
theorem
  919 is prime
proof
  now
    919 = 2*459 + 1; hence not 2 divides 919 by NAT_4:9;
    919 = 3*306 + 1; hence not 3 divides 919 by NAT_4:9;
    919 = 5*183 + 4; hence not 5 divides 919 by NAT_4:9;
    919 = 7*131 + 2; hence not 7 divides 919 by NAT_4:9;
    919 = 11*83 + 6; hence not 11 divides 919 by NAT_4:9;
    919 = 13*70 + 9; hence not 13 divides 919 by NAT_4:9;
    919 = 17*54 + 1; hence not 17 divides 919 by NAT_4:9;
    919 = 19*48 + 7; hence not 19 divides 919 by NAT_4:9;
    919 = 23*39 + 22; hence not 23 divides 919 by NAT_4:9;
    919 = 29*31 + 20; hence not 29 divides 919 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 919 & n is prime
  holds not n divides 919 by XPRIMET1:20;
  hence thesis by NAT_4:14;
