A prime number is a natural number larger than 1 that cannot be divided by two lesser natural numbers. Prime Numbers are a part of the number system. An understanding of prime numbers is basic mathematics and is an important topic of algebra.. A prime number is a positive natural number with only one and the number itself as positive natural number divisors. Prime numbers are a subset of natural numbers. For example, the only divisors of 11 are 1 and 11, making 11 a prime number, while the number 48 has divisors 1, 2, 3, 4, 6, 8, 12, and 24, making 48, not a prime number. Positive integers other than 1 which are not prime are called composite numbers. In this article, we will study what are prime numbers, prime numbers 1 t0 100, and how to find them and their facts with the help of Solved Examples and FAQs.

## Prime Numbers 1 to 100

Here is a list of prime numbers from 1 to 100.

Sequence | Prime Number |

1 | 2 |

2 | 3 |

3 | 5 |

4 | 7 |

5 | 11 |

6 | 13 |

7 | 17 |

8 | 19 |

9 | 23 |

10 | 29 |

11 | 31 |

12 | 37 |

13 | 41 |

14 | 43 |

15 | 47 |

16 | 53 |

17 | 59 |

18 | 61 |

19 | 67 |

20 | 71 |

21 | 73 |

22 | 79 |

23 | 83 |

24 | 89 |

25 | 97 |

Learn more about Logarithmic Functions here.

## How to Find Prime Numbers from 1 to 100?

There are a few methods for determining if an integer is prime or not. Any of the following can be used. Let’s take a look at them one by one.

### Prime Numbers 1 to 100 using Divisibility Test

To prove whether a number is a prime number, follow the steps below:

**Step 1**: First try dividing it by 2. Use the test for divisibility of 2.

**Step 2:** See if you get a whole number. If you do, it can’t be a prime number.

**Step 3**: If you don’t get a whole number, next try dividing it by prime numbers: 3, 5, 7, 11 (not by 9 as 9 is divisible by 3) by using their divisibility test and so on, always dividing by prime numbers. See if you get a whole number. If you do, it can’t be a prime number.

### For Prime Numbers greater than 40.

If you need to list out all the prime numbers greater than 40, use the formula \(n^2 + n + 41\). All you need to do is put all the whole numbers in place of ‘n’ one by one.

However, this formula will only give you all the prime numbers greater than 40.

Put n = 0, \(0^2 + 0 + 41 = 0 + 41 = 41\)

Put n = 1, \(1^2 + 1 + 41 = 2 + 41 = 43\)

Put n = 2, \(2^2 + 2 + 41 = 6 + 41 = 47\)

### For Prime Numbers except 2 or 3.

There is a simple formula to calculate the prime numbers other than 2 and 3. We can use the formula \(6n \pm 1\).

Put n = 1, \(6(1) \pm 1\) = 5 and 7.

Put n = 2, \(6(2) \pm 1\) = 11 and 13.

Check out this article on Arithmetic Mean.

### Prime Numbers 1 to 100 using Sieve of Eratosthenes

Eratosthenes, who lived a few decades after Euclid, was one of the finest Hellenistic scholars. He worked as the main librarian of Alexandria’s library. He devised a brilliant method for locating all prime numbers up to a specific amount. The Sieve of Eratosthenes is so named because it is based on the principle of sieving (sifting) composite numbers. Here’s a demonstration of Eratosthenes’ sieve.

- Circle the number 2, since it is the first prime number, and then erase all its higher multiples, namely all the composite even numbers.
- Move on to the next non-erased number, the number 3. Erase all its higher multiples of 3 too.
- Repeat the same texts for the next non-erased numbers.

## Properties of Prime Numbers

Some of the important properties of prime numbers are given below:

- A prime number is a composite number greater than 1. Hence, while dividing the prime number we always get the reminder 1.
- Prime Numbers has exactly two factors, that is, 1 and the number itself.
- There is one and only one even prime number, that is, 2.
- 1 is neither prime nor composite.
- When a set of integers or numbers has only the number 1 as the common factor then they are known as Co-Prime Numbers. Hence, any two prime numbers are always co-prime to each other.
- Every number can be expressed as the product of prime numbers.
- Every even integer bigger than 2 can be split into two prime numbers, such as 6 = 3 + 3 or 8 = 3 + 5.

