3967 = (2 * 1983) + 1 ;
hence not 2 divides 3967 by NAT_4:9; :: thesis:
3967 = (3 * 1322) + 1 ;
hence not 3 divides 3967 by NAT_4:9; :: thesis:
3967 = (5 * 793) + 2 ;
hence not 5 divides 3967 by NAT_4:9; :: thesis:
3967 = (7 * 566) + 5 ;
hence not 7 divides 3967 by NAT_4:9; :: thesis:
3967 = (11 * 360) + 7 ;
hence not 11 divides 3967 by NAT_4:9; :: thesis:
3967 = (13 * 305) + 2 ;
hence not 13 divides 3967 by NAT_4:9; :: thesis:
3967 = (17 * 233) + 6 ;
hence not 17 divides 3967 by NAT_4:9; :: thesis:
3967 = (19 * 208) + 15 ;
hence not 19 divides 3967 by NAT_4:9; :: thesis:
3967 = (23 * 172) + 11 ;
hence not 23 divides 3967 by NAT_4:9; :: thesis:
3967 = (29 * 136) + 23 ;
hence not 29 divides 3967 by NAT_4:9; :: thesis:
3967 = (31 * 127) + 30 ;
hence not 31 divides 3967 by NAT_4:9; :: thesis:
3967 = (37 * 107) + 8 ;
hence not 37 divides 3967 by NAT_4:9; :: thesis:
3967 = (41 * 96) + 31 ;
hence not 41 divides 3967 by NAT_4:9; :: thesis:
3967 = (43 * 92) + 11 ;
hence not 43 divides 3967 by NAT_4:9; :: thesis:
3967 = (47 * 84) + 19 ;
hence not 47 divides 3967 by NAT_4:9; :: thesis:
3967 = (53 * 74) + 45 ;
hence not 53 divides 3967 by NAT_4:9; :: thesis:
3967 = (59 * 67) + 14 ;
hence not 59 divides 3967 by NAT_4:9; :: thesis:
3967 = (61 * 65) + 2 ;
hence not 61 divides 3967 by NAT_4:9; :: thesis:

end;

then for n being Element of NAT st 1 < n & n * n <= 3967 & n is prime holds
not n divides 3967 by XPRIMET1:36;
hence 3967 is prime by NAT_4:14; :: thesis: