
theorem
  2113 is prime
proof
  now
    2113 = 2*1056 + 1; hence not 2 divides 2113 by NAT_4:9;
    2113 = 3*704 + 1; hence not 3 divides 2113 by NAT_4:9;
    2113 = 5*422 + 3; hence not 5 divides 2113 by NAT_4:9;
    2113 = 7*301 + 6; hence not 7 divides 2113 by NAT_4:9;
    2113 = 11*192 + 1; hence not 11 divides 2113 by NAT_4:9;
    2113 = 13*162 + 7; hence not 13 divides 2113 by NAT_4:9;
    2113 = 17*124 + 5; hence not 17 divides 2113 by NAT_4:9;
    2113 = 19*111 + 4; hence not 19 divides 2113 by NAT_4:9;
    2113 = 23*91 + 20; hence not 23 divides 2113 by NAT_4:9;
    2113 = 29*72 + 25; hence not 29 divides 2113 by NAT_4:9;
    2113 = 31*68 + 5; hence not 31 divides 2113 by NAT_4:9;
    2113 = 37*57 + 4; hence not 37 divides 2113 by NAT_4:9;
    2113 = 41*51 + 22; hence not 41 divides 2113 by NAT_4:9;
    2113 = 43*49 + 6; hence not 43 divides 2113 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 2113 & n is prime
  holds not n divides 2113 by XPRIMET1:28;
  hence thesis by NAT_4:14;
end;
