1447 = (2 * 723) + 1 ;
hence not 2 divides 1447 by NAT_4:9; :: thesis:
1447 = (3 * 482) + 1 ;
hence not 3 divides 1447 by NAT_4:9; :: thesis:
1447 = (5 * 289) + 2 ;
hence not 5 divides 1447 by NAT_4:9; :: thesis:
1447 = (7 * 206) + 5 ;
hence not 7 divides 1447 by NAT_4:9; :: thesis:
1447 = (11 * 131) + 6 ;
hence not 11 divides 1447 by NAT_4:9; :: thesis:
1447 = (13 * 111) + 4 ;
hence not 13 divides 1447 by NAT_4:9; :: thesis:
1447 = (17 * 85) + 2 ;
hence not 17 divides 1447 by NAT_4:9; :: thesis:
1447 = (19 * 76) + 3 ;
hence not 19 divides 1447 by NAT_4:9; :: thesis:
1447 = (23 * 62) + 21 ;
hence not 23 divides 1447 by NAT_4:9; :: thesis:
1447 = (29 * 49) + 26 ;
hence not 29 divides 1447 by NAT_4:9; :: thesis:
1447 = (31 * 46) + 21 ;
hence not 31 divides 1447 by NAT_4:9; :: thesis:
1447 = (37 * 39) + 4 ;
hence not 37 divides 1447 by NAT_4:9; :: thesis:

end;

then for n being Element of NAT st 1 < n & n * n <= 1447 & n is prime holds
not n divides 1447 by XPRIMET1:24;
hence 1447 is prime by NAT_4:14; :: thesis: