Chiral Prime Concatenations

TL;DR

This paper explores a recursive method for constructing prime numbers through chiral concatenations, analyzing symmetry, infinity, and the largest primes generated, including anomalous cases that challenge existing limits.

Contribution

It introduces the concept of chiral prime concatenations, constructs the largest known chiral prime, and proposes conjectures about prime chirality under anomalous concatenations.

Findings

Constructed the largest 24-digit left-concatenated prime.

Discovered anomalous concatenations can produce primes beyond 24 digits.

Proposed conjecture that primes are left chiral under anomalous concatenations.

Abstract

The notion of chiral prime concatenations is studied as a recursive construction of prime numbers starting from a seed set and with appropriate blocks to define the primality growth, generation by generation, either from the right or from the left. Several basic questions are addressed like whether chiral concatenation is a symmetric process, an endless process, as well as the calculation of largest chiral prime numbers. In particular, the largest left-concatenated prime number is constructed. It is a unique prime number of 24 digits. By introducing anomalous left-concatenations of primes we can surpass the limit of 24 digits for left-concatenated primes. It is conjectured that prime numbers are left chiral under anomalous concatenations.