
theorem
  1777 is prime
proof
  now
    1777 = 2*888 + 1; hence not 2 divides 1777 by NAT_4:9;
    1777 = 3*592 + 1; hence not 3 divides 1777 by NAT_4:9;
    1777 = 5*355 + 2; hence not 5 divides 1777 by NAT_4:9;
    1777 = 7*253 + 6; hence not 7 divides 1777 by NAT_4:9;
    1777 = 11*161 + 6; hence not 11 divides 1777 by NAT_4:9;
    1777 = 13*136 + 9; hence not 13 divides 1777 by NAT_4:9;
    1777 = 17*104 + 9; hence not 17 divides 1777 by NAT_4:9;
    1777 = 19*93 + 10; hence not 19 divides 1777 by NAT_4:9;
    1777 = 23*77 + 6; hence not 23 divides 1777 by NAT_4:9;
    1777 = 29*61 + 8; hence not 29 divides 1777 by NAT_4:9;
    1777 = 31*57 + 10; hence not 31 divides 1777 by NAT_4:9;
    1777 = 37*48 + 1; hence not 37 divides 1777 by NAT_4:9;
    1777 = 41*43 + 14; hence not 41 divides 1777 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 1777 & n is prime
  holds not n divides 1777 by XPRIMET1:26;
  hence thesis by NAT_4:14;
end;
