
theorem
  2467 is prime
proof
  now
    2467 = 2*1233 + 1; hence not 2 divides 2467 by NAT_4:9;
    2467 = 3*822 + 1; hence not 3 divides 2467 by NAT_4:9;
    2467 = 5*493 + 2; hence not 5 divides 2467 by NAT_4:9;
    2467 = 7*352 + 3; hence not 7 divides 2467 by NAT_4:9;
    2467 = 11*224 + 3; hence not 11 divides 2467 by NAT_4:9;
    2467 = 13*189 + 10; hence not 13 divides 2467 by NAT_4:9;
    2467 = 17*145 + 2; hence not 17 divides 2467 by NAT_4:9;
    2467 = 19*129 + 16; hence not 19 divides 2467 by NAT_4:9;
    2467 = 23*107 + 6; hence not 23 divides 2467 by NAT_4:9;
    2467 = 29*85 + 2; hence not 29 divides 2467 by NAT_4:9;
    2467 = 31*79 + 18; hence not 31 divides 2467 by NAT_4:9;
    2467 = 37*66 + 25; hence not 37 divides 2467 by NAT_4:9;
    2467 = 41*60 + 7; hence not 41 divides 2467 by NAT_4:9;
    2467 = 43*57 + 16; hence not 43 divides 2467 by NAT_4:9;
    2467 = 47*52 + 23; hence not 47 divides 2467 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 2467 & n is prime
  holds not n divides 2467 by XPRIMET1:30;
  hence thesis by NAT_4:14;
end;
