
theorem
  4523 is prime
proof
  now
    4523 = 2*2261 + 1; hence not 2 divides 4523 by NAT_4:9;
    4523 = 3*1507 + 2; hence not 3 divides 4523 by NAT_4:9;
    4523 = 5*904 + 3; hence not 5 divides 4523 by NAT_4:9;
    4523 = 7*646 + 1; hence not 7 divides 4523 by NAT_4:9;
    4523 = 11*411 + 2; hence not 11 divides 4523 by NAT_4:9;
    4523 = 13*347 + 12; hence not 13 divides 4523 by NAT_4:9;
    4523 = 17*266 + 1; hence not 17 divides 4523 by NAT_4:9;
    4523 = 19*238 + 1; hence not 19 divides 4523 by NAT_4:9;
    4523 = 23*196 + 15; hence not 23 divides 4523 by NAT_4:9;
    4523 = 29*155 + 28; hence not 29 divides 4523 by NAT_4:9;
    4523 = 31*145 + 28; hence not 31 divides 4523 by NAT_4:9;
    4523 = 37*122 + 9; hence not 37 divides 4523 by NAT_4:9;
    4523 = 41*110 + 13; hence not 41 divides 4523 by NAT_4:9;
    4523 = 43*105 + 8; hence not 43 divides 4523 by NAT_4:9;
    4523 = 47*96 + 11; hence not 47 divides 4523 by NAT_4:9;
    4523 = 53*85 + 18; hence not 53 divides 4523 by NAT_4:9;
    4523 = 59*76 + 39; hence not 59 divides 4523 by NAT_4:9;
    4523 = 61*74 + 9; hence not 61 divides 4523 by NAT_4:9;
    4523 = 67*67 + 34; hence not 67 divides 4523 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 4523 & n is prime
  holds not n divides 4523 by XPRIMET1:38;
  hence thesis by NAT_4:14;
end;
