
theorem
  619 is prime
proof
  now
    619 = 2*309 + 1; hence not 2 divides 619 by NAT_4:9;
    619 = 3*206 + 1; hence not 3 divides 619 by NAT_4:9;
    619 = 5*123 + 4; hence not 5 divides 619 by NAT_4:9;
    619 = 7*88 + 3; hence not 7 divides 619 by NAT_4:9;
    619 = 11*56 + 3; hence not 11 divides 619 by NAT_4:9;
    619 = 13*47 + 8; hence not 13 divides 619 by NAT_4:9;
    619 = 17*36 + 7; hence not 17 divides 619 by NAT_4:9;
    619 = 19*32 + 11; hence not 19 divides 619 by NAT_4:9;
    619 = 23*26 + 21; hence not 23 divides 619 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 619 & n is prime
  holds not n divides 619 by XPRIMET1:18;
  hence thesis by NAT_4:14;
