
theorem
  3067 is prime
proof
  now
    3067 = 2*1533 + 1; hence not 2 divides 3067 by NAT_4:9;
    3067 = 3*1022 + 1; hence not 3 divides 3067 by NAT_4:9;
    3067 = 5*613 + 2; hence not 5 divides 3067 by NAT_4:9;
    3067 = 7*438 + 1; hence not 7 divides 3067 by NAT_4:9;
    3067 = 11*278 + 9; hence not 11 divides 3067 by NAT_4:9;
    3067 = 13*235 + 12; hence not 13 divides 3067 by NAT_4:9;
    3067 = 17*180 + 7; hence not 17 divides 3067 by NAT_4:9;
    3067 = 19*161 + 8; hence not 19 divides 3067 by NAT_4:9;
    3067 = 23*133 + 8; hence not 23 divides 3067 by NAT_4:9;
    3067 = 29*105 + 22; hence not 29 divides 3067 by NAT_4:9;
    3067 = 31*98 + 29; hence not 31 divides 3067 by NAT_4:9;
    3067 = 37*82 + 33; hence not 37 divides 3067 by NAT_4:9;
    3067 = 41*74 + 33; hence not 41 divides 3067 by NAT_4:9;
    3067 = 43*71 + 14; hence not 43 divides 3067 by NAT_4:9;
    3067 = 47*65 + 12; hence not 47 divides 3067 by NAT_4:9;
    3067 = 53*57 + 46; hence not 53 divides 3067 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 3067 & n is prime
  holds not n divides 3067 by XPRIMET1:32;
  hence thesis by NAT_4:14;
end;
