
theorem
  2549 is prime
proof
  now
    2549 = 2*1274 + 1; hence not 2 divides 2549 by NAT_4:9;
    2549 = 3*849 + 2; hence not 3 divides 2549 by NAT_4:9;
    2549 = 5*509 + 4; hence not 5 divides 2549 by NAT_4:9;
    2549 = 7*364 + 1; hence not 7 divides 2549 by NAT_4:9;
    2549 = 11*231 + 8; hence not 11 divides 2549 by NAT_4:9;
    2549 = 13*196 + 1; hence not 13 divides 2549 by NAT_4:9;
    2549 = 17*149 + 16; hence not 17 divides 2549 by NAT_4:9;
    2549 = 19*134 + 3; hence not 19 divides 2549 by NAT_4:9;
    2549 = 23*110 + 19; hence not 23 divides 2549 by NAT_4:9;
    2549 = 29*87 + 26; hence not 29 divides 2549 by NAT_4:9;
    2549 = 31*82 + 7; hence not 31 divides 2549 by NAT_4:9;
    2549 = 37*68 + 33; hence not 37 divides 2549 by NAT_4:9;
    2549 = 41*62 + 7; hence not 41 divides 2549 by NAT_4:9;
    2549 = 43*59 + 12; hence not 43 divides 2549 by NAT_4:9;
    2549 = 47*54 + 11; hence not 47 divides 2549 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 2549 & n is prime
  holds not n divides 2549 by XPRIMET1:30;
  hence thesis by NAT_4:14;
end;
