
theorem
  2377 is prime
proof
  now
    2377 = 2*1188 + 1; hence not 2 divides 2377 by NAT_4:9;
    2377 = 3*792 + 1; hence not 3 divides 2377 by NAT_4:9;
    2377 = 5*475 + 2; hence not 5 divides 2377 by NAT_4:9;
    2377 = 7*339 + 4; hence not 7 divides 2377 by NAT_4:9;
    2377 = 11*216 + 1; hence not 11 divides 2377 by NAT_4:9;
    2377 = 13*182 + 11; hence not 13 divides 2377 by NAT_4:9;
    2377 = 17*139 + 14; hence not 17 divides 2377 by NAT_4:9;
    2377 = 19*125 + 2; hence not 19 divides 2377 by NAT_4:9;
    2377 = 23*103 + 8; hence not 23 divides 2377 by NAT_4:9;
    2377 = 29*81 + 28; hence not 29 divides 2377 by NAT_4:9;
    2377 = 31*76 + 21; hence not 31 divides 2377 by NAT_4:9;
    2377 = 37*64 + 9; hence not 37 divides 2377 by NAT_4:9;
    2377 = 41*57 + 40; hence not 41 divides 2377 by NAT_4:9;
    2377 = 43*55 + 12; hence not 43 divides 2377 by NAT_4:9;
    2377 = 47*50 + 27; hence not 47 divides 2377 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 2377 & n is prime
  holds not n divides 2377 by XPRIMET1:30;
  hence thesis by NAT_4:14;
end;
