
theorem
  2137 is prime
proof
  now
    2137 = 2*1068 + 1; hence not 2 divides 2137 by NAT_4:9;
    2137 = 3*712 + 1; hence not 3 divides 2137 by NAT_4:9;
    2137 = 5*427 + 2; hence not 5 divides 2137 by NAT_4:9;
    2137 = 7*305 + 2; hence not 7 divides 2137 by NAT_4:9;
    2137 = 11*194 + 3; hence not 11 divides 2137 by NAT_4:9;
    2137 = 13*164 + 5; hence not 13 divides 2137 by NAT_4:9;
    2137 = 17*125 + 12; hence not 17 divides 2137 by NAT_4:9;
    2137 = 19*112 + 9; hence not 19 divides 2137 by NAT_4:9;
    2137 = 23*92 + 21; hence not 23 divides 2137 by NAT_4:9;
    2137 = 29*73 + 20; hence not 29 divides 2137 by NAT_4:9;
    2137 = 31*68 + 29; hence not 31 divides 2137 by NAT_4:9;
    2137 = 37*57 + 28; hence not 37 divides 2137 by NAT_4:9;
    2137 = 41*52 + 5; hence not 41 divides 2137 by NAT_4:9;
    2137 = 43*49 + 30; hence not 43 divides 2137 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 2137 & n is prime
  holds not n divides 2137 by XPRIMET1:28;
  hence thesis by NAT_4:14;
end;
