## Document Type

Conference Proceeding

## Publication Date

5-30-2015

## Abstract

Home primes and foreign primes are produced by a simple recipe that blends prime factorizations with recursion. The home prime of a positive integer *n* is formed by concatenating the prime factors of *n* in non-decreasing order. If the resulting integer is prime, then we have found the home prime of *n*. If not, then we repeat the process as many times as needed to obtain a prime. For instance, 35 = 5·7. After concatenation, we have 57 = 3·19, which is followed by 319 = 11·29, which is followed by 1129, which is prime. Thus, the home prime of 35 is 1129. To obtain the foreign prime of a positive integer *n*, we form the next integer by concatenating the prime factors of *n* in nonincreasing order. For example, starting with 35 = 7·5, we next consider 75 = 5·5·3, followed by 553 = 79·7, followed by 797, which is prime. Thus, 797 is the foreign prime of 35. In this talk we give some results about home primes and foreign primes for integers *n* <100. As one might expect from the arbitrary nature of the concatenation process, there are few easily discernible patterns.

## Recommended Citation

Zoller, Nicholas, "Home Primes and Foreign Primes" (2015). *ACMS Conference Proceedings 2015*. 23.

https://pillars.taylor.edu/acms-2015/23

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