First, off are you assuming Trump or the White House gave it that file name?  They didn't, that's the filename from Twitter's database.  Are you assuming that Twitter's database filenames have meaning?  Because that way lies madness. If you are just asking the likelihood or randomly generating this string, I think it would be 1 out of 11,881,376 if just letters are used.  1 out of about 60,000,000 if numbers were used.  So "Q's" math is off by..........  EDIT:  I forgot about case sensitivity.  1 in a billion is probably right. However, why are you assuming this is random? Let's look at it another way.  What's the likelihood that Twitter's database would eventually need DOITQ as a string in a filename as it saves million and millions of photos, that probability is about 100%.  The full filename is DOITQJ8UIAAowsQ.jpg Look at the other part of the filename J8UIAAowsQ that's 10 characters way more than the five characters of DOITQ.  What does this mean? It means there can be an enormous number of files that begin with DOITQ in Twitter's database. I just went and saved 4 images from twitter this morning.  I looked for recently user-posted images, not memes or gifs that would have been saved, not news photos that would be pulled from another database.  Look at the first four characters in each filename. Dmf9 Dmf3 Dmfe DmcF Dmaq This is not random.  They all begin with capital D lowercase m.  Three of them beginning with Dmf.   So files uploaded on the same day share similiar filenames.  There are probably well over a million DOITQ images and files in Twitter's database.  Once you understand this, the probability is pretty high to get a DOITQ filename.  If you posted an image to twitter on this day, you have a very, very good chance of having a DOITQ file name. Go ahead and try it yourself.  Upload a couple of images to Twitter in quick succession.  not save them from twitter, what do you see?