First off, the original mail went to 13,000 users.  Assuming that 1,000 of those 13,000 users replied, that means that there are 1,000 replies being sent to those 13,000 users.  And it turns out that a number of these people had their email client set to request read receipts and delivery receipts.  Each read and delivery receipt causes ANOTHER email to be sent from the recipient back to the sender (all 13,000 recipients).  Assuming that 20% of the 1,000 users replying had read receipts or delivery receipts set, that meant that every one of the message that they sent caused another message to be sent for every one of the 13,000 recipients. So how many messages were sent?

Source: Me Too! – You Had Me At EHLO…