## Facts about Prime Numbers from 1 to 100

Here are some cool facts about prime numbers from 1 to 100

- Prime numbers that are two spaces apart are called twin prime numbers. Here are twin prime numbers from 1 to 100: (3, 5), (5, 7), (11, 13), (17, 19), (29, 31), (41, 43), (59, 61), (71, 73).
- 1 is the only even prime numbers from 1 to 100
- Prime numbers are infinite.
- No prime number greater than 5 ends in a 5. This is because the rest of the numbers ending with 5 are divisible by 5 itself.
- The product of two prime numbers is called semiprime. A semiprime is a natural number that is the product of exactly two prime numbers. The two primes in the product may equal each other, so the semiprimes include the squares of prime numbers. The first semiprime is 4. Why? Its prime factors are (2 x 2).
- Living beings use prime numbers.
- Cicadas’ life cycle revolves around prime numbers.
- Modern screens are made using prime numbers.
- Manufacturers use prime numbers to balance their products.

Also, learn about Mean Deviation.

## Solved Examples of Prime Numbers 1 to 100

Here are some solved examples of Prime Numbers 1 to 100 for you to prepare for your exam.

**Solved Example: ****The number of Prime between 1 to 100 is …………………………**

**Solution:** There are 25 prime numbers under 100. The list of all prime numbers between 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, and 97.

**Solved Example:**** Is 51 a prime number?**

**Solution:** Let’s use the divisibility test on 51.

**Divisibility Test of 2:** It does not end with 0, 2, 4, 6, 8. Hence, it is not divisible by 2.

**Divisibility Test of 3:** To check the divisibility by 3, we need to add the digits of the number 51. 5 + 1 = 6. 6 is divisible by 3. Hence, 51 is divisible by 3. 3 x 17 = 51

Thus, 51 is not a prime number because it can be divided by 3 and 17, as well as by itself and 1. ie it has four factors.

**Solved Example:** What are the prime numbers from 1 to 100?

**Solution:** The prime numbers from 1 to 100 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.

**Solved Example:** Why is 1 not a prime number?

**Solution:** 1 is not a prime number because it has only one factor, namely 1. Prime numbers need to have exactly two factors.

**Solved Example: **List out twin prime numbers between 1 to 100.

**Solution: **Here are twin prime numbers from 1 to 100: (3, 5), (5, 7), (11, 13), (17, 19), (29, 31), (41, 43), (59, 61), (71, 73).

Hope this article on the Prime Numbers 1 to 100 was informative. Get some practice of the same on our free Testbook App. Download Now!

If you are checking Prime Numbers 1 to 100 article, also check the related maths articles in the table below: | |

Less than | Less than or equal to |

Decimals | Convert decimal to octal |

Like fractions | Indian place value chart |

## Prime Numbers 1 to 100 FAQs

**Q.1Why is 11 a prime number?**

**Ans.1 **Let’s use the divisibility test on 11.

Divisibility Test of 2: It does not end with 0, 2, 4, 6, 8. Hence, it is not divisible by 2.

Divisibility Test of 3: To check the divisibility by 3, we need to add the digits of the number 11. 1 + 1 = 2. 2 is not divisible by 3.

Divisibility Test of 5: Since there are no 0 or 5 at the end, 11 is not divisible by 5.

Divisibility Test of 6: Since 11 is not divisible by 2 and 3. It is not divisible by 6.

Thus, 11 is a prime number because it can be divided by 2, 3, 4, 5, 6, 7, 8, 9, or 10. So it is divisible by itself and 1.

**Q.2What are the prime and composite numbers from 1 to 100?**

**Ans.2 **The total prime numbers between 1 to 100 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. The no of prime numbers from 1 to 100 is 25.

The composite numbers from 1 to 100 are: 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, 70, 72, 74, 75, 76, 77, 78, 80, 81,82, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 98, 99, 100.

**Q.3What is the probability of prime numbers from 1 to 100?**

**Ans.3 **As a result, the chance of a prime being chosen at random is 15/50 = 30%. As long as we have a list of primes, we can carry out this method by just counting them.

**Q.4How do you find a prime number?**

**Ans.4 **To prove whether a number is a prime number, follow the steps below:

**Step 1**: First try dividing it by 2. Use the test for divisibility of 2.

**Step 2**: See if you get a whole number. If you do, it can’t be a prime number.

**Step 3**: If you don’t get a whole number, next try dividing it by prime numbers: 3, 5, 7, 11 (not by 9 as 9 is divisible by 3) by using their divisibility test and so on, always dividing by prime numbers. See if you get a whole number. If you do, it can’t be a prime number.

**Q.5What are co-prime numbers?**

**Ans.5 **When a set of integers or numbers has only the number 1 as the common factor then they are known as co-prime numbers.