
theorem
  1019 is prime
proof
  now
    1019 = 2*509 + 1; hence not 2 divides 1019 by NAT_4:9;
    1019 = 3*339 + 2; hence not 3 divides 1019 by NAT_4:9;
    1019 = 5*203 + 4; hence not 5 divides 1019 by NAT_4:9;
    1019 = 7*145 + 4; hence not 7 divides 1019 by NAT_4:9;
    1019 = 11*92 + 7; hence not 11 divides 1019 by NAT_4:9;
    1019 = 13*78 + 5; hence not 13 divides 1019 by NAT_4:9;
    1019 = 17*59 + 16; hence not 17 divides 1019 by NAT_4:9;
    1019 = 19*53 + 12; hence not 19 divides 1019 by NAT_4:9;
    1019 = 23*44 + 7; hence not 23 divides 1019 by NAT_4:9;
    1019 = 29*35 + 4; hence not 29 divides 1019 by NAT_4:9;
    1019 = 31*32 + 27; hence not 31 divides 1019 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 1019 & n is prime
  holds not n divides 1019 by XPRIMET1:22;
  hence thesis by NAT_4:14;
end;
