
theorem
  1249 is prime
proof
  now
    1249 = 2*624 + 1; hence not 2 divides 1249 by NAT_4:9;
    1249 = 3*416 + 1; hence not 3 divides 1249 by NAT_4:9;
    1249 = 5*249 + 4; hence not 5 divides 1249 by NAT_4:9;
    1249 = 7*178 + 3; hence not 7 divides 1249 by NAT_4:9;
    1249 = 11*113 + 6; hence not 11 divides 1249 by NAT_4:9;
    1249 = 13*96 + 1; hence not 13 divides 1249 by NAT_4:9;
    1249 = 17*73 + 8; hence not 17 divides 1249 by NAT_4:9;
    1249 = 19*65 + 14; hence not 19 divides 1249 by NAT_4:9;
    1249 = 23*54 + 7; hence not 23 divides 1249 by NAT_4:9;
    1249 = 29*43 + 2; hence not 29 divides 1249 by NAT_4:9;
    1249 = 31*40 + 9; hence not 31 divides 1249 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 1249 & n is prime
  holds not n divides 1249 by XPRIMET1:22;
  hence thesis by NAT_4:14;
