
theorem
  1049 is prime
proof
  now
    1049 = 2*524 + 1; hence not 2 divides 1049 by NAT_4:9;
    1049 = 3*349 + 2; hence not 3 divides 1049 by NAT_4:9;
    1049 = 5*209 + 4; hence not 5 divides 1049 by NAT_4:9;
    1049 = 7*149 + 6; hence not 7 divides 1049 by NAT_4:9;
    1049 = 11*95 + 4; hence not 11 divides 1049 by NAT_4:9;
    1049 = 13*80 + 9; hence not 13 divides 1049 by NAT_4:9;
    1049 = 17*61 + 12; hence not 17 divides 1049 by NAT_4:9;
    1049 = 19*55 + 4; hence not 19 divides 1049 by NAT_4:9;
    1049 = 23*45 + 14; hence not 23 divides 1049 by NAT_4:9;
    1049 = 29*36 + 5; hence not 29 divides 1049 by NAT_4:9;
    1049 = 31*33 + 26; hence not 31 divides 1049 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 1049 & n is prime
  holds not n divides 1049 by XPRIMET1:22;
  hence thesis by NAT_4:14;
