Amazon's Fire Phone does not appear to be on fire.

According to an estimate by Charles Arthur, technology editor at The Guardian, the world's largest online retailer sold fewer than 35,000 of its new smartphones in the first 20 days it was on the market.

To put that in perspective: Apple sold 9 million iPhone 5C and 5S devices within three days of the phones' release last September. It's not an entirely fair comparison, because iPhones are the most popular smartphone in the world and are available in more stores, in more countries and on more carriers.

But 35,000 is indeed a very small number. Amazon itself has 132,600 employees, according to the company's latest public filings.

Amazon's entry into the smartphone market comes at a time when the company is under intense pressure from shareholders to make a profit. Shares of the company plummeted after Amazon reported a loss of $126 million for the three-month period ending June 30, and the company told investors it could lose as much as $810 million this quarter. Just this week, Amazon said it would buy Twitch, the live-streaming video game network, for about $1 billion.

Amazon would never actually give figures for how many phones (or tablets, e-readers or streaming media players, for that matter) it has sold. Arthur's estimate, which he bases on an analysis of the phone's web traffic from Chitika, an online ad network, and numbers from comScore, the analytics company, should be taken with a grain of salt. As Arthur himself writes, "Lots of caveats apply: this is a calculation based on two non-congruent sets of samples, though both are large enough to be robust."

Still, Amazon, which did not respond to an email requesting comment, doesn't have a lot going for it when it comes to the Fire Phone.

It got tepidreviews, at best. For starters, it's just as expensive as a new iPhone or premium Android device, and not nearly as good. Although it's based on Android, it has its own operating system. Therefore, many apps -- such as Google's popular suite that includes Google Maps, Gmail and YouTube -- aren't available for it. It's also only available on AT&T, and unlike the iPhone, when it first came out and was only available on AT&T, the Fire Phone is not a product most people would switch carriers for.

As I wrote in my review, Amazon is asking customers to sacrifice a lot to switch to the Fire Phone.

That said, Amazon has put its huge marketing muscle behind the Fire Phone, hawking it on its highly trafficked home page as well as sealing delivery boxes with colorful tape promoting the phone.

But even the power of the world's largest online retailer doesn't seem to be enough to sell the Fire Phone.