given a, b, c being Prime such that a,b,c are_mutually_distinct and
A1: (8 |^ 2) + 1 = (a * b) * c ; :: according to NUMBER07:def 2 :: thesis: contradiction
8 |^ 2 = 8 * 8 by WSIERP_1:1;

per cases then ( ( a * b = 1 & c = 65 ) or ( a * b = 5 & c = 13 ) or ( a * b = 13 & c = 5 ) or ( a * b = 65 & c = 1 ) ) by A1, Th31;

suppose ( a * b = 1 & c = 65 ) ; :: thesis: contradiction

hence contradiction by XPRIMES0:65; :: thesis: verum

end;

suppose ( a * b = 5 & c = 13 ) ; :: thesis: contradiction

hence contradiction by XPRIMES1:5; :: thesis: verum

end;

suppose ( a * b = 13 & c = 5 ) ; :: thesis: contradiction

hence contradiction by XPRIMES1:13; :: thesis: verum

end;

suppose ( a * b = 65 & c = 1 ) ; :: thesis: contradiction

hence contradiction by XPRIMES0:1; :: thesis: verum

end;

end;