1217 = (2 * 608) + 1 ;
hence not 2 divides 1217 by NAT_4:9; :: thesis:
1217 = (3 * 405) + 2 ;
hence not 3 divides 1217 by NAT_4:9; :: thesis:
1217 = (5 * 243) + 2 ;
hence not 5 divides 1217 by NAT_4:9; :: thesis:
1217 = (7 * 173) + 6 ;
hence not 7 divides 1217 by NAT_4:9; :: thesis:
1217 = (11 * 110) + 7 ;
hence not 11 divides 1217 by NAT_4:9; :: thesis:
1217 = (13 * 93) + 8 ;
hence not 13 divides 1217 by NAT_4:9; :: thesis:
1217 = (17 * 71) + 10 ;
hence not 17 divides 1217 by NAT_4:9; :: thesis:
1217 = (19 * 64) + 1 ;
hence not 19 divides 1217 by NAT_4:9; :: thesis:
1217 = (23 * 52) + 21 ;
hence not 23 divides 1217 by NAT_4:9; :: thesis:
1217 = (29 * 41) + 28 ;
hence not 29 divides 1217 by NAT_4:9; :: thesis:
1217 = (31 * 39) + 8 ;
hence not 31 divides 1217 by NAT_4:9; :: thesis:

end;

then for n being Element of NAT st 1 < n & n * n <= 1217 & n is prime holds
not n divides 1217 by XPRIMET1:22;
hence 1217 is prime by NAT_4:14; :: thesis: