 ## What is a Prime Number?

A prime number is a natural number that is only divisible by 1 and itself. When being divided, the answer must be a positive integer (natural number), without any fractions, decimals, or remainders being left over.

Another way of explaining this is to say that If p is a prime number, then the only factors it can be 1 and p itself.

Prime Number Definition: A prime number is a natural number greater than 1 that can be divided exactly only by itself and 1, for example,- 5, 7, 19 and 23. In Hindi Prime Number is known as रूढ़ या अभाज्‍य संख्‍या.

The first 10 prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23 and 29.

The first 20 prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67 and 71.

Note: Number 1 is neither a prime number nor a composite number.

## Prime Numbers List

Along with the definition of Prime Numbers, we are also providing the list of prime numbers from 1 to 100 and 1 to 1000. There are a total of 25 prime numbers between 1 to 100 and 168 prime numbers between 1 to 1000.

## Prime Numbers from 1 to 100

There are 25 prime numbers between 1 to 100. The list of 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 and 97. The complete list of prime numbers from 1 to 100 is given below:

### Prime Numbers from 1 to 1000

There are a total of 168 prime numbers between 1 to 1000. The list of Prime Numbers from 1 to 1000 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.

## Properties of Prime Numbers

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

1. A prime number is a whole number greater than 1.
2. It has exactly two factors i.e., 1 and the number itself.
3. There is only one even prime number i.e. 2.
4. Except 2, all other prime numbers are odd. In other words, we can say that 2 is the only even prime number.
5. Any two prime numbers are always co-prime to each other.
6. Every number can be expressed as the product of prime numbers.
7. The prime numbers 2 and 3 are the only two natural numbers that are prime in consecutive order.

## Terms Related to Prime Numbers

Some important points and terms related to Prime Numbers are discussed below.

### Twin Prime Numbers

The prime numbers with only one composite number between them are called twin prime numbers or we can say twin prime numbers are the pair of prime numbers that differ by 2 only. Some twin prime numbers are (3, 5), (5, 7) and (11, 13). (2,3) are not considered as twin primes, since there is no composite number in between them and the difference between the two primes is not equal to 2. The first ten twin prime numbers are (3, 5), (5, 7), (11, 13), (17, 19), (29, 31), (41, 43), (59, 61), (71, 73), (101, 103), (107, 109) and (137, 139).

### Smallest Prime Number

2 is the smallest prime number in Mathematics. 1 can only be divided by one number, 1 itself, so with this definition 1 is not a prime number. Due to this reason, 2 is the smallest prime number.

### Largest Prime Number

As of now, 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 Number

2 is the only even prime number in Mathematics. All prime numbers except 2 are odd numbers, that's why 2 is called an even prime number

### Twist Prime Number

When we reverse the position of digits and both numbers are prime numbers then it is called Twist Prime Numbers. Some examples of Twist Prime Numbers are (13, 31) and (17, 71). 13 and 31 are the twisted prime numbers and 17 and 71 are the twisted prime numbers.

## How to check a prime number?

To check if the number is prime or not, we can use the factorization method.

The steps involved to check prime numbers are:

• Step 1: Find out the factors for the given number.
• Step 2: Count the number of factors for that number.
• Step 3: Hence, if there are more than 2 factors, it is a composite number. Otherwise, It is a prime number.

### How to find prime numbers?

The two approaches below will assist you in determining whether a particular number is a prime or not.

1. Tests of Divisibility
2. Factorization

### Method 1: Tests of Divisibility

To find out if the number is prime or not, some prime number formulas can be used. Follow the steps below to determine whether a number is a prime number or not:

Step 1: Look at the number's unit place. It is not a prime number if it ends in 0, 2, 4, 6, or 8. Numbers ending in 0, 2, 4, 6, and 8 are never prime numbers.

Step 2: Add the digits of that number together. The sum is not a prime number if it is divisible by three.

Step 3: Determine the square root of the given number after checking the result of stages 1 and 2.

Step 4: Simply divide the provided number from all prime numbers below its square root value.

Note: If a large number is ending with 5, then it is always divisible by 5. Hence, it is not a prime number.

### Method 2: Factorization

Factorization is the most popular approach for finding prime numbers. The following are the stages involved in using the factorization method to find prime numbers:

Step 1: We'll look for the factors of the given integer (factors are the number that completely divides the given number)

Step 2: Next, determine the total number of factors associated with that number.

Step 3: As a result, if the total number of factors is greater than two, the number is a composite number rather than a prime number.

### Prime Numbers and Co-prime Numbers

There is a difference between prime numbers and co-prime numbers. Co-prime numbers are always considered in pairs, while a single number can be interpreