
theorem
  491 is prime
proof
  now
    491 = 2*245 + 1; hence not 2 divides 491 by NAT_4:9;
    491 = 3*163 + 2; hence not 3 divides 491 by NAT_4:9;
    491 = 5*98 + 1; hence not 5 divides 491 by NAT_4:9;
    491 = 7*70 + 1; hence not 7 divides 491 by NAT_4:9;
    491 = 11*44 + 7; hence not 11 divides 491 by NAT_4:9;
    491 = 13*37 + 10; hence not 13 divides 491 by NAT_4:9;
    491 = 17*28 + 15; hence not 17 divides 491 by NAT_4:9;
    491 = 19*25 + 16; hence not 19 divides 491 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 491 & n is prime
  holds not n divides 491 by XPRIMET1:16;
  hence thesis by NAT_4:14;
end;
