
theorem
  877 is prime
proof
  now
    877 = 2*438 + 1; hence not 2 divides 877 by NAT_4:9;
    877 = 3*292 + 1; hence not 3 divides 877 by NAT_4:9;
    877 = 5*175 + 2; hence not 5 divides 877 by NAT_4:9;
    877 = 7*125 + 2; hence not 7 divides 877 by NAT_4:9;
    877 = 11*79 + 8; hence not 11 divides 877 by NAT_4:9;
    877 = 13*67 + 6; hence not 13 divides 877 by NAT_4:9;
    877 = 17*51 + 10; hence not 17 divides 877 by NAT_4:9;
    877 = 19*46 + 3; hence not 19 divides 877 by NAT_4:9;
    877 = 23*38 + 3; hence not 23 divides 877 by NAT_4:9;
    877 = 29*30 + 7; hence not 29 divides 877 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 877 & n is prime
  holds not n divides 877 by XPRIMET1:20;
  hence thesis by NAT_4:14;
end;
