3067 = (2 * 1533) + 1 ;
hence not 2 divides 3067 by NAT_4:9; :: thesis:
3067 = (3 * 1022) + 1 ;
hence not 3 divides 3067 by NAT_4:9; :: thesis:
3067 = (5 * 613) + 2 ;
hence not 5 divides 3067 by NAT_4:9; :: thesis:
3067 = (7 * 438) + 1 ;
hence not 7 divides 3067 by NAT_4:9; :: thesis:
3067 = (11 * 278) + 9 ;
hence not 11 divides 3067 by NAT_4:9; :: thesis:
3067 = (13 * 235) + 12 ;
hence not 13 divides 3067 by NAT_4:9; :: thesis:
3067 = (17 * 180) + 7 ;
hence not 17 divides 3067 by NAT_4:9; :: thesis:
3067 = (19 * 161) + 8 ;
hence not 19 divides 3067 by NAT_4:9; :: thesis:
3067 = (23 * 133) + 8 ;
hence not 23 divides 3067 by NAT_4:9; :: thesis:
3067 = (29 * 105) + 22 ;
hence not 29 divides 3067 by NAT_4:9; :: thesis:
3067 = (31 * 98) + 29 ;
hence not 31 divides 3067 by NAT_4:9; :: thesis:
3067 = (37 * 82) + 33 ;
hence not 37 divides 3067 by NAT_4:9; :: thesis:
3067 = (41 * 74) + 33 ;
hence not 41 divides 3067 by NAT_4:9; :: thesis:
3067 = (43 * 71) + 14 ;
hence not 43 divides 3067 by NAT_4:9; :: thesis:
3067 = (47 * 65) + 12 ;
hence not 47 divides 3067 by NAT_4:9; :: thesis:
3067 = (53 * 57) + 46 ;
hence not 53 divides 3067 by NAT_4:9; :: thesis:

end;

then for n being Element of NAT st 1 < n & n * n <= 3067 & n is prime holds
not n divides 3067 by XPRIMET1:32;
hence 3067 is prime by NAT_4:14; :: thesis: