Prime numbers are natural numbers that are divisible by only1 and the number itself. In other words, prime numbers are positive integers greater than 1 with exactly two factors, 1 and the number itself.Some of the prime numbers include 2, 3, 5, 7, 11, 13, etc. Always remember that 1 is neither prime nor composite. Also, we can say that except for 1, the remaining numbers are classified as prime and composite numbers. All prime numbers are odd numbers except 2, 2 is the smallest prime number and is the only even prime number.
Prime numbers are the natural numbers greater than 1 with exactly two factors, i.e. 1 and the number itself.
In this article, you will learn the meaning and definition of prime numbers, their history, properties, list of prime numbers from 1 to 1000, chart, differences between prime numbers and composite numbers, how to find the prime numbers using formulas, along with video lesson and examples.
Learn: Mathematics
- Definition
- History
- Properties
- Chart
- Video lesson
- List
- Prime numbers 1 to 200
- Prime numbers 1 to 1000
- Facts
- How to Find
- Prime numbers vs Composite numbers
- Solved examples
- Practice problems
- FAQs
What are Prime Numbers?
A prime number is a positive integer having exactly two factors, i.e. 1 and the number itself. If p is a prime, then its only factors are necessarily 1 and p itself. Any number that does not follow this is termed a composite number, which can be factored into other positive integers. Another way of defining it is a positive number or integer, which is not a product of any other two positive integers other than 1 and the number itself.
First Ten Prime Numbers
The first ten primes are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29.
Note: It should be noted that 1 is a non-prime number. It is a unique number.
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History of Prime Numbers
The prime number was discovered by Eratosthenes (275-194 B.C., Greece). He took the example of a sieve to filter out the prime numbers from a list of natural numbers and drain out the composite numbers.
Students can practise this method by writing the positive integers from 1 to 100, circling the prime numbers, and putting a cross mark on composites. This kind of activity refers to the Sieve of Eratosthenes.
Properties of Prime Numbers
Some of the properties of prime numbers are listed below:
- Every number greater than 1 can be divided by at least one prime number.
- Every even positive integer greater than 2 can be expressed as the sum of two primes.
- Except 2, all other prime numbers are odd. In other words, we can say that 2 is the only even prime number.
- Two prime numbers are always coprime to each other.
- Each composite number can be factored into prime factors and individually all of these are unique in nature.
Prime Numbers Chart
Before calculators and computers, numerical tables were used for recording all of the primes or prime factorizations up to a specified limit and are usually printed. The most beloved method for producing a list of prime numbers is called the sieve of Eratosthenes. This method results in a chart called Eratosthenes chart, as given below. The chart below shows the prime numbers up to 100, represented in coloured boxes.
Video Lesson on Prime Numbers
A prime number is a whole number greater than 1 whose only factors are 1 and itself. The first ten primes are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29. It should be noted that 1 is a non-prime number. Conferring to the definition of prime number, which states that a number should have exactly two factors, but number 1 has one and only one factor. Thus 1 is not considered a Prime number.
To learn more about prime numbers watch the video given below.
List of Prime Numbers 1 to 100
There are several primes in the number system. As we know, the prime numbers are the numbers that have only two factors which are 1 and the number itself.
The list of prime numbers from 1 to 100 are given below:
| Prime Numbers between 1 and 100 | |
| Prime numbers between 1 and 10 | 2, 3, 5, 7 |
| Prime numbers between 10 and 20 | 11, 13, 17, 19 |
| Prime numbers between 20 and 30 | 23, 29 |
| Prime numbers between 30 and 40 | 31, 37 |
| Prime numbers between 40 and 50 | 41, 43, 47 |
| Prime numbers between 50 and 60 | 53, 59 |
| Prime numbers between 60 and 70 | 61, 67 |
| Prime numbers between 70 and 80 | 71, 73, 79 |
| Prime numbers between 80 and 90 | 83, 89 |
| Prime numbers between 90 and 100 | 97 |
Thus, there are 25 prime numbers between 1 and 100, i.e.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. All these numbers are divisible by only 1 and the number itself. Hence, these numbers are called prime numbers. Also, these are the first 25 prime numbers.
Prime Numbers 1 to 200
Here is the list of prime numbers from 1 to 200, which we can learn and crosscheck if there are any other factors for them.
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
Prime Numbers 1 to 1000
There are a total of 168 prime numbers between 1 to 1000. They 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, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797, 809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911, 919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997.
Also, get the list of prime numbers from 1 to 1000 along with detailed factors here.
Facts About Prime Numbers
The table below shows the important points about prime numbers. These will help you to solve many problems in mathematics.
| Smallest Prime Number | 2 |
| Largest Prime Number | As of November 2022, the largest known prime number is 282,589,933 – 1, with 24,862,048 digits. It was founded by the Great Internet Mersenne Prime Search (GIMPS) in 2018. |
| Even Prime Number | 2 is the only even prime number, and the rest of the prime numbers are odd numbers, hence called odd prime numbers. |
| Twin Prime numbers | The prime numbers with only one composite number between them are called twin prime numbers or twin primes. The other definition of twin prime numbers is the pair of prime numbers that differ by 2 only. For example, 3 and 5 are twin primes because 5 – 3 = 2. The other examples of twin prime numbers are:
|
| Coprime numbers | Two numbers are called coprime to each other if their highest common factor is 1. Prime numbers and coprime numbers are not the same. For example, 6 and 13 are coprime because the common factor is 1 only. |
Click here to learn more about twin prime numbers.
How to Find Prime Numbers?
The following two methods will help you to find whether the given number is a prime or not.
Method 1:
We know that 2 is the only even prime number. And only two consecutive natural numbers which are prime are 2 and 3. Apart from those, every prime number can be written in the form of 6n + 1 or 6n – 1 (except the multiples of prime numbers, i.e. 2, 3, 5, 7, 11), where n is a natural number.
For example:
6(1) – 1 = 5
6(1) + 1 = 7
6(2) – 1 = 11
6(2) + 1 = 13
6(3) – 1 = 17
6(3) + 1 = 19
6(4) – 1 = 23
6(4) + 1 = 25 (multiple of 5)
…
Method 2:
To know the prime numbers greater than 40, the below formula can be used.
n2 + n + 41, where n = 0, 1, 2, ….., 39
For example:
(0)2 + 0 + 0 = 41
(1)2 + 1 + 41 = 43
(2)2 + 2 + 41 = 47
…..
Is 1 a Prime Number?
Conferring to the definition of the prime number, which states that a number should have exactly two factors for it to be considered a prime number. But, number 1 has one and only one factor which is 1 itself. Thus, 1 is not considered a Prime number.
Examples: 2, 3, 5, 7, 11, etc.
In all the positive integers given above, all are either divisible by 1 or itself, i.e. precisely two positive integers.
- Is 97 a prime number?
- Is 61 a prime number?
- Is 57 a prime number?
- Is 83 a prime number?
Prime Numbers vs Composite Numbers
A few differences between prime numbers and composite numbers are tabulated below:
| Prime Numbers | Composite Numbers |
| A prime number has two factors only. | A composite number has more than two factors. |
| It can be divided by 1 and the number itself. For example, 2 is divisible by 1 and 2. | It can be divided by all its factors. For example, 6 is divisible by 2,3 and 6. |
| Examples: 2, 3, 7, 11, 109, 113, 181, 191, etc. | Examples: 4, 8, 10, 15, 85, 114, 184, etc. |
Prime Numbers Related Articles
- Co-prime Numbers
- Composite numbers
- How To Find Prime Numbers
- Prime number formula
- Prime Factors
Solved Examples on Prime Numbers
Example 1:
Is 10 a Prime Number?
Solution:
No, because it can be divided evenly by 2 or 5, 2×5=10, as well as by 1 and 10.
Alternatively,
Using method 1, let us write in the form of 6n ± 1.
10 = 6(1) + 4 = 6(2) – 2
This is not of the form 6n + 1 or 6n – 1.
Hence, 10 is not a prime number.
Example 2:
Is 19 a Prime Number?
Solution:
Let us write the given number in the form of 6n ± 1.
6(3) + 1 = 18 + 1 = 19
Therefore, 19 is a prime number.
