mixedprimes

Mixed primes is not a single, formally defined concept in mathematics. In practice, the term is used informally in different sources to describe a few related notions concerning primes and their representations. The lack of a universal definition means that any discussion of mixed primes should begin by clarifying which meaning is intended.

One common interpretation in recreational number theory is that a mixed prime is a prime that can be written as the sum of a finite run of consecutive primes. For example, 5 = 2 + 3, 17 = 2 + 3 + 5 + 7, and 41 = 2 + 3 + 5 + 7 + 11 + 13. In this sense, a prime p is mixed if there exists a sequence of consecutive primes whose sum equals p. Not all primes have such a representation, and the property is of interest mainly in additive prime problems and prime-density studies.

Some discussions treat mixed primes as a broader class that includes primes expressible as sums of consecutive primes in various positions within the prime sequence, not necessarily starting at 2. In any case, the precise definition should be checked in the given source, as different authors may extend or restrict the idea in distinct ways.

See also: prime sums, additive number theory, consecutive primes.

Note: This article summarizes common informal uses; it does not imply a canonical, universally accepted definition.