1327 = (2 * 663) + 1 ;
hence not 2 divides 1327 by NAT_4:9; :: thesis:
1327 = (3 * 442) + 1 ;
hence not 3 divides 1327 by NAT_4:9; :: thesis:
1327 = (5 * 265) + 2 ;
hence not 5 divides 1327 by NAT_4:9; :: thesis:
1327 = (7 * 189) + 4 ;
hence not 7 divides 1327 by NAT_4:9; :: thesis:
1327 = (11 * 120) + 7 ;
hence not 11 divides 1327 by NAT_4:9; :: thesis:
1327 = (13 * 102) + 1 ;
hence not 13 divides 1327 by NAT_4:9; :: thesis:
1327 = (17 * 78) + 1 ;
hence not 17 divides 1327 by NAT_4:9; :: thesis:
1327 = (19 * 69) + 16 ;
hence not 19 divides 1327 by NAT_4:9; :: thesis:
1327 = (23 * 57) + 16 ;
hence not 23 divides 1327 by NAT_4:9; :: thesis:
1327 = (29 * 45) + 22 ;
hence not 29 divides 1327 by NAT_4:9; :: thesis:
1327 = (31 * 42) + 25 ;
hence not 31 divides 1327 by NAT_4:9; :: thesis:

end;

then for n being Element of NAT st 1 < n & n * n <= 1327 & n is prime holds
not n divides 1327 by XPRIMET1:22;
hence 1327 is prime by NAT_4:14; :: thesis: