1201 = (2 * 600) + 1 ;
hence not 2 divides 1201 by NAT_4:9; :: thesis:
1201 = (3 * 400) + 1 ;
hence not 3 divides 1201 by NAT_4:9; :: thesis:
1201 = (5 * 240) + 1 ;
hence not 5 divides 1201 by NAT_4:9; :: thesis:
1201 = (7 * 171) + 4 ;
hence not 7 divides 1201 by NAT_4:9; :: thesis:
1201 = (11 * 109) + 2 ;
hence not 11 divides 1201 by NAT_4:9; :: thesis:
1201 = (13 * 92) + 5 ;
hence not 13 divides 1201 by NAT_4:9; :: thesis:
1201 = (17 * 70) + 11 ;
hence not 17 divides 1201 by NAT_4:9; :: thesis:
1201 = (19 * 63) + 4 ;
hence not 19 divides 1201 by NAT_4:9; :: thesis:
1201 = (23 * 52) + 5 ;
hence not 23 divides 1201 by NAT_4:9; :: thesis:
1201 = (29 * 41) + 12 ;
hence not 29 divides 1201 by NAT_4:9; :: thesis:
1201 = (31 * 38) + 23 ;
hence not 31 divides 1201 by NAT_4:9; :: thesis:

end;

then for n being Element of NAT st 1 < n & n * n <= 1201 & n is prime holds
not n divides 1201 by XPRIMET1:22;
hence 1201 is prime by NAT_4:14; :: thesis: