
theorem
  4561 is prime
proof
  now
    4561 = 2*2280 + 1; hence not 2 divides 4561 by NAT_4:9;
    4561 = 3*1520 + 1; hence not 3 divides 4561 by NAT_4:9;
    4561 = 5*912 + 1; hence not 5 divides 4561 by NAT_4:9;
    4561 = 7*651 + 4; hence not 7 divides 4561 by NAT_4:9;
    4561 = 11*414 + 7; hence not 11 divides 4561 by NAT_4:9;
    4561 = 13*350 + 11; hence not 13 divides 4561 by NAT_4:9;
    4561 = 17*268 + 5; hence not 17 divides 4561 by NAT_4:9;
    4561 = 19*240 + 1; hence not 19 divides 4561 by NAT_4:9;
    4561 = 23*198 + 7; hence not 23 divides 4561 by NAT_4:9;
    4561 = 29*157 + 8; hence not 29 divides 4561 by NAT_4:9;
    4561 = 31*147 + 4; hence not 31 divides 4561 by NAT_4:9;
    4561 = 37*123 + 10; hence not 37 divides 4561 by NAT_4:9;
    4561 = 41*111 + 10; hence not 41 divides 4561 by NAT_4:9;
    4561 = 43*106 + 3; hence not 43 divides 4561 by NAT_4:9;
    4561 = 47*97 + 2; hence not 47 divides 4561 by NAT_4:9;
    4561 = 53*86 + 3; hence not 53 divides 4561 by NAT_4:9;
    4561 = 59*77 + 18; hence not 59 divides 4561 by NAT_4:9;
    4561 = 61*74 + 47; hence not 61 divides 4561 by NAT_4:9;
    4561 = 67*68 + 5; hence not 67 divides 4561 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 4561 & n is prime
  holds not n divides 4561 by XPRIMET1:38;
  hence thesis by NAT_4:14;
end;
