883 = (2 * 441) + 1 ;
hence not 2 divides 883 by NAT_4:9; :: thesis:
883 = (3 * 294) + 1 ;
hence not 3 divides 883 by NAT_4:9; :: thesis:
883 = (5 * 176) + 3 ;
hence not 5 divides 883 by NAT_4:9; :: thesis:
883 = (7 * 126) + 1 ;
hence not 7 divides 883 by NAT_4:9; :: thesis:
883 = (11 * 80) + 3 ;
hence not 11 divides 883 by NAT_4:9; :: thesis:
883 = (13 * 67) + 12 ;
hence not 13 divides 883 by NAT_4:9; :: thesis:
883 = (17 * 51) + 16 ;
hence not 17 divides 883 by NAT_4:9; :: thesis:
883 = (19 * 46) + 9 ;
hence not 19 divides 883 by NAT_4:9; :: thesis:
883 = (23 * 38) + 9 ;
hence not 23 divides 883 by NAT_4:9; :: thesis:
883 = (29 * 30) + 13 ;
hence not 29 divides 883 by NAT_4:9; :: thesis:

end;

then for n being Element of NAT st 1 < n & n * n <= 883 & n is prime holds
not n divides 883 by XPRIMET1:20;
hence 883 is prime by NAT_4:14; :: thesis: