Prime Blues is the fourth widely available studio album by American musician and computer scientist Jim Allchin.

The front grill cover of the amplifier shown on the album artwork highlights all the prime numbers through one million.

[4] "Give It Up" the first track from Prime Blues was a finalist in the 2018 UK Songwriting Contest in the Jazz/Blues category.

[5] Prime Blues was first reviewed September 6, 2018 by Rick Bowen and published in the NorthWest Music Scene magazine.

[6] Album reviews especially noted Allchin's songwriting, musicianship, and guitar technique.