
theorem
  797 is prime
proof
  now
    797 = 2*398 + 1; hence not 2 divides 797 by NAT_4:9;
    797 = 3*265 + 2; hence not 3 divides 797 by NAT_4:9;
    797 = 5*159 + 2; hence not 5 divides 797 by NAT_4:9;
    797 = 7*113 + 6; hence not 7 divides 797 by NAT_4:9;
    797 = 11*72 + 5; hence not 11 divides 797 by NAT_4:9;
    797 = 13*61 + 4; hence not 13 divides 797 by NAT_4:9;
    797 = 17*46 + 15; hence not 17 divides 797 by NAT_4:9;
    797 = 19*41 + 18; hence not 19 divides 797 by NAT_4:9;
    797 = 23*34 + 15; hence not 23 divides 797 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 797 & n is prime
  holds not n divides 797 by XPRIMET1:18;
  hence thesis by NAT_4:14;
end;
