887 = (2 * 443) + 1 ;
hence not 2 divides 887 by NAT_4:9; :: thesis:
887 = (3 * 295) + 2 ;
hence not 3 divides 887 by NAT_4:9; :: thesis:
887 = (5 * 177) + 2 ;
hence not 5 divides 887 by NAT_4:9; :: thesis:
887 = (7 * 126) + 5 ;
hence not 7 divides 887 by NAT_4:9; :: thesis:
887 = (11 * 80) + 7 ;
hence not 11 divides 887 by NAT_4:9; :: thesis:
887 = (13 * 68) + 3 ;
hence not 13 divides 887 by NAT_4:9; :: thesis:
887 = (17 * 52) + 3 ;
hence not 17 divides 887 by NAT_4:9; :: thesis:
887 = (19 * 46) + 13 ;
hence not 19 divides 887 by NAT_4:9; :: thesis:
887 = (23 * 38) + 13 ;
hence not 23 divides 887 by NAT_4:9; :: thesis:
887 = (29 * 30) + 17 ;
hence not 29 divides 887 by NAT_4:9; :: thesis:

end;

then for n being Element of NAT st 1 < n & n * n <= 887 & n is prime holds
not n divides 887 by XPRIMET1:20;
hence 887 is prime by NAT_4:14; :: thesis: