# Elementary Number Theory Problems 3.3 Solution (David M. Burton's 7th Edition) - Q15

My Solution for "Another unanswered question is whether there exists an infinite number of sets of five consecutive odd integers of which four are primes. Find five such sets of integers."

## Table of Contents

Background

All theorems, corollaries, and definitions listed in the book's order:

**I will only use theorems or facts that are proved before this question**. So you will not see that I quote theorems or facts from the later chapters.

## Question

Another unanswered question is whether there exists an infinite number of sets of five consecutive odd integers of which four are primes. Find five such sets of integers.

## Solution

(I wrote a program for this question.)

$3, 5, 7, 9, 11$

$5, 7, 9, 11, 13$

$11, 13, 15, 17, 19$

$101, 103, 105, 107, 109$

$191, 193, 195, 197, 199$

**Read More:** All My Solutions for This Book

## Related Pages

### Ranblog Newsletter

Join the newsletter to receive the latest updates in your inbox.