907 = (2 * 453) + 1 ;
hence not 2 divides 907 by NAT_4:9; :: thesis:
907 = (3 * 302) + 1 ;
hence not 3 divides 907 by NAT_4:9; :: thesis:
907 = (5 * 181) + 2 ;
hence not 5 divides 907 by NAT_4:9; :: thesis:
907 = (7 * 129) + 4 ;
hence not 7 divides 907 by NAT_4:9; :: thesis:
907 = (11 * 82) + 5 ;
hence not 11 divides 907 by NAT_4:9; :: thesis:
907 = (13 * 69) + 10 ;
hence not 13 divides 907 by NAT_4:9; :: thesis:
907 = (17 * 53) + 6 ;
hence not 17 divides 907 by NAT_4:9; :: thesis:
907 = (19 * 47) + 14 ;
hence not 19 divides 907 by NAT_4:9; :: thesis:
907 = (23 * 39) + 10 ;
hence not 23 divides 907 by NAT_4:9; :: thesis:
907 = (29 * 31) + 8 ;
hence not 29 divides 907 by NAT_4:9; :: thesis:

end;

then for n being Element of NAT st 1 < n & n * n <= 907 & n is prime holds
not n divides 907 by XPRIMET1:20;
hence 907 is prime by NAT_4:14; :: thesis: