
theorem
  1721 is prime
proof
  now
    1721 = 2*860 + 1; hence not 2 divides 1721 by NAT_4:9;
    1721 = 3*573 + 2; hence not 3 divides 1721 by NAT_4:9;
    1721 = 5*344 + 1; hence not 5 divides 1721 by NAT_4:9;
    1721 = 7*245 + 6; hence not 7 divides 1721 by NAT_4:9;
    1721 = 11*156 + 5; hence not 11 divides 1721 by NAT_4:9;
    1721 = 13*132 + 5; hence not 13 divides 1721 by NAT_4:9;
    1721 = 17*101 + 4; hence not 17 divides 1721 by NAT_4:9;
    1721 = 19*90 + 11; hence not 19 divides 1721 by NAT_4:9;
    1721 = 23*74 + 19; hence not 23 divides 1721 by NAT_4:9;
    1721 = 29*59 + 10; hence not 29 divides 1721 by NAT_4:9;
    1721 = 31*55 + 16; hence not 31 divides 1721 by NAT_4:9;
    1721 = 37*46 + 19; hence not 37 divides 1721 by NAT_4:9;
    1721 = 41*41 + 40; hence not 41 divides 1721 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 1721 & n is prime
  holds not n divides 1721 by XPRIMET1:26;
  hence thesis by NAT_4:14;
end;
