2221 = (2 * 1110) + 1 ;
hence not 2 divides 2221 by NAT_4:9; :: thesis:
2221 = (3 * 740) + 1 ;
hence not 3 divides 2221 by NAT_4:9; :: thesis:
2221 = (5 * 444) + 1 ;
hence not 5 divides 2221 by NAT_4:9; :: thesis:
2221 = (7 * 317) + 2 ;
hence not 7 divides 2221 by NAT_4:9; :: thesis:
2221 = (11 * 201) + 10 ;
hence not 11 divides 2221 by NAT_4:9; :: thesis:
2221 = (13 * 170) + 11 ;
hence not 13 divides 2221 by NAT_4:9; :: thesis:
2221 = (17 * 130) + 11 ;
hence not 17 divides 2221 by NAT_4:9; :: thesis:
2221 = (19 * 116) + 17 ;
hence not 19 divides 2221 by NAT_4:9; :: thesis:
2221 = (23 * 96) + 13 ;
hence not 23 divides 2221 by NAT_4:9; :: thesis:
2221 = (29 * 76) + 17 ;
hence not 29 divides 2221 by NAT_4:9; :: thesis:
2221 = (31 * 71) + 20 ;
hence not 31 divides 2221 by NAT_4:9; :: thesis:
2221 = (37 * 60) + 1 ;
hence not 37 divides 2221 by NAT_4:9; :: thesis:
2221 = (41 * 54) + 7 ;
hence not 41 divides 2221 by NAT_4:9; :: thesis:
2221 = (43 * 51) + 28 ;
hence not 43 divides 2221 by NAT_4:9; :: thesis:
2221 = (47 * 47) + 12 ;
hence not 47 divides 2221 by NAT_4:9; :: thesis:

end;

then for n being Element of NAT st 1 < n & n * n <= 2221 & n is prime holds
not n divides 2221 by XPRIMET1:30;
hence 2221 is prime by NAT_4:14; :: thesis: