Amazon Music officially noted: "Prime Music and Amazon Music Unlimited titles are not available for download to computers. You can download these titles to your Amazon Music app for offline playback."
If you have Amazon Prime, congrats -- you already have access to Prime Music. This is definitely a nice added perk to the Prime membership, especially since it's at no extra cost to you. Meanwhile, like other music streaming service giants, Amazon Prime Music also supports downloading music for offline playback, but the downloaded files are accessible only on its own app. So what if you need to download Prime Music songs to PC as local files for some reason? Fret not, this page will show you a new solution.
For Mac users, please check "How to Download Songs from Amazon Music to Mac".

A Way to Download Prime Music to PC
As the lead-in stated, songs from Prime Music are not available to be downloaded as local files on computers. The reason why is because all tracks on Amazon Music are encoded with proprietary technology to hold users back to enjoy Amazon Music outside its app. Hereby, to get Prime Music songs downloaded to PC locally, we will need a prowerful audio recorder, TuneBoto Amazon Music Converter, to download and record Prime Music to plain music format and save them on computer.
What's TuneBoto Amazon Music Converter
Configured with the most advanced music downloading core, TuneBoto will always empower both Amazon Music Unlimited and Prime Music users to download or record any Amazon songs, albums, or playlist in MP3/AAC/WAV/FLAC/AIFF format, with original audio quality kept. What's more, TuneBoto has the independent ability to complete the whole process of Amazon music downloading and converting, so no additional apps (including Amazon Music) is required to download on your PC. With it, you can download Amazon Prime Music to computers with ease.
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Amazon Music Converter
Tutorial on How to Download Amazon Prime Songs to PC
Next, let's see how to download tracks from Prime Music to computer with the help of TuneBoto Amazon Music Converter. Before that, please make sure you have downloaded and installed the program on your PC computer.
Step 1 Sign in Amazon Prime Music Account
Run TuneBoto Amazon Music Converter and log into your Amazon Prime Music account.
Note: TuneBoto needs to work with an Amazon account. But don't worry, it will not take any other information from your account than the songs.

Step 2 Customize Output Settings
Click the "Setting" icon at the upper right, followed that the setting window will pop up allowing you to set the output format (MP3/AAC/WAV/FLAC/AIFF), path, quality (256kbps, 192kbps, 128kbps) and more.

Step 3 Add Amazon Prime Music to TuneBoto
Open one of your Amazon albums, artists or playlists, and tap the blue "Add" button suspended on the right side, then the program will list all songs immediately in the Add window. Now, please select the Prime music you would like to download.

Step 4 Start Downloading Amazon Prime Music
The final step is clicking the "Convert" button. The conversion will be succeeded after a few minutes. All your Prime songs will be saved to the output path in MP3/AAC/WAV/FLAC/AIFF format quickly.

Then, please click the "History" button to find out the downloaded Amazon Prime Music tracks. Here you will find that ID3 tags, including title, artist, artwork, and,album, are preserved in the output audio.
Now, all of your favorite songs from Amazon Prime Music have been downloaded to PC and you can keep them playable forever. Start to enjoy!
Final Words
Carried with the most advanced audio downloading core, a concise and intuitive interface, and broad compatibility with the Windows & Mac system, TuneBoto Amazon Music Converter must be the most powerful Amazon Music Downloader in the market. With TuneBoto, you can not only download Prime Music to computer with ease, but also transfer Amazon Music to any device without limits. TuneBoto offers the free trial version for users to test its features. Now, give it a shot!
Note: The free trial version of TuneBoto Amazon Music Converter enables you to convert the first three minutes of each song and convert 3 music files at a time. You can unlock the limits and enable all its features by purchasing the full version.