
theorem
  773 is prime
proof
  now
    773 = 2*386 + 1; hence not 2 divides 773 by NAT_4:9;
    773 = 3*257 + 2; hence not 3 divides 773 by NAT_4:9;
    773 = 5*154 + 3; hence not 5 divides 773 by NAT_4:9;
    773 = 7*110 + 3; hence not 7 divides 773 by NAT_4:9;
    773 = 11*70 + 3; hence not 11 divides 773 by NAT_4:9;
    773 = 13*59 + 6; hence not 13 divides 773 by NAT_4:9;
    773 = 17*45 + 8; hence not 17 divides 773 by NAT_4:9;
    773 = 19*40 + 13; hence not 19 divides 773 by NAT_4:9;
    773 = 23*33 + 14; hence not 23 divides 773 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 773 & n is prime
  holds not n divides 773 by XPRIMET1:18;
  hence thesis by NAT_4:14;
