What are the first prime numbers?

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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.

Examples and Non-examples of Prime Numbers

Difference Between Prime Number and Composite Number

The Sieve of Eratosthenes

In third century BCE, the Greek mathematician Eratosthenes found a very simple method of finding the prime numbers. 

Follow the given steps to identify the prime numbers between 1 and 100.

Step 1: Make a hundred charts. 

Step 2: Leave 1 as it is neither a prime number nor a composite number.

Step 3: Encircle 2 and cross out all its multiples as they are not prime. 

Step 4: Encircle the next uncrossed number, which is 3, and cross out all its multiples. Ignore the previously crossed out numbers like 6, 12, 18, and so on.

Step 5: Continue the process of encircling the next uncrossed number and crossing out its multiples till all the numbers in the table are either encircled or crossed out, except 1.

So, from the table it is clear that 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 are the prime numbers. 

There are 25 prime numbers between 1 and 100.

Terms Related to Prime Numbers

Co-Primes: Two numbers are said to be co-prime if they have only one common factor, that is, 1. It is not necessary for these numbers to be prime numbers. For example, 9 and 10 are co-primes. Let’s verify.

Note that pairs of any 2 prime numbers are always co-primes. This is because, out of their two factors, the common factor can only be 1. So, (3, 5), (11, 19) are some examples of co-primes.

Twin-Primes: A pair of prime numbers are known as twin primes if there is only one composite number between them. For example, (3, 5), (5, 7), (11, 13), (17, 19), etc.

List of Prime Numbers between 1 and 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

There are 25 prime numbers between 1 and 100.

List of Prime Numbers between 1 and 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

There are 46 prime numbers between 1 and 200.

List of Prime Numbers between 1 and 1,000

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.

Some Facts about Prime Numbers

• 2 is the smallest prime number.
• 2 is the only prime number that is even.
• 2 and 3 are the only consecutive prime numbers.
• Except for 0 and 1, a whole number is either a prime number or a composite number.
• All odd numbers are not prime numbers. For example, 21, 39, etc.
• No prime number greater than 5 ends in a 5.
• Sieve of Eratosthenes is one of the earliest methods of finding prime numbers.
• Prime numbers get rarer as the number gets bigger.
• There is no largest prime number. The largest known prime number (as of September 2021) is 282,589,933 − 1, a number that has 24,862,048 digits. By the time you read this, it may be even larger than this.

  Prime numbers are natural numbers that are divisible by only 1 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

  Table of Contents:

  • Definition
  • PDF
  • 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.

  Download PDF – Prime Numbers

  Click here to download the PDF of Prime numbers:-

  Download PDF

  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 100Prime numbers between 1 and 102, 3, 5, 7Prime numbers between 10 and 2011, 13, 17, 19Prime numbers between 20 and 3023, 29Prime numbers between 30 and 4031, 37Prime numbers between 40 and 5041, 43, 47Prime numbers between 50 and 6053, 59Prime numbers between 60 and 7061, 67Prime numbers between 70 and 8071, 73, 79Prime numbers between 80 and 9083, 89Prime numbers between 90 and 10097

  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 Number2Largest Prime NumberAs of January 2020, the largest known prime number is 2^(82,589,933) – 1, with 24,862,048 digits.

  It was founded by the Great Internet Mersenne Prime Search (GIMPS) in 2018.

  Even Prime Number2 is the only even prime number, and the rest of the prime numbers are odd numbers, hence called odd prime numbers. Twin Prime numbersThe 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:

  • (5, 7) [7 – 5 = 2]
  • (11, 13) [13 – 11 = 2]
  • (17, 19) [19 – 17 = 2]
  • (29, 31) [31 – 29 = 2]
  • (41, 43) [43 – 41 = 2]
  • (59, 61) [61 – 59 = 2]
  • (71, 73) [73 – 71 = 2]
  Coprime numbersTwo 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.

  Related questions on Prime numbers:

  • 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 NumbersComposite NumbersA 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

  1. Identify the prime numbers from the following numbers:
     34, 27, 29, 41, 67, 83
  2. Which of the following is not a prime number?
     2, 19, 91, 57
  3. Write the prime numbers less than 50.

  Keep visiting BYJU’S to get more such Maths articles explained in an easy and concise way. Also, register now and get access to 1000+ hours of video lessons on different topics.
  
  

  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 January 2020, the largest known prime number is 2^(82,589,933) – 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.

  What are the first 10 prime numbers?

  The first 10 prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29. There are 25 prime numbers between 1 and 100. Prime numbers include large numbers and can continue well past 100. For example, 21,577 is a prime number.

  Why 1 is not a prime number?

  1 can only be divided by one number, 1 itself, so with this definition 1 is not a prime number.

  Why is 2 the first prime number?

  Prime numbers need to have exactly two factors. Why is 2 a prime number? 2 is a prime number because its only factors are 1 and itself.

  What is the first prime?

  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.