Novel Sequences of Prime Palindromes in Various Bases

Rama Venkat, Michael R. Schwob


Palindromic numbers have intrigued amateur mathematicians and number theorists alike. Initially regarded as recreational mathematics, these numbers have been extensively explored and are well-documented in the On-Line Encyclopedia of Integer Sequences (OEIS). Within the last few decades, an exhaustive list of sequences has been compiled regarding palindromic numbers, notably palindromic primes and appended palindromic numbers. Both palindromic primes and appended palindromic numbers have been well-studied within bases 2-10, yet are poorly documented in larger bases. To extend the literature on appended palindromic numbers, a novel algorithm is proposed that computes sequences of primes with prime mirrors in bases 2-62, resulting in 52 novel sequences. A second algorithm is proposed that computes the list of primes that require an additional base to obtain a prime mirror, providing yet another novel sequence.


prime, palindrome, base, conversion, cryptography

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