let k be Nat; :: thesis: for p being Prime st p * p <= k & k < 5041 & not p = 2 & not p = 3 & not p = 5 & not p = 7 & not p = 11 & not p = 13 & not p = 17 & not p = 19 & not p = 23 & not p = 29 & not p = 31 & not p = 37 & not p = 41 & not p = 43 & not p = 47 & not p = 53 & not p = 59 & not p = 61 holds
p = 67
let p be Prime; :: thesis: ( p * p <= k & k < 5041 & not p = 2 & not p = 3 & not p = 5 & not p = 7 & not p = 11 & not p = 13 & not p = 17 & not p = 19 & not p = 23 & not p = 29 & not p = 31 & not p = 37 & not p = 41 & not p = 43 & not p = 47 & not p = 53 & not p = 59 & not p = 61 implies p = 67 )
assume ( p * p <= k & k < 5041 ) ; :: thesis: ( p = 2 or p = 3 or p = 5 or p = 7 or p = 11 or p = 13 or p = 17 or p = 19 or p = 23 or p = 29 or p = 31 or p = 37 or p = 41 or p = 43 or p = 47 or p = 53 or p = 59 or p = 61 or p = 67 )
then p * p < 71 * 71 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 or p = 23 or p = 29 or p = 31 or p = 37 or p = 41 or p = 43 or p = 47 or p = 53 or p = 59 or p = 61 or p = 67 ) by Th37, NAT_4:1; :: thesis: verum