
theorem
  2351 is prime
proof
  now
    2351 = 2*1175 + 1; hence not 2 divides 2351 by NAT_4:9;
    2351 = 3*783 + 2; hence not 3 divides 2351 by NAT_4:9;
    2351 = 5*470 + 1; hence not 5 divides 2351 by NAT_4:9;
    2351 = 7*335 + 6; hence not 7 divides 2351 by NAT_4:9;
    2351 = 11*213 + 8; hence not 11 divides 2351 by NAT_4:9;
    2351 = 13*180 + 11; hence not 13 divides 2351 by NAT_4:9;
    2351 = 17*138 + 5; hence not 17 divides 2351 by NAT_4:9;
    2351 = 19*123 + 14; hence not 19 divides 2351 by NAT_4:9;
    2351 = 23*102 + 5; hence not 23 divides 2351 by NAT_4:9;
    2351 = 29*81 + 2; hence not 29 divides 2351 by NAT_4:9;
    2351 = 31*75 + 26; hence not 31 divides 2351 by NAT_4:9;
    2351 = 37*63 + 20; hence not 37 divides 2351 by NAT_4:9;
    2351 = 41*57 + 14; hence not 41 divides 2351 by NAT_4:9;
    2351 = 43*54 + 29; hence not 43 divides 2351 by NAT_4:9;
    2351 = 47*50 + 1; hence not 47 divides 2351 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 2351 & n is prime
  holds not n divides 2351 by XPRIMET1:30;
  hence thesis by NAT_4:14;
end;