Example 3:
Find if 53 is a prime number or not.
Solution:
The only factors of 53 are 1 and 53.
Or
Let us write the given number in the form of 6n ± 1.
6(9) – 1 = 54 – 1 = 53
So, 53 is a prime number.
Example 4:
Check if 64 is a prime number or not.
Solution:
The factors of 64 are 1, 2, 4, 8, 16, 32, 64.
It has factors other than 1 and 64.
Hence, it is a composite number and not a prime number.
Example 5:
Which is the greatest prime number between 1 to 10?
Solution:
As we know, the first 5 prime numbers are 2, 3, 5, 7, 11.
There are 4 prime numbers between 1 and 10 and the greatest prime number between 1 and 10 is 7.
Practice Problems
- Identify the prime numbers from the following numbers:
34, 27, 29, 41, 67, 83 - Which of the following is not a prime number?
2, 19, 91, 57 - Write the prime numbers less than 50.
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Frequently Asked Questions on Prime Numbers
What are Prime Numbers in Maths?
The numbers which have only two factors, i.e. 1 and the number itself are called prime numbers. In other words, prime numbers are divisible by only 1 and the number itself. That means they are not divisible by any other numbers. Some examples of prime numbers are 7, 11, 13, 17,…
How to find prime numbers?
To find whether a number is prime, try dividing it with the prime numbers 2, 3, 5, 7 and 11. If the number is exactly divisible by any of these numbers, it is not a prime number, otherwise, it is a prime. Alternatively, we can find the prime numbers by writing their factors since a prime number has exactly two factors, 1 and the number itself.
What are the examples of prime numbers?
As we know, prime numbers are whole numbers greater than 1 with exactly two factors, i.e. 1 and the number itself. Some of the examples of prime numbers are 11, 23, 31, 53, 89, 179, 227, etc.
What is the smallest prime number?
2 is the smallest prime number. Also, it is the only even prime number in maths.
What is the largest prime number so far?
As of November 2022, the largest known prime number is 282,589,933– 1, with 24,862,048 digits. It was founded by the Great Internet Mersenne Prime Search (GIMPS) in 2018.
Which is the largest 4 digit prime number?
The largest 4 digits prime number is 9973, which has only two factors namely 1 and the number itself.
What are prime numbers between 1 and 50?
The list of prime numbers between 1 and 50 are:
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47
Why 1 is not a prime number?
As per the definition of prime numbers, 1 is not considered as the prime number since a prime number is a natural number greater than 1 that is not a product of two smaller natural numbers.
FAQs
What are examples of prime numbers from 1 to 1000? ›
The first few prime numbers from 1 to 1000 are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, and so on.
What is prime number and examples? ›Prime numbers are numbers that have only 2 factors: 1 and themselves. For example, the first 5 prime numbers are 2, 3, 5, 7, and 11. By contrast, numbers with more than 2 factors are call composite numbers.
What are the prime factors list 1000? ›Prime Factorization of 1000: 1000 = 2 × 2 × 2 × 5 × 5 × 5.
How many prime numbers are there in 1 to 1000? ›How many prime numbers are there in between 1 to 1000? There are a total of 168 prime numbers in between 1 to 1000.
How do you know if a number is prime? ›How do you know a prime number? If a number has only two factors 1 and itself, then the number is prime.
How do you teach prime numbers? ›The easiest way for your kid to find out if a number is prime is to try and divide that number by all the numbers that are smaller. If it can only be divided by 1 and itself then it's a prime number.
Why 3 is a prime number example? ›A prime number is the one which has exactly two factors, which means, it can be divided by only “1” and itself. But “1” is not a prime number. 3 is a prime number because 3 can be divided by only two number's i.e. 1 and 3 itself. In the same way, 2, 5, 7, 11, 13, 17 are prime numbers.
Why is 9 a prime number? ›9 is not a prime number. It can be divided by 3 as well as 1 and 9. The prime numbers below 20 are: 2, 3, 5, 7, 11, 13, 17, 19.
What are 24 prime numbers? ›So, the prime factorisation of 24 is 2 × 2 × 2 × 3 or 23 × 3, where 2 and 3 are the prime numbers.
