Definition
The term “dihedral prime” does not correspond to a widely recognized concept in mainstream mathematics or number theory according to available scholarly sources. Consequently, a precise, universally accepted definition cannot be provided.
Overview
Because the expression is not documented in standard mathematical literature, it is unclear whether it refers to a specific class of prime numbers, a property of primes under certain geometric transformations, or a term used only in niche or recreational contexts. Some informal discussions on internet forums have hinted at possible interpretations—such as primes that retain primality under the actions of the dihedral group (rotations and reflections) when their decimal representations are transformed—but these uses lack citation in peer‑reviewed publications.
Etymology/Origin
The word “dihedral” originates from geometry, describing the symmetry group consisting of rotations and reflections of a regular polygon (the dihedral group). “Prime” denotes a natural number greater than 1 with no positive divisors other than 1 and itself. The compound term likely attempts to combine these ideas, suggesting a relationship between prime numbers and dihedral symmetries. Accurate information about who coined the term, when, or in what context is not confirmed.
Characteristics
Without authoritative sources, no definitive properties can be listed. If the term were to describe primes invariant under dihedral transformations of their digit strings, potential characteristics might include:
- Stability of primality under digit reversal (mirror symmetry) and 180° rotation (as in strobogrammatic primes).
- Dependence on the choice of numeral system and the set of digits that map to valid digits under rotation/reflection.
However, these characteristics are speculative and not substantiated by reliable references.
Related Topics
- Rotational prime / Strobogrammatic prime – primes that remain prime when their digits are rotated 180°.
- Palindromic prime – primes that read the same forwards and backwards.
- Dihedral group – the group of symmetries (rotations and reflections) of a regular polygon.
- Recreational number theory – the study of interesting or unusual properties of numbers, often including digit‑based transformations.
Note
Accurate information is not confirmed. The term “dihedral prime” appears to be either a very recent, niche, or informal concept lacking coverage in established mathematical references.