
theorem
  4507 is prime
proof
  now
    4507 = 2*2253 + 1; hence not 2 divides 4507 by NAT_4:9;
    4507 = 3*1502 + 1; hence not 3 divides 4507 by NAT_4:9;
    4507 = 5*901 + 2; hence not 5 divides 4507 by NAT_4:9;
    4507 = 7*643 + 6; hence not 7 divides 4507 by NAT_4:9;
    4507 = 11*409 + 8; hence not 11 divides 4507 by NAT_4:9;
    4507 = 13*346 + 9; hence not 13 divides 4507 by NAT_4:9;
    4507 = 17*265 + 2; hence not 17 divides 4507 by NAT_4:9;
    4507 = 19*237 + 4; hence not 19 divides 4507 by NAT_4:9;
    4507 = 23*195 + 22; hence not 23 divides 4507 by NAT_4:9;
    4507 = 29*155 + 12; hence not 29 divides 4507 by NAT_4:9;
    4507 = 31*145 + 12; hence not 31 divides 4507 by NAT_4:9;
    4507 = 37*121 + 30; hence not 37 divides 4507 by NAT_4:9;
    4507 = 41*109 + 38; hence not 41 divides 4507 by NAT_4:9;
    4507 = 43*104 + 35; hence not 43 divides 4507 by NAT_4:9;
    4507 = 47*95 + 42; hence not 47 divides 4507 by NAT_4:9;
    4507 = 53*85 + 2; hence not 53 divides 4507 by NAT_4:9;
    4507 = 59*76 + 23; hence not 59 divides 4507 by NAT_4:9;
    4507 = 61*73 + 54; hence not 61 divides 4507 by NAT_4:9;
    4507 = 67*67 + 18; hence not 67 divides 4507 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 4507 & n is prime
  holds not n divides 4507 by XPRIMET1:38;
  hence thesis by NAT_4:14;
end;
