let k be Nat; :: thesis: for p being Prime st p * p <= k & k < 529 & not p = 2 & not p = 3 & not p = 5 & not p = 7 & not p = 11 & not p = 13 & not p = 17 holds
p = 19
let p be Prime; :: thesis: ( p * p <= k & k < 529 & not p = 2 & not p = 3 & not p = 5 & not p = 7 & not p = 11 & not p = 13 & not p = 17 implies p = 19 )
assume ( p * p <= k & k < 529 ) ; :: thesis: ( p = 2 or p = 3 or p = 5 or p = 7 or p = 11 or p = 13 or p = 17 or p = 19 )
then p * p < 23 * 23 by XXREAL_0:2;
hence ( p = 2 or p = 3 or p = 5 or p = 7 or p = 11 or p = 13 or p = 17 or p = 19 ) by Th15, NAT_4:1; :: thesis: verum