
theorem
  1753 is prime
proof
  now
    1753 = 2*876 + 1; hence not 2 divides 1753 by NAT_4:9;
    1753 = 3*584 + 1; hence not 3 divides 1753 by NAT_4:9;
    1753 = 5*350 + 3; hence not 5 divides 1753 by NAT_4:9;
    1753 = 7*250 + 3; hence not 7 divides 1753 by NAT_4:9;
    1753 = 11*159 + 4; hence not 11 divides 1753 by NAT_4:9;
    1753 = 13*134 + 11; hence not 13 divides 1753 by NAT_4:9;
    1753 = 17*103 + 2; hence not 17 divides 1753 by NAT_4:9;
    1753 = 19*92 + 5; hence not 19 divides 1753 by NAT_4:9;
    1753 = 23*76 + 5; hence not 23 divides 1753 by NAT_4:9;
    1753 = 29*60 + 13; hence not 29 divides 1753 by NAT_4:9;
    1753 = 31*56 + 17; hence not 31 divides 1753 by NAT_4:9;
    1753 = 37*47 + 14; hence not 37 divides 1753 by NAT_4:9;
    1753 = 41*42 + 31; hence not 41 divides 1753 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 1753 & n is prime
  holds not n divides 1753 by XPRIMET1:26;
  hence thesis by NAT_4:14;
end;
