
theorem
  2477 is prime
proof
  now
    2477 = 2*1238 + 1; hence not 2 divides 2477 by NAT_4:9;
    2477 = 3*825 + 2; hence not 3 divides 2477 by NAT_4:9;
    2477 = 5*495 + 2; hence not 5 divides 2477 by NAT_4:9;
    2477 = 7*353 + 6; hence not 7 divides 2477 by NAT_4:9;
    2477 = 11*225 + 2; hence not 11 divides 2477 by NAT_4:9;
    2477 = 13*190 + 7; hence not 13 divides 2477 by NAT_4:9;
    2477 = 17*145 + 12; hence not 17 divides 2477 by NAT_4:9;
    2477 = 19*130 + 7; hence not 19 divides 2477 by NAT_4:9;
    2477 = 23*107 + 16; hence not 23 divides 2477 by NAT_4:9;
    2477 = 29*85 + 12; hence not 29 divides 2477 by NAT_4:9;
    2477 = 31*79 + 28; hence not 31 divides 2477 by NAT_4:9;
    2477 = 37*66 + 35; hence not 37 divides 2477 by NAT_4:9;
    2477 = 41*60 + 17; hence not 41 divides 2477 by NAT_4:9;
    2477 = 43*57 + 26; hence not 43 divides 2477 by NAT_4:9;
    2477 = 47*52 + 33; hence not 47 divides 2477 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 2477 & n is prime
  holds not n divides 2477 by XPRIMET1:30;
  hence thesis by NAT_4:14;
end;
