Palindrome Studies (Part I): the Palindrome Concept and Its Applications to Prime Numbers‪.‬

Abstract This article originates from a proposal by M. L. Perez of American Research Press to carry out a study on Smarandache generalized palindromes [1]. The prime numbers were chosen as a first set of numbers to apply the development of ideas and computer programs on. The study begins by exploring regular prime number palindromes. To continue the study it proved useful to introduce a new concept, that of extended palindromes with the property that the union of regular palindromes and extended palindromes form the set of Smarandache generalized palindromes. An interesting observation is proved in the article, namely that the only regular prime number palindrome with an even number of digits is 11. Keywords Equation, solutions, Mersenne prime, perfect number