
theorem
  4547 is prime
proof
  now
    4547 = 2*2273 + 1; hence not 2 divides 4547 by NAT_4:9;
    4547 = 3*1515 + 2; hence not 3 divides 4547 by NAT_4:9;
    4547 = 5*909 + 2; hence not 5 divides 4547 by NAT_4:9;
    4547 = 7*649 + 4; hence not 7 divides 4547 by NAT_4:9;
    4547 = 11*413 + 4; hence not 11 divides 4547 by NAT_4:9;
    4547 = 13*349 + 10; hence not 13 divides 4547 by NAT_4:9;
    4547 = 17*267 + 8; hence not 17 divides 4547 by NAT_4:9;
    4547 = 19*239 + 6; hence not 19 divides 4547 by NAT_4:9;
    4547 = 23*197 + 16; hence not 23 divides 4547 by NAT_4:9;
    4547 = 29*156 + 23; hence not 29 divides 4547 by NAT_4:9;
    4547 = 31*146 + 21; hence not 31 divides 4547 by NAT_4:9;
    4547 = 37*122 + 33; hence not 37 divides 4547 by NAT_4:9;
    4547 = 41*110 + 37; hence not 41 divides 4547 by NAT_4:9;
    4547 = 43*105 + 32; hence not 43 divides 4547 by NAT_4:9;
    4547 = 47*96 + 35; hence not 47 divides 4547 by NAT_4:9;
    4547 = 53*85 + 42; hence not 53 divides 4547 by NAT_4:9;
    4547 = 59*77 + 4; hence not 59 divides 4547 by NAT_4:9;
    4547 = 61*74 + 33; hence not 61 divides 4547 by NAT_4:9;
    4547 = 67*67 + 58; hence not 67 divides 4547 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 4547 & n is prime
  holds not n divides 4547 by XPRIMET1:38;
  hence thesis by NAT_4:14;
end;
