
theorem
  3049 is prime
proof
  now
    3049 = 2*1524 + 1; hence not 2 divides 3049 by NAT_4:9;
    3049 = 3*1016 + 1; hence not 3 divides 3049 by NAT_4:9;
    3049 = 5*609 + 4; hence not 5 divides 3049 by NAT_4:9;
    3049 = 7*435 + 4; hence not 7 divides 3049 by NAT_4:9;
    3049 = 11*277 + 2; hence not 11 divides 3049 by NAT_4:9;
    3049 = 13*234 + 7; hence not 13 divides 3049 by NAT_4:9;
    3049 = 17*179 + 6; hence not 17 divides 3049 by NAT_4:9;
    3049 = 19*160 + 9; hence not 19 divides 3049 by NAT_4:9;
    3049 = 23*132 + 13; hence not 23 divides 3049 by NAT_4:9;
    3049 = 29*105 + 4; hence not 29 divides 3049 by NAT_4:9;
    3049 = 31*98 + 11; hence not 31 divides 3049 by NAT_4:9;
    3049 = 37*82 + 15; hence not 37 divides 3049 by NAT_4:9;
    3049 = 41*74 + 15; hence not 41 divides 3049 by NAT_4:9;
    3049 = 43*70 + 39; hence not 43 divides 3049 by NAT_4:9;
    3049 = 47*64 + 41; hence not 47 divides 3049 by NAT_4:9;
    3049 = 53*57 + 28; hence not 53 divides 3049 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 3049 & n is prime
  holds not n divides 3049 by XPRIMET1:32;
  hence thesis by NAT_4:14;
end;
