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Siteswaps may be considered either prime or composite.<ref name=":1" /> A siteswap is prime if the path created in its state diagram does not traverse any state more than once. Siteswaps that are not prime are called composite.
A non-rigorous but simpler method of determining if a siteswap is prime is to try to split it into any valid shorter pattern which uses the same number of props.<ref name=":1" /> For example, 44404413 can be split into 4440, 441, and 3; therefore, 44404413 is a composite. Another example, 441, which uses three props, is prime, as 1, 4, 41, and 44 are not valid three prop patterns (as 1/
It has been shown empirically that the longest prime siteswaps bounded by height <math>h</math> contain mostly the throws <math>0</math> and <math>h</math>.<ref>{{Cite web|url=https://www.jonglage.net/theorie/notation/siteswap-avancee/refs/Jack%20Boyce%20-%20The%20Longest%20Prime%20Siteswap%20Patterns.pdf|title=The Longest Prime Siteswap Patterns|last=Boyce|first=Jack|date=|website=jonglage.net|url-status=live|archive-url=|archive-date=|access-date=April 27, 2020}}</ref> The longest prime patterns with height 22 (with 3 ball maximum), for 9 balls (with 13 maximum height), and for heights and ball counts in between, were enumerated by Jack Boyce in February 1999 using a program called jdeep.<ref>{{Cite web|url=http://www.sonic.net/~boyce/jdeep5.c|title=jdeep.c|last=Boyce|first=Jack|date=February 17, 1999|website=sonic.net|url-status=dead|archive-url=https://web.archive.org/web/20041207120815/http://www.sonic.net/~boyce/jdeep5.c|archive-date=December 7, 2004|access-date=April 27, 2020}}</ref> The full list of longest prime siteswaps generated by jdeep (with '0' throws represented by a '-' and maximum height throws represented by a '+') can be found [https://web.archive.org/web/20110317025440/http://www.jugglingdb.com:80/compendium/boyce/prime_list.html here].
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