
theorem
  2753 is prime
proof
  now
    2753 = 2*1376 + 1; hence not 2 divides 2753 by NAT_4:9;
    2753 = 3*917 + 2; hence not 3 divides 2753 by NAT_4:9;
    2753 = 5*550 + 3; hence not 5 divides 2753 by NAT_4:9;
    2753 = 7*393 + 2; hence not 7 divides 2753 by NAT_4:9;
    2753 = 11*250 + 3; hence not 11 divides 2753 by NAT_4:9;
    2753 = 13*211 + 10; hence not 13 divides 2753 by NAT_4:9;
    2753 = 17*161 + 16; hence not 17 divides 2753 by NAT_4:9;
    2753 = 19*144 + 17; hence not 19 divides 2753 by NAT_4:9;
    2753 = 23*119 + 16; hence not 23 divides 2753 by NAT_4:9;
    2753 = 29*94 + 27; hence not 29 divides 2753 by NAT_4:9;
    2753 = 31*88 + 25; hence not 31 divides 2753 by NAT_4:9;
    2753 = 37*74 + 15; hence not 37 divides 2753 by NAT_4:9;
    2753 = 41*67 + 6; hence not 41 divides 2753 by NAT_4:9;
    2753 = 43*64 + 1; hence not 43 divides 2753 by NAT_4:9;
    2753 = 47*58 + 27; hence not 47 divides 2753 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 2753 & n is prime
  holds not n divides 2753 by XPRIMET1:30;
  hence thesis by NAT_4:14;
end;