Why is 6 a prime number? ›No, 6 is not a prime number. The number 6 is divisible by 1, 2, 3, 6. For a number to be classified as a prime number, it should have exactly two factors. Since 6 has more than two factors, i.e. 1, 2, 3, 6, it is not a prime number.
What number has the most factors from 1 to 1000? ›
Sanika and Amy both said that the number under 1000 with the most factors is 840 (32 factors).
Why is 1000 not a prime number? ›For a number to be classified as a prime number, it should have exactly two factors. Since 1000 has more than two factors, i.e. 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 200, 250, 500, 1000, it is not a prime number.
How do you find the greatest prime factor of 1000? ›Answer. Use prime factorization to find the greatest prime factor of 1000: 1000 = 2 × 2 × 2 × 5 × 5 × 5. The greatest prime factor of 1000 is 5.
How do you find prime numbers easily? ›To prove whether a number is a prime number, first try dividing it by 2, and see if you get a whole number. If you do, it can't be a prime number. If you don't get a whole number, next try dividing it by prime numbers: 3, 5, 7, 11 (9 is divisible by 3) and so on, always dividing by a prime number (see table below).
Are all prime numbers odd? ›First, except for the number 2, all prime numbers are odd, since an even number is divisible by 2, which makes it composite. So, the distance between any two prime numbers in a row (called successive prime numbers) is at least 2.
Why is 27 not a prime number? ›Is 27 a prime number? No. 27 is divisible by other numbers (3 and 9), so it is not prime. The factors of 27 are 1, 3, 9, and 27, so it is not prime.
What is the logic for prime number? ›A natural number is said to be prime if it is only divisible by itself and 1. In short, a prime number has only two factors that are 1 and the number itself. The numbers that are not prime are called composite numbers. A prime number can be written as a product of only two numbers.
How do you know if a number is prime or long? ›The easiest way to identify a prime number is by finding the factors of the given number. If the number has more than two factors, then it is not a prime number. However, if the given number has only two factors - 1 and the number itself, then it is a prime number.
Can negative numbers be prime? ›Answer One: No.
By the usual definition of prime for integers, negative integers can not be prime. By this definition, primes are integers greater than one with no positive divisors besides one and itself. Negative numbers are excluded.
A prime number is a whole number greater than 1 whose only factors are 1 and itself. A factor is a whole number that can be divided evenly into another number. The first few prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23 and 29.
Why is 69 not a prime number? ›
The number 69 is a composite number. Its factors are 1, 3, 23, and 69. Because 69 has more than two factors, it is a composite number rather than a prime number.
What are prime numbers for 5th grade? ›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.
How do you explain prime numbers to 6th grade? ›Prime numbers are numbers greater than 1. They only have two factors, 1 and the number itself. This means these numbers cannot be divided by any number other than 1 and the number itself without leaving a remainder. Numbers that have more than 2 factors are known as composite numbers.
Why do we teach prime numbers? ›One of the reasons primes are important in number theory is that they are, in a certain sense, the building blocks of the natural numbers. The fundamental theorem of arithmetic (the name of which indicates its basic importance) states that any number can be factored into a unique list of primes.
Is 2 a prime number yes or no? ›The number 2 is prime. (It is the only even prime.)
Why is 45 a prime number? ›No, 45 is not a prime number. The number 45 is divisible by 1, 3, 5, 9, 15, 45. For a number to be classified as a prime number, it should have exactly two factors. Since 45 has more than two factors, i.e. 1, 3, 5, 9, 15, 45, it is not a prime number.
Why is 8 not a prime number? ›The factors of 8 are: 1, 8, 2, and 4. Since 8 is evenly divisible by more numbers than just itself (8) and 1, it is not a prime number.
Why is only 2 prime number? ›Why is 2 a prime number? 2 is a prime number because its only factors are 1 and itself.
Is 73 a mirror prime number? ›"73 is the 21st prime number," Sheldon explains. "Its mirror, 37, is the 12th and its mirror, 21, is the product of multiplying 7 and 3 ... and in binary 73 is a palindrome, 1001001, which backwards is 1001001."
Why 2 is a prime number? ›Yes, 2 is a prime number.
