
theorem
  1153 is prime
proof
  now
    1153 = 2*576 + 1; hence not 2 divides 1153 by NAT_4:9;
    1153 = 3*384 + 1; hence not 3 divides 1153 by NAT_4:9;
    1153 = 5*230 + 3; hence not 5 divides 1153 by NAT_4:9;
    1153 = 7*164 + 5; hence not 7 divides 1153 by NAT_4:9;
    1153 = 11*104 + 9; hence not 11 divides 1153 by NAT_4:9;
    1153 = 13*88 + 9; hence not 13 divides 1153 by NAT_4:9;
    1153 = 17*67 + 14; hence not 17 divides 1153 by NAT_4:9;
    1153 = 19*60 + 13; hence not 19 divides 1153 by NAT_4:9;
    1153 = 23*50 + 3; hence not 23 divides 1153 by NAT_4:9;
    1153 = 29*39 + 22; hence not 29 divides 1153 by NAT_4:9;
    1153 = 31*37 + 6; hence not 31 divides 1153 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 1153 & n is prime
  holds not n divides 1153 by XPRIMET1:22;
  hence thesis by NAT_4:14;
