How about this? /(7|8|9)d{9}/
It starts by either looking for 7 or 8 or 9, and then followed by 9 digits.
<input type="text" class="form-control" id="packet_name" name="packet_name" pattern="[^/:x22*?<>|]+" oninvalid="setCustomValidity('Invalid character in name:
/ : * ? < >.')" oninput="setCustomValidity('')" maxlength="100" required>