According to the definition of prime numbers, any whole number which has only 2 factors is known as a prime number. Now, the factors of 2 are 1 and 2. Since there are exactly two factors of 2, it is a prime number.
What are 50 prime numbers? ›
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. Prime Numbers Facts: The only even prime number is 2 and the remaining even numbers can be divided by 2.
Is 12 a prime number yes or no? ›No, 12 is not a prime number. The number 12 is divisible by 1, 2, 3, 4, 6, 12. For a number to be classified as a prime number, it should have exactly two factors. Since 12 has more than two factors, i.e. 1, 2, 3, 4, 6, 12, it is not a prime number.
Why is 77 not a prime number? ›The number 77 is a composite number. Since 77 has more than two factors, it is not a prime number. The factors of 77 are 1, 7, 11, and 77. The number 77 has four factors which makes it a composite number.
What is the largest prime number? ›The largest known prime number (as of February 2023) is 282,589,933 − 1, a number which has 24,862,048 digits when written in base 10.
Is 1 a prime number yes or no? ›1 can only be divided by one number, 1 itself, so with this definition 1 is not a prime number. It is important to remember that mathematical definitions develop and evolve. Throughout history, many mathematicians considered 1 to be a prime number although that is not now a commonly held view.
What is 1 called if it is not a prime? ›The number one is neither a prime nor a composite. In mathematics, there are various categories of numbers in which number 1 falls. So, 1 can be called by any of the following: A natural number. An odd number.
What is the 1000th prime number? ›So is 7919 (in fact it is the 1000th prime). There are 25 primes between 1 and 100. From 1 to 1000 there are 168 of them.
What are common prime factors? ›If two numbers have a prime factor in common, then we say that the prime factor is a common prime factor of those two numbers. For example, consider the numbers 12 and 42. The factors of 12 and 42 are as follows: Factors of 12: 1, 2, 3, 4, 6, 12.
What are the common factors of 1000? ›All the numbers in the product are factors. Hence, the factors of 1000 are 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 200, 250, 500 and 1000.
Can prime numbers zero? ›0 is less than 1 so can't be prime. Composite integers are those that are the products of primes such as 6 = 2x3. 0 cannot be expressed as a product of primes because such products are non-zero.
Why is 22 not a prime number? ›
Answer and Explanation: No, 22 is not a prime number because it can be evenly divided by 1, 22 and 2. The closest prime number to 22 is 23.
When did 1 stop being a prime number? ›By the early 20th century, mathematicians began to agree that 1 should not be listed as prime, but rather in its own special category as a "unit".
What is the fastest way to find prime factors? ›The simplest algorithm to find the prime factors of a number is to keep on dividing the original number by prime factors until we get the remainder equal to 1. For example, prime factorizing the number 30 we get, 30/2 = 15, 15/3 = 5, 5/5 = 1.
What is the easiest way to find the prime factor of a large number? ›How to Find Factors of Large Numbers? To calculate the factors of large numbers, divide the numbers with the least prime number, i.e. 2. If the number is not divisible by 2, move to the next prime numbers, i.e. 3 and so on until 1 is reached.
Why 51 is not a prime number? ›No, 51 is not a prime number since it has more than two factors. The factors of 51 can be written as 1, 3, 17, 51.
Why is 99 not a prime number? ›No, 99 is not a prime number. The number 99 is divisible by 1, 3, 9, 11, 33, 99. For a number to be classified as a prime number, it should have exactly two factors. Since 99 has more than two factors, i.e. 1, 3, 9, 11, 33, 99, it is not a prime number.
Are all odd numbers prime? ›No, every odd number is not a prime number. Example: 9 is an odd number having factors 1, 3 and 9 and is not a prime number.
Is 473 a prime no? ›The number 473 is composite and therefore it will have prime factors.
What are factors of prime numbers? ›A prime number is a counting number that only has two factors, itself and one.
Is 53 a prime number yes or no? ›53 (fifty-three) is the natural number following 52 and preceding 54. It is the 16th prime number.
Why is 7 not a prime number? ›
Seven is a prime number because it doesn't have proper factors. In other words, the only factors of 7 are 1 and itself.