( ph -> R e. ( 1 ... ( |^ ` ( ( 2 log N ) ^ 5 ) ) ) ) $. $e |- ( ph -> A e. ( 1 ... ( |_ ` ( ( sqrt ` ( phi ` R ) ) x. ( 2 log N ) ) ) ) ) $. $p |- ( ph -> A < N ) $.
Eliminate lower values of n: the hypotheses of Theorem 2.2 only need to be checked for fairly large n.