
theorem
  2161 is prime
proof
  now
    2161 = 2*1080 + 1; hence not 2 divides 2161 by NAT_4:9;
    2161 = 3*720 + 1; hence not 3 divides 2161 by NAT_4:9;
    2161 = 5*432 + 1; hence not 5 divides 2161 by NAT_4:9;
    2161 = 7*308 + 5; hence not 7 divides 2161 by NAT_4:9;
    2161 = 11*196 + 5; hence not 11 divides 2161 by NAT_4:9;
    2161 = 13*166 + 3; hence not 13 divides 2161 by NAT_4:9;
    2161 = 17*127 + 2; hence not 17 divides 2161 by NAT_4:9;
    2161 = 19*113 + 14; hence not 19 divides 2161 by NAT_4:9;
    2161 = 23*93 + 22; hence not 23 divides 2161 by NAT_4:9;
    2161 = 29*74 + 15; hence not 29 divides 2161 by NAT_4:9;
    2161 = 31*69 + 22; hence not 31 divides 2161 by NAT_4:9;
    2161 = 37*58 + 15; hence not 37 divides 2161 by NAT_4:9;
    2161 = 41*52 + 29; hence not 41 divides 2161 by NAT_4:9;
    2161 = 43*50 + 11; hence not 43 divides 2161 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 2161 & n is prime
  holds not n divides 2161 by XPRIMET1:28;
  hence thesis by NAT_4:14;
end;
