Question

1. # HOW MANY PRIME NUMBERS ARE THERE BETWEEN 1 TO 100

## Introduction

We often hear about prime numbers in mathematics, but what are they exactly? Prime numbers are those that can only be divided by 1 and themselves. For example, the number 7 is a prime number because the only numbers it can be divided by are 1 and 7. So, how many prime numbers are there between 1 and 100? Let’s take a look.

## The Sieve of Eratosthenes

There are an infinite number of prime numbers, but the Sieve of Eratosthenes is a simple way to find all of the prime numbers between two specific numbers.

To use the Sieve of Eratosthenes, you start by writing down all of the numbers between your two chosen numbers. Then, you cross out all of the numbers that are not prime. You do this by starting with the first number that is not crossed out and crossing out every number that is a multiple of that number. Once you have gone through all of the numbers and crossed out all of the non-prime ones, what is left are the prime numbers between your original two chosen numbers.

## The Fundamental Theorem of Arithmetic

The Fundamental Theorem of Arithmetic is a theorem in mathematics that states that any positive integer can be written as a product of prime numbers, in just one way, up to the order of the factors.

This theorem is the foundation for understanding prime numbers, and has far-reaching implications in number theory and other areas of mathematics. It is one of the most important theorems in mathematics.

## Euclid’s Elements

Euclid’s Elements is perhaps the most famous work in mathematics. It is a collection of 13 books that cover a wide range of mathematical topics. Book I, for example, deals with plane geometry, while Book II deals with number theory.

The Elements was written around 300 BC by the Greek mathematician Euclid. It is one of the oldest surviving mathematical texts and has been immensely influential throughout history. In fact, it is considered to be one of the most important works in the history of mathematics.

There are an infinite number of prime numbers, but there are only a finite number between any two given numbers. For example, there are only finitely many prime numbers between 1 and 100. This can be proved using Euclid’s Elements.

## Conclusion

In conclusion, the number of prime numbers between 1-100 is twenty five. This can be easily deduced by the Sieve of Eratosthenes algorithm or by manually checking each number for divisibility. Although there are 25 primes in this range, there are an infinite number of primes as we continue to larger numbers.