
theorem
  4019 is prime
proof
  now
    4019 = 2*2009 + 1; hence not 2 divides 4019 by NAT_4:9;
    4019 = 3*1339 + 2; hence not 3 divides 4019 by NAT_4:9;
    4019 = 5*803 + 4; hence not 5 divides 4019 by NAT_4:9;
    4019 = 7*574 + 1; hence not 7 divides 4019 by NAT_4:9;
    4019 = 11*365 + 4; hence not 11 divides 4019 by NAT_4:9;
    4019 = 13*309 + 2; hence not 13 divides 4019 by NAT_4:9;
    4019 = 17*236 + 7; hence not 17 divides 4019 by NAT_4:9;
    4019 = 19*211 + 10; hence not 19 divides 4019 by NAT_4:9;
    4019 = 23*174 + 17; hence not 23 divides 4019 by NAT_4:9;
    4019 = 29*138 + 17; hence not 29 divides 4019 by NAT_4:9;
    4019 = 31*129 + 20; hence not 31 divides 4019 by NAT_4:9;
    4019 = 37*108 + 23; hence not 37 divides 4019 by NAT_4:9;
    4019 = 41*98 + 1; hence not 41 divides 4019 by NAT_4:9;
    4019 = 43*93 + 20; hence not 43 divides 4019 by NAT_4:9;
    4019 = 47*85 + 24; hence not 47 divides 4019 by NAT_4:9;
    4019 = 53*75 + 44; hence not 53 divides 4019 by NAT_4:9;
    4019 = 59*68 + 7; hence not 59 divides 4019 by NAT_4:9;
    4019 = 61*65 + 54; hence not 61 divides 4019 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 4019 & n is prime
  holds not n divides 4019 by XPRIMET1:36;
  hence thesis by NAT_4:14;
end;
