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."

Ran
Ran

Table of Contents


Background

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

Theorems and Corollaries in Elementary Number Theory (Ch 1 - 3)
All theorems and corollaries mentioned in David M. Burton’s Elementary Number Theory are listed by following the book’s order. (7th Edition) (Currently Ch 1 - 3)
RanblogRan

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

< Chapter 3.3, Q14 Chapter 3.3, Q16 >

MathNumber TheorySolution
Ran

Ran

Comments

You might also like

Elementary Number Theory Problems 4.3 Solution (David M. Burton's 7th Edition) - Q10 Members Public

My Solution for "Prove that no integer whose digits add up to $15$ can be a square or a cube. [Hint: For any $a$, $a^{3} \equiv 0$, $1$, or $8$ $\pmod 9$.]"

Ran
Ran
Math

Elementary Number Theory Problems 4.3 Solution (David M. Burton's 7th Edition) - Q9 Members Public

My Solution for "Find the remainder when $4444^{4444}$ is divided by $9$. [Hint: Observe that $2^{3} \equiv -1 \pmod {9}$.]"

Ran
Ran
Math