"Salt Peanuts" is a bebop

Bebop

Bebop differed drastically from the straightforward compositions of the swing era, and was instead characterized by fast tempos, asymmetrical phrasing, intricate melodies, and rhythm sections that expanded on their role as tempo-keepers...

 tune reportedly composed by Dizzy Gillespie

Dizzy Gillespie

John Birks "Dizzy" Gillespie was an American jazz trumpet player, bandleader, singer, and composer dubbed "the sound of surprise".Together with Charlie Parker, he was a major figure in the development of bebop and modern jazz...

 in 1942, credited "with the collaboration of" bebop drummer Kenny Clarke

Kenny Clarke

Kenny Clarke , born Kenneth Spearman Clarke, nicknamed "Klook" and later known as Liaqat Ali Salaam, was a jazz drummer and an early innovator of the bebop style of drumming...

. It is also cited as Charlie Parker's.

In fact, while the verbal exhortation "Salt Peanuts, Salt Peanuts!" is closely identified with Dizzy Gillespie, the musical motif

Motif (music)

In music, a motif or motive is a short musical idea, a salient recurring figure, musical fragment or succession of notes that has some special importance in or is characteristic of a composition....

 upon which it is based actually predates Gillespie/Clarke by at least several months, as it appears as a repeated six-note instrumental phrase played on piano by Count Basie

Count Basie

William "Count" Basie was an American jazz pianist, organist, bandleader, and composer. Basie led his jazz orchestra almost continuously for nearly 50 years...

 on his July 2, 1941 recording of "Basie Boogie" for the Columbia/OKeh label. Basie also played it in a recorded live performance at Cafe Society

Café Society

Café society was the collective description for the so-called "Beautiful People" and "Bright Young Things" who gathered in fashionable cafes and restaurants in New York, Paris, and London beginning in the late 19th century...

 later that year. Both recordings are available on CD for verification as examples that predate Dizzy Gillespie's first use of the phrase.

Salt Peanuts was most famously recorded by Dizzy Gillespie and His All-Stars on May 11, 1945 in New York City for Guild Records.
The lineup was as follows: Dizzy Gillespie (trumpet)--Charlie Parker

Charlie Parker

Charles Parker, Jr. , famously called Bird or Yardbird, was an American jazz saxophonist and composer....

 (alto sax)--Al Haig (piano)--Curley Russell

Curley Russell

Dillon "Curley" Russell was an American jazz double-bassist, who played bass on many bebop recordings.A member of the Tadd Dameron Sextet, in his heyday he was in demand for his ability to play at the rapid tempos typical of bebop, and appears on several key recordings of the period...

 (bass)-- Sid Catlett (drums)

A few notes of the song are used in "Tiger in a Spotlight" by Emerson, Lake & Palmer

Emerson, Lake & Palmer

Emerson, Lake & Palmer, also known as ELP, are an English progressive rock supergroup. They found success in the 1970s and sold over forty million albums and headlined large stadium concerts. The band consists of Keith Emerson , Greg Lake and Carl Palmer...

.