POTUS's 'old, unsecure Android phone' is probably a Samsung Galaxy S3 — a model from almost five years ago.
The New York Times has reported that Donald Trump still tweets from the White House on his "old, unsecured Android phone, to the protests of some of his aides," contradicting earlier reports that the president had turned in the handset in exchange for a "secure, encrypted device approved by the Secret Service." It's difficult to know with 100% certainty which Android device Trump currently uses to tweet (or whether it's the off-the-shelf model he likely used during his campaign, or some secured variant.)
But we sure can offer you some informed speculation!
There are only a few photos out in the wild of Trump using his smartphone, usually reported to be a "Samsung Galaxy." That doesn't exactly narrow it down, and most of the photos available online are low-res, making the matter trickier still. What's more, the device appears to be in a case, obscuring some identifying features. Of the two clearest images we have of Trump using his Android phone, one comes from a NYT report dated October 2015:
The back is pretty revealing, but you have to zoom in close to pick out identifying features. The two dead giveaways are the features flanking the camera bump — even in this low-res shot, Trump's phone quite clearly has an LED flash on the left, and a less reflective marking in the same place over on the right. The only major Samsung phone released in the U.S. with these features is the Galaxy S3, launched way back in 2012. (A different angle of the same shot shows a device roughly the right size and shape to be a GS3, with the familiar LED - camera - speaker arrangement only found on this phone.)
You have to look really close to see exactly which Galaxy Trump is using.
The GS3 is very similar in appearance to 2013's Galaxy S4, but the GS4's LED is below the camera bulge, not to the side. Same deal with the Galaxy S5. And the headphone jack being situated on the top-left side (as you face the phone) eliminates the Galaxy S6 or anything newer.
In 2017, a GS3 certainly fits the description of an "old, unsecure Android phone."
Further evidence comes from a more recent pic of Trump on his phone, dated February 2016. Here, Trump the presidential candidate is using what appears to be the same Samsung phone — note the home button — in a similar case. But there's another important clue in this pic — the bottom edge of the device, showing a USB port and no headphone jack. Again, this eliminates the GS6 and newer. The USB port is also too small for it to be a GS5, which used a weird double-width USB 3.0 port. Another important clue is the mic hole placement — to the right of the charging port here, like the GS3. The GS4 relocated the mic to the left of the USB port. (The irregular shape of the home key — wider at the top, narrower at the bottom — also matches the GS3, but not the GS4.)
So there you go. Trump's personal Android phone is more than likely a Samsung Galaxy S3, released in 2012, and which last received a software update in mid-2015, with firmware based on Android 4.3 Jelly Bean.
As noted in the intro, we don't know for sure that Trump is still using this specific Galaxy S3. The two NYT reports conflict on whether he turned it in, or is still using it to fire out tweets from the White House. But if he is, and it's the same consumer GS3 model he was apparently using as of February 2016, it's safe to say it's a good three years out of step with the latest Android security updates. Many Android security scares have come and gone since the GS3 got its last update in August of 2015.
Naturally, there's huge (YUGE!) interest in which smartphone — secured, or otherwise — the most powerful man in the world is using. (And understandable concern over how protected it is from digital threats.) We may never have an entirely clear answer. Nevertheless, in 2017, a GS3 certainly fits the description of an "old, unsecure Android phone."
Update, January 27: Further photos from recent interviews at Trump Tower by German outlets Bild.de and Die Welt reveal the president's Android phone — quite clearly a Galaxy S3 — in higher resolution, showing the features noted above in greater detail. (Thanks, Tim!)