
theorem
  353 is prime
proof
  now
    353 = 2*176 + 1; hence not 2 divides 353 by NAT_4:9;
    353 = 3*117 + 2; hence not 3 divides 353 by NAT_4:9;
    353 = 5*70 + 3; hence not 5 divides 353 by NAT_4:9;
    353 = 7*50 + 3; hence not 7 divides 353 by NAT_4:9;
    353 = 11*32 + 1; hence not 11 divides 353 by NAT_4:9;
    353 = 13*27 + 2; hence not 13 divides 353 by NAT_4:9;
    353 = 17*20 + 13; hence not 17 divides 353 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 353 & n is prime
  holds not n divides 353 by XPRIMET1:14;
  hence thesis by NAT_4:14;
end;
