
theorem
  577 is prime
proof
  now
    577 = 2*288 + 1; hence not 2 divides 577 by NAT_4:9;
    577 = 3*192 + 1; hence not 3 divides 577 by NAT_4:9;
    577 = 5*115 + 2; hence not 5 divides 577 by NAT_4:9;
    577 = 7*82 + 3; hence not 7 divides 577 by NAT_4:9;
    577 = 11*52 + 5; hence not 11 divides 577 by NAT_4:9;
    577 = 13*44 + 5; hence not 13 divides 577 by NAT_4:9;
    577 = 17*33 + 16; hence not 17 divides 577 by NAT_4:9;
    577 = 19*30 + 7; hence not 19 divides 577 by NAT_4:9;
    577 = 23*25 + 2; hence not 23 divides 577 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 577 & n is prime
  holds not n divides 577 by XPRIMET1:18;
  hence thesis by NAT_4:14;
