
theorem
  2341 is prime
proof
  now
    2341 = 2*1170 + 1; hence not 2 divides 2341 by NAT_4:9;
    2341 = 3*780 + 1; hence not 3 divides 2341 by NAT_4:9;
    2341 = 5*468 + 1; hence not 5 divides 2341 by NAT_4:9;
    2341 = 7*334 + 3; hence not 7 divides 2341 by NAT_4:9;
    2341 = 11*212 + 9; hence not 11 divides 2341 by NAT_4:9;
    2341 = 13*180 + 1; hence not 13 divides 2341 by NAT_4:9;
    2341 = 17*137 + 12; hence not 17 divides 2341 by NAT_4:9;
    2341 = 19*123 + 4; hence not 19 divides 2341 by NAT_4:9;
    2341 = 23*101 + 18; hence not 23 divides 2341 by NAT_4:9;
    2341 = 29*80 + 21; hence not 29 divides 2341 by NAT_4:9;
    2341 = 31*75 + 16; hence not 31 divides 2341 by NAT_4:9;
    2341 = 37*63 + 10; hence not 37 divides 2341 by NAT_4:9;
    2341 = 41*57 + 4; hence not 41 divides 2341 by NAT_4:9;
    2341 = 43*54 + 19; hence not 43 divides 2341 by NAT_4:9;
    2341 = 47*49 + 38; hence not 47 divides 2341 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 2341 & n is prime
  holds not n divides 2341 by XPRIMET1:30;
  hence thesis by NAT_4:14;
end;
