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Which of the Following is a Prime Number?

 

Introduction

Prime numbers are a fascinating concept in mathematics. They are numbers that are only divisible by 1 and themselves, with no other factors. In this article, we will explore the concept of prime numbers, discuss their properties, and provide examples to help you understand which of the following numbers are prime.

What is a Prime Number?

A prime number is a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers. In other words, it has no divisors other than 1 and itself. For example, 2, 3, 5, 7, 11, and 13 are all prime numbers.

Properties of Prime Numbers

Prime numbers have several interesting properties:

  • Prime numbers are always odd, except for the number 2, which is the only even prime number.
  • There are infinitely many prime numbers. This was proven by the ancient Greek mathematician Euclid more than 2,000 years ago.
  • Prime numbers cannot be negative or fractions. They are always positive integers.
  • The prime factorization of a composite number is unique. This means that every composite number can be expressed as a product of prime numbers in only one way.

Identifying Prime Numbers

Now, let’s look at the following numbers and determine which of them are prime:

  1. 17
  2. 25
  3. 31
  4. 42
  5. 53

Number 17

Number 17 is a prime number. It is only divisible by 1 and 17, with no other factors. Therefore, it meets the criteria of a prime number.

Number 25

Number 25 is not a prime number. It is divisible by 1, 5, and 25. Since it has factors other than 1 and itself, it is not a prime number.

Number 31

Number 31 is a prime number. It is only divisible by 1 and 31, making it a prime number.

Number 42

Number 42 is not a prime number. It is divisible by 1, 2, 3, 6, 7, 14, 21, and 42. Since it has factors other than 1 and itself, it is not a prime number.

Number 53

Number 53 is a prime number. It is only divisible by 1 and 53, satisfying the criteria of a prime number.

Q&A

Q1: How many prime numbers are there between 1 and 100?

A1: There are 25 prime numbers between 1 and 100. Some examples include 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, and 97.

Q2: Is 1 a prime number?

A2: No, 1 is not considered a prime number. Prime numbers are defined as natural numbers greater than 1 that have no divisors other than 1 and themselves. Since 1 only has one divisor, it does not meet the criteria of a prime number.

Q3: Can prime numbers be negative?

A3: No, prime numbers are always positive integers. By definition, prime numbers are natural numbers greater than 1 that have no divisors other than 1 and themselves. Negative numbers do not fit this definition.

Q4: Are there any prime numbers between 100 and 200?

A4: Yes, there are 21 prime numbers between 100 and 200. Some examples include 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, and 199.

Q5: What is the largest known prime number?

A5: As of 2021, the largest known prime number is 2^82,589,933 − 1. It was discovered on December 7, 2018, as part of the Great Internet Mersenne Prime Search (GIMPS) project.

Summary

Prime numbers are fascinating mathematical entities that have unique properties. They are numbers that are only divisible by 1 and themselves, with no other factors. Prime numbers play a crucial role in various fields, including cryptography, number theory, and computer science.

In this article, we discussed the concept of prime numbers, their properties, and how to identify them. We also provided examples to help you understand which of the following numbers are prime. Remember, prime numbers are essential building blocks in mathematics, and their study continues to intrigue mathematicians and researchers around the world.

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