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Chapter 10: Problem 4

Let \(p\) and \(q\) be two prime numbers. If \(p=q+2\) then \(p\) and \(q\) are called "twin prime numbers." Find two pairs of twin prime numbers.

Short Answer

Expert verified
The pairs of twin prime numbers are (3, 5) and (5, 7).

Step by step solution

01

Understanding Prime Numbers

Prime numbers are numbers that have only two factors: 1 and the number itself. For example, the first six prime numbers are 2, 3, 5, 7, 11, and 13.
02

Identifying Twin Primes

Twin primes are pairs of prime numbers that differ by two. This difference means that if you have a prime number and you add 2 to it, if the result is also a prime number, then you have a pair of twin primes. This pair satisfies the given equation \(p=q+2\). Working through the list of given prime numbers, start with 2. Add 2 to 2, you get 4 which is not a prime number. Move on to 3, add 2 to 3 and you get 5 which is a prime number, so 3 and 5 form a pair. The same goes for 5, adding 2 to 5, gives 7 which is also a prime number, hence another pair.
03

Giving Final Pairs of Twin Primes

The pairs (3, 5) and (5, 7) are solutions to this problem since both these pairs satisfy the definition of twin primes, i.e., one number is 2 greater than the other and both numbers are prime.

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