
theorem
  839 is prime
proof
  now
    839 = 2*419 + 1; hence not 2 divides 839 by NAT_4:9;
    839 = 3*279 + 2; hence not 3 divides 839 by NAT_4:9;
    839 = 5*167 + 4; hence not 5 divides 839 by NAT_4:9;
    839 = 7*119 + 6; hence not 7 divides 839 by NAT_4:9;
    839 = 11*76 + 3; hence not 11 divides 839 by NAT_4:9;
    839 = 13*64 + 7; hence not 13 divides 839 by NAT_4:9;
    839 = 17*49 + 6; hence not 17 divides 839 by NAT_4:9;
    839 = 19*44 + 3; hence not 19 divides 839 by NAT_4:9;
    839 = 23*36 + 11; hence not 23 divides 839 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 839 & n is prime
  holds not n divides 839 by XPRIMET1:18;
  hence thesis by NAT_4:14;
