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