
theorem
  3011 is prime
proof
  now
    3011 = 2*1505 + 1; hence not 2 divides 3011 by NAT_4:9;
    3011 = 3*1003 + 2; hence not 3 divides 3011 by NAT_4:9;
    3011 = 5*602 + 1; hence not 5 divides 3011 by NAT_4:9;
    3011 = 7*430 + 1; hence not 7 divides 3011 by NAT_4:9;
    3011 = 11*273 + 8; hence not 11 divides 3011 by NAT_4:9;
    3011 = 13*231 + 8; hence not 13 divides 3011 by NAT_4:9;
    3011 = 17*177 + 2; hence not 17 divides 3011 by NAT_4:9;
    3011 = 19*158 + 9; hence not 19 divides 3011 by NAT_4:9;
    3011 = 23*130 + 21; hence not 23 divides 3011 by NAT_4:9;
    3011 = 29*103 + 24; hence not 29 divides 3011 by NAT_4:9;
    3011 = 31*97 + 4; hence not 31 divides 3011 by NAT_4:9;
    3011 = 37*81 + 14; hence not 37 divides 3011 by NAT_4:9;
    3011 = 41*73 + 18; hence not 41 divides 3011 by NAT_4:9;
    3011 = 43*70 + 1; hence not 43 divides 3011 by NAT_4:9;
    3011 = 47*64 + 3; hence not 47 divides 3011 by NAT_4:9;
    3011 = 53*56 + 43; hence not 53 divides 3011 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 3011 & n is prime
  holds not n divides 3011 by XPRIMET1:32;
  hence thesis by NAT_4:14;
end;
