
theorem
  4049 is prime
proof
  now
    4049 = 2*2024 + 1; hence not 2 divides 4049 by NAT_4:9;
    4049 = 3*1349 + 2; hence not 3 divides 4049 by NAT_4:9;
    4049 = 5*809 + 4; hence not 5 divides 4049 by NAT_4:9;
    4049 = 7*578 + 3; hence not 7 divides 4049 by NAT_4:9;
    4049 = 11*368 + 1; hence not 11 divides 4049 by NAT_4:9;
    4049 = 13*311 + 6; hence not 13 divides 4049 by NAT_4:9;
    4049 = 17*238 + 3; hence not 17 divides 4049 by NAT_4:9;
    4049 = 19*213 + 2; hence not 19 divides 4049 by NAT_4:9;
    4049 = 23*176 + 1; hence not 23 divides 4049 by NAT_4:9;
    4049 = 29*139 + 18; hence not 29 divides 4049 by NAT_4:9;
    4049 = 31*130 + 19; hence not 31 divides 4049 by NAT_4:9;
    4049 = 37*109 + 16; hence not 37 divides 4049 by NAT_4:9;
    4049 = 41*98 + 31; hence not 41 divides 4049 by NAT_4:9;
    4049 = 43*94 + 7; hence not 43 divides 4049 by NAT_4:9;
    4049 = 47*86 + 7; hence not 47 divides 4049 by NAT_4:9;
    4049 = 53*76 + 21; hence not 53 divides 4049 by NAT_4:9;
    4049 = 59*68 + 37; hence not 59 divides 4049 by NAT_4:9;
    4049 = 61*66 + 23; hence not 61 divides 4049 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 4049 & n is prime
  holds not n divides 4049 by XPRIMET1:36;
  hence thesis by NAT_4:14;
end;
