
theorem
  379 is prime
proof
  now
    379 = 2*189 + 1; hence not 2 divides 379 by NAT_4:9;
    379 = 3*126 + 1; hence not 3 divides 379 by NAT_4:9;
    379 = 5*75 + 4; hence not 5 divides 379 by NAT_4:9;
    379 = 7*54 + 1; hence not 7 divides 379 by NAT_4:9;
    379 = 11*34 + 5; hence not 11 divides 379 by NAT_4:9;
    379 = 13*29 + 2; hence not 13 divides 379 by NAT_4:9;
    379 = 17*22 + 5; hence not 17 divides 379 by NAT_4:9;
    379 = 19*19 + 18; hence not 19 divides 379 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 379 & n is prime
  holds not n divides 379 by XPRIMET1:16;
  hence thesis by NAT_4:14;
end;
