
theorem
  2347 is prime
proof
  now
    2347 = 2*1173 + 1; hence not 2 divides 2347 by NAT_4:9;
    2347 = 3*782 + 1; hence not 3 divides 2347 by NAT_4:9;
    2347 = 5*469 + 2; hence not 5 divides 2347 by NAT_4:9;
    2347 = 7*335 + 2; hence not 7 divides 2347 by NAT_4:9;
    2347 = 11*213 + 4; hence not 11 divides 2347 by NAT_4:9;
    2347 = 13*180 + 7; hence not 13 divides 2347 by NAT_4:9;
    2347 = 17*138 + 1; hence not 17 divides 2347 by NAT_4:9;
    2347 = 19*123 + 10; hence not 19 divides 2347 by NAT_4:9;
    2347 = 23*102 + 1; hence not 23 divides 2347 by NAT_4:9;
    2347 = 29*80 + 27; hence not 29 divides 2347 by NAT_4:9;
    2347 = 31*75 + 22; hence not 31 divides 2347 by NAT_4:9;
    2347 = 37*63 + 16; hence not 37 divides 2347 by NAT_4:9;
    2347 = 41*57 + 10; hence not 41 divides 2347 by NAT_4:9;
    2347 = 43*54 + 25; hence not 43 divides 2347 by NAT_4:9;
    2347 = 47*49 + 44; hence not 47 divides 2347 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 2347 & n is prime
  holds not n divides 2347 by XPRIMET1:30;
  hence thesis by NAT_4:14;
end;
