Elementary Number Theory Problems 3.3 Solution (David M. Burton's 7th Edition) - Q1
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
Verify that the integers $1949$ and $1951$ are twin primes.
Solution
By the Property of Composite Number, we can test all the primes $p \leq \sqrt{1949} \approx 44$ and all the primes $p \leq \sqrt{1951} \approx 44$ to see whether $1949$ and $1951$ are both primes.
The primes that are $\leq 44$ are $2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43$. Neither $1949$ nor $1951$ is divisible by any of these primes. Thus $1949$ and $1951$ are both primes. Therefore, they are twin primes.
Read More: All My Solutions for This Book