The prime numbers up to 200 are: **2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73 , 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199**.

In this article, we will learn about prime numbers. We will start with a description of prime numbers. Then, we will look at some of their most important properties. Also, we will use a table to understand how we can find prime numbers.

## What is the definition of prime numbers?

Prime numbers are defined as positive integers that have exactly two factors. Numbers that have more than two factors are called composite numbers. If we have that *p* is a prime number, then by definition it only has two factors that are 1 and *p*.

### The first ten prime numbers

The first ten prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29.

### EXAMPLES

- The number 6 is not a prime number because it has the factors 1, 2, 3 and 6.
- The number 7 is a prime number since it only has the factors 1 and 7.
- The number 16 is not a prime number since it has the factors 1, 2, 4, 8, 16.
- The number 17 is a prime number since it only has the factors 1 and 17.

## Is 1 considered a prime number?

1 is not a prime number since all prime numbers are defined as positive integers that only have two factors.

The number 1 only has one factor that is itself, therefore, 1 is not considered a prime number. If 1 were to be considered a prime number, we would have to redefine some mathematical properties.

Keep in mind that 1 is not a composite number either since it has no other factors apart from itself.

## Important properties of prime numbers

The following are some of the most important properties of prime numbers:

- Each of the numbers greater than 1 can be divided by at least one prime number without leaving a remainder.
- All positive integers greater than 2 can be expressed as the sum of two prime numbers.
- All prime numbers are odd with the exception of 2. Therefore, 2 is the only prime number that is even.
- All composite numbers can be factored into prime factors and they are all unique.

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## Table of prime numbers from 1 to 100

To visualize the first prime numbers up to 100, we can form a table with all the numbers and cross out the composite numbers.

To find composite numbers, we look for all numbers that are multiples of 2, 3, 5, 7, and 11.

Since we have eliminated all composite numbers, we only have the remaining prime numbers. The following list of prime numbers from 1 to 100: **2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71 , 73, 79, 83, 89, 97**.

You don’t have to memorize all the prime numbers, however, it is advisable to memorize the first prime numbers: 2, 3, 5, 7, 11, 13.

## Prime numbers up to 200

Since we have already obtained a list with the first prime numbers up to 100, now we can form a list with the prime numbers from 1 to 200:

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199

## Examples of prime numbers

The following are some examples to determine whether a number is prime or not:

#### EXAMPLES

- Determine whether 35 is prime or not

**Answer:** The factors of 35 are 1, 5, 7, 35. 35 has more than two factors, therefore it is not prime.

- Determine whether 37 is prime or not

**Answer:** The factors of 37 are 1 and 37. 37 has exactly two factors, so it is prime.

- Determine whether 45 is prime or not

**Answer:** The factors of 45 are 1, 3, 5, 9, 15, 45. 45 has more than two factors, so it is not prime.

- Determine whether 41 is prime or not

**Answer:** The factors of 41 are 1 and 41. 41 has exactly two factors, so it is prime.

## Frequent questions

### How can I find prime numbers?

We can determine whether a number is prime or not by dividing it by 2, 3, 5, 7, and 11. If we do not get a remainder by dividing by these numbers, then the number is not prime.

### Can we have negative prime numbers?

No, we cannot have negative prime numbers. One definition of prime numbers is that prime numbers are numbers greater than 1 that have exactly two factors.

### How many factors does a prime number have in total?

In total, a prime number has exactly two factors, itself and 1.

### What is the largest known prime number?

The largest known prime number as of November 2020 is 2^{82,589,933} − 1. These numbers are found using computers and numerical methods.

## See also

Interested in learning more about prime numbers? Take a look at these pages:

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