need the number of seconds since....

T = Time
Z = Zone
So that parsers know where to start looking.

U = Seconds since the Unix Epoch (January 1 1970 00:00:00 GMT)
This is the same as time(), like you wanted.

Personally I'm using UUIDv4 instead of auto incremented. And storing them as BINARY(16). But you can store them as strings too.

PHP Code:

<?php
defined('BASEPATH') OR exit('No direct script access allowed');

if ( ! function_exists('UUID_TO_BIN'))
{
    function UUID_TO_BIN($uuid) {
        $uuid = hex2bin(str_replace('-','',$uuid));
        return $uuid;
    }
}

if ( ! function_exists('BIN_TO_UUID'))
{
    function BIN_TO_UUID($uuid) {
        if( empty($uuid) ) return;
        $uuid = bin2hex($uuid);
        $uuid = substr($uuid, 0, 8) . '-' . substr($uuid, 8, 4) . '-' . substr($uuid, 12, 4) . '-' . substr($uuid, 16, 4)  . '-' . substr($uuid, 20);
        return $uuid;
    }
}


if ( ! function_exists('UUIDv4'))
{
    /**
     * Generates a random UUID using the secure RNG.
     *
     * Returns Version 4 UUID format: xxxxxxxx-xxxx-4xxx-Yxxx-xxxxxxxxxxxx where x is
     * any random hex digit and Y is a random choice from 8, 9, a, or b.
     *
     * @return string the UUID
     */
    function UUIDv4()
    {
        $bytes = random_bytes(16);
        $bytes[6] = chr((ord($bytes[6]) & 0x0f) | 0x40);
        $bytes[8] = chr((ord($bytes[8]) & 0x3f) | 0x80);
        $uuid = vsprintf('%s%s-%s-%s-%s-%s%s%s', str_split(bin2hex($bytes), 4));
        return $uuid;
    }
}

if ( ! function_exists('VALID_UUIDv4'))
{
    function VALID_UUIDv4($uuid)
    {
        return preg_match('/^[0-9A-F]{8}-[0-9A-F]{4}-4[0-9A-F]{3}-[89AB][0-9A-F]{3}-[0-9A-F]{12}$/i',$uuid);
    }
} 


PHP Code:

$date = new DateTime();
echo $date->format("Y-m-d\TH:i:s\Z");
// 2018-08-14T23:53:57Z

$date = new DateTime();
echo $date->format("Y-m-d\TH:i:s\Z");
// 20180814T235439Z 


YOU NEED TO INSTALL CALENDAR TO USE THIS FUNCTION
http://php.net/manual/en/book.calendar.php
http://php.net/manual/en/datetime.settime.php
http://php.net/manual/en/function.gregoriantojd.php

This assumes that days are counted like this:
1, 2, 3, 4 ...
NOT
01, 02, 03, 04 ...

PHP Code:

$gregorian = DateTime::createFromFormat("D M j Y","Thu Aug 16 2018");
$gregorian->setTime(0, 0);                        
echo gregoriantojd( $gregorian->format('n'), $gregorian->format('j'), $gregorian->format('Y') );