
theorem
  1151 is prime
proof
  now
    1151 = 2*575 + 1; hence not 2 divides 1151 by NAT_4:9;
    1151 = 3*383 + 2; hence not 3 divides 1151 by NAT_4:9;
    1151 = 5*230 + 1; hence not 5 divides 1151 by NAT_4:9;
    1151 = 7*164 + 3; hence not 7 divides 1151 by NAT_4:9;
    1151 = 11*104 + 7; hence not 11 divides 1151 by NAT_4:9;
    1151 = 13*88 + 7; hence not 13 divides 1151 by NAT_4:9;
    1151 = 17*67 + 12; hence not 17 divides 1151 by NAT_4:9;
    1151 = 19*60 + 11; hence not 19 divides 1151 by NAT_4:9;
    1151 = 23*50 + 1; hence not 23 divides 1151 by NAT_4:9;
    1151 = 29*39 + 20; hence not 29 divides 1151 by NAT_4:9;
    1151 = 31*37 + 4; hence not 31 divides 1151 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 1151 & n is prime
  holds not n divides 1151 by XPRIMET1:22;
  hence thesis by NAT_4:14;
