
theorem
  2129 is prime
proof
  now
    2129 = 2*1064 + 1; hence not 2 divides 2129 by NAT_4:9;
    2129 = 3*709 + 2; hence not 3 divides 2129 by NAT_4:9;
    2129 = 5*425 + 4; hence not 5 divides 2129 by NAT_4:9;
    2129 = 7*304 + 1; hence not 7 divides 2129 by NAT_4:9;
    2129 = 11*193 + 6; hence not 11 divides 2129 by NAT_4:9;
    2129 = 13*163 + 10; hence not 13 divides 2129 by NAT_4:9;
    2129 = 17*125 + 4; hence not 17 divides 2129 by NAT_4:9;
    2129 = 19*112 + 1; hence not 19 divides 2129 by NAT_4:9;
    2129 = 23*92 + 13; hence not 23 divides 2129 by NAT_4:9;
    2129 = 29*73 + 12; hence not 29 divides 2129 by NAT_4:9;
    2129 = 31*68 + 21; hence not 31 divides 2129 by NAT_4:9;
    2129 = 37*57 + 20; hence not 37 divides 2129 by NAT_4:9;
    2129 = 41*51 + 38; hence not 41 divides 2129 by NAT_4:9;
    2129 = 43*49 + 22; hence not 43 divides 2129 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 2129 & n is prime
  holds not n divides 2129 by XPRIMET1:28;
  hence thesis by NAT_4:14;
end;
