
theorem
  4567 is prime
proof
  now
    4567 = 2*2283 + 1; hence not 2 divides 4567 by NAT_4:9;
    4567 = 3*1522 + 1; hence not 3 divides 4567 by NAT_4:9;
    4567 = 5*913 + 2; hence not 5 divides 4567 by NAT_4:9;
    4567 = 7*652 + 3; hence not 7 divides 4567 by NAT_4:9;
    4567 = 11*415 + 2; hence not 11 divides 4567 by NAT_4:9;
    4567 = 13*351 + 4; hence not 13 divides 4567 by NAT_4:9;
    4567 = 17*268 + 11; hence not 17 divides 4567 by NAT_4:9;
    4567 = 19*240 + 7; hence not 19 divides 4567 by NAT_4:9;
    4567 = 23*198 + 13; hence not 23 divides 4567 by NAT_4:9;
    4567 = 29*157 + 14; hence not 29 divides 4567 by NAT_4:9;
    4567 = 31*147 + 10; hence not 31 divides 4567 by NAT_4:9;
    4567 = 37*123 + 16; hence not 37 divides 4567 by NAT_4:9;
    4567 = 41*111 + 16; hence not 41 divides 4567 by NAT_4:9;
    4567 = 43*106 + 9; hence not 43 divides 4567 by NAT_4:9;
    4567 = 47*97 + 8; hence not 47 divides 4567 by NAT_4:9;
    4567 = 53*86 + 9; hence not 53 divides 4567 by NAT_4:9;
    4567 = 59*77 + 24; hence not 59 divides 4567 by NAT_4:9;
    4567 = 61*74 + 53; hence not 61 divides 4567 by NAT_4:9;
    4567 = 67*68 + 11; hence not 67 divides 4567 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 4567 & n is prime
  holds not n divides 4567 by XPRIMET1:38;
  hence thesis by NAT_4:14;
end;
