let s be positive Nat; :: thesis: (2 |^ (2 |^ ((6 * s) + 2))) + 21 is composite
set m = (2 |^ (2 |^ ((6 * s) + 2))) + 21;
A1: (2 |^ (2 |^ ((6 * s) + 2))) + 21 >= (2 |^ 256) + 21 by Lm16, XREAL_1:6;
2 <= ((2 |^ 256) + 19) + 2 by NAT_1:11;
hence (2 |^ (2 |^ ((6 * s) + 2))) + 21 >= 2 by A1, XXREAL_0:2; :: according to NUMBER02:def 1 :: thesis: not (2 |^ (2 |^ ((6 * s) + 2))) + 21 is prime
(2 |^ (2 |^ ((6 * s) + 2))) + 21 <> 37 by Lm16, Lm3, PEPIN:66;
hence not (2 |^ (2 |^ ((6 * s) + 2))) + 21 is prime by Th82; :: thesis: verum