let k be Nat; :: thesis: for p being Prime st p * p <= k & k < 289 & not p = 2 & not p = 3 & not p = 5 & not p = 7 & not p = 11 holds
p = 13
let p be Prime; :: thesis: ( p * p <= k & k < 289 & not p = 2 & not p = 3 & not p = 5 & not p = 7 & not p = 11 implies p = 13 )
assume ( p * p <= k & k < 289 ) ; :: thesis: ( p = 2 or p = 3 or p = 5 or p = 7 or p = 11 or p = 13 )
then p * p < 17 * 17 by XXREAL_0:2;
hence ( p = 2 or p = 3 or p = 5 or p = 7 or p = 11 or p = 13 ) by Th11, NAT_4:1; :: thesis: verum