
theorem
  977 is prime
proof
  now
    977 = 2*488 + 1; hence not 2 divides 977 by NAT_4:9;
    977 = 3*325 + 2; hence not 3 divides 977 by NAT_4:9;
    977 = 5*195 + 2; hence not 5 divides 977 by NAT_4:9;
    977 = 7*139 + 4; hence not 7 divides 977 by NAT_4:9;
    977 = 11*88 + 9; hence not 11 divides 977 by NAT_4:9;
    977 = 13*75 + 2; hence not 13 divides 977 by NAT_4:9;
    977 = 17*57 + 8; hence not 17 divides 977 by NAT_4:9;
    977 = 19*51 + 8; hence not 19 divides 977 by NAT_4:9;
    977 = 23*42 + 11; hence not 23 divides 977 by NAT_4:9;
    977 = 29*33 + 20; hence not 29 divides 977 by NAT_4:9;
    977 = 31*31 + 16; hence not 31 divides 977 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 977 & n is prime
  holds not n divides 977 by XPRIMET1:22;
  hence thesis by NAT_4:14;
