3361 = (2 * 1680) + 1 ;
hence not 2 divides 3361 by NAT_4:9; :: thesis:
3361 = (3 * 1120) + 1 ;
hence not 3 divides 3361 by NAT_4:9; :: thesis:
3361 = (5 * 672) + 1 ;
hence not 5 divides 3361 by NAT_4:9; :: thesis:
3361 = (7 * 480) + 1 ;
hence not 7 divides 3361 by NAT_4:9; :: thesis:
3361 = (11 * 305) + 6 ;
hence not 11 divides 3361 by NAT_4:9; :: thesis:
3361 = (13 * 258) + 7 ;
hence not 13 divides 3361 by NAT_4:9; :: thesis:
3361 = (17 * 197) + 12 ;
hence not 17 divides 3361 by NAT_4:9; :: thesis:
3361 = (19 * 176) + 17 ;
hence not 19 divides 3361 by NAT_4:9; :: thesis:
3361 = (23 * 146) + 3 ;
hence not 23 divides 3361 by NAT_4:9; :: thesis:
3361 = (29 * 115) + 26 ;
hence not 29 divides 3361 by NAT_4:9; :: thesis:
3361 = (31 * 108) + 13 ;
hence not 31 divides 3361 by NAT_4:9; :: thesis:
3361 = (37 * 90) + 31 ;
hence not 37 divides 3361 by NAT_4:9; :: thesis:
3361 = (41 * 81) + 40 ;
hence not 41 divides 3361 by NAT_4:9; :: thesis:
3361 = (43 * 78) + 7 ;
hence not 43 divides 3361 by NAT_4:9; :: thesis:
3361 = (47 * 71) + 24 ;
hence not 47 divides 3361 by NAT_4:9; :: thesis:
3361 = (53 * 63) + 22 ;
hence not 53 divides 3361 by NAT_4:9; :: thesis:

end;

then for n being Element of NAT st 1 < n & n * n <= 3361 & n is prime holds
not n divides 3361 by XPRIMET1:32;
hence 3361 is prime by NAT_4:14; :: thesis: