Chapter 6.CT, Problem 1CT

Use the Sieve of Eratosthenes to find all prime numbers between 100 and 120.

To determine

To find:

All prime numbers between 100 and 120, using the Sieve of Eratosthenes calculation.

Answer to Problem 1CT

Solution:

The prime numbers between 100 and 120 are $101,103,107,109,\text{ and }113.$

Explanation of Solution

1) Approach:

Find the list of prime number using the sieve of using the Sieve of Eratosthenes calculation.

2) Calculation:

Given,

The numbers between 100 and 120,

First list all the natural numbers from 100 to 120 as shown below.

1. Cross off 100 is multiple of 2.

2. The next number is 101, which is a prime so, circle it and cross all the multiples of 2

3. Cross off 102 and all other multiples of 2 which are $104,106,\dots ,120.$

4. The next number is 103, which is a prime so, circle it and cross all the multiples of 3.

5. Also cross all the multiples of 5 and 7.

6. The next prime number is 11, which is greater that the square root of 120, so stop looking for composites and circle all remaining numbers in the list.

Hence, the prime numbers between 100 and 120 are $101,103,107,109,\text{ and }113.$

Final statement:

Therefore, the prime numbers between 100 and 120 are $101,103,107,109,\text{ and }113.$