This is the update to, and current version of, a paper that was originally written around 2014.

It discusses connections between periodic functions and primes, composites, and factors. Speciﬁcally, it shows how to use periodic functions to construct formulas for the following: the number of factors of a number, the speciﬁc factors of a number, the exact prime counting function and distribution, the nth prime, primes of any size, ”product polynomials” as periodic functions, primality and composite tests, prime gap ﬁnders, and ”anti-pulses.”

You can download the pdf, and the pages are also provided online. If you are having trouble reading the pages, the pdf version is more scalable and easier to read. The paper can also be found at vixra here:

https://vixra.org/pdf/1606.0109v2.pdf

Contact me if you would like to discuss the topics further, offer suggestions, or if you find any errors.

## Using Periodic Functions to Determine Pr | ## Using Periodic Functions to Determine Pr | ## Using Periodic Functions to Determine Pr |
---|---|---|

## Using Periodic Functions to Determine Pr | ## Using Periodic Functions to Determine Pr | ## Using Periodic Functions to Determine Pr |

## Using Periodic Functions to Determine Pr | ## Using Periodic Functions to Determine Pr | ## Using Periodic Functions to Determine Pr |

## Using Periodic Functions to Determine Pr | ## Using Periodic Functions to Determine Pr | ## Using Periodic Functions to Determine Pr |

## Using Periodic Functions to Determine Pr | ## Using Periodic Functions to Determine Pr | ## Using Periodic Functions to Determine Pr |

## Using Periodic Functions to Determine Pr | ## Using Periodic Functions to Determine Pr | ## Using Periodic Functions to Determine Pr |

## Using Periodic Functions to Determine Pr | ## Using Periodic Functions to Determine Pr | ## Using Periodic Functions to Determine Pr |

## Using Periodic Functions to Determine Pr |