Umbilical cord stump

Baby is 1w4d old and his cord still is still attached. No redness, swelling, oozing, or smell. No sign of infection whatsoever, it doesn’t bother him if it’s touched (clothing/diaper changes, wiggles, etc.) We have not bathed him since we were in the hospital, so we haven’t gotten it wet or anything. I feel like we’re following all the rules and doing everything right, but it’s still there and I’m starting to worry just a tiny little bit 😅 How long did your baby’s cord stick around? Is this actually something we should be concerned about?