
theorem
  1549 is prime
proof
  now
    1549 = 2*774 + 1; hence not 2 divides 1549 by NAT_4:9;
    1549 = 3*516 + 1; hence not 3 divides 1549 by NAT_4:9;
    1549 = 5*309 + 4; hence not 5 divides 1549 by NAT_4:9;
    1549 = 7*221 + 2; hence not 7 divides 1549 by NAT_4:9;
    1549 = 11*140 + 9; hence not 11 divides 1549 by NAT_4:9;
    1549 = 13*119 + 2; hence not 13 divides 1549 by NAT_4:9;
    1549 = 17*91 + 2; hence not 17 divides 1549 by NAT_4:9;
    1549 = 19*81 + 10; hence not 19 divides 1549 by NAT_4:9;
    1549 = 23*67 + 8; hence not 23 divides 1549 by NAT_4:9;
    1549 = 29*53 + 12; hence not 29 divides 1549 by NAT_4:9;
    1549 = 31*49 + 30; hence not 31 divides 1549 by NAT_4:9;
    1549 = 37*41 + 32; hence not 37 divides 1549 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 1549 & n is prime
  holds not n divides 1549 by XPRIMET1:24;
  hence thesis by NAT_4:14;
end;
