Prime Implicants

Any single 1 or group of 1's that can be combined together on a
Karnaugh map of the function F represents a product term which
is called an IMPLICANT.

A PRIME IMPLICANT is a product term that cannot be combined with
another term to eliminate a variable.


A single 1 is a prime implicant if it is not adjacent to any other 1's.

Two adjacent 1's form a prime implicant if they are not contained in
a group of four adjacent 1's.

Four adjacent 1's form a prime implicant if they are not contained in
a group of eight adjacent 1's.

The minimum sum-of-products expression for a function consists of
some (BUT NOT NECESSARILY ALL) of the prime implicants of a function.

source; http://www.mrc.uidaho.edu/mrc/people/jff/349/lect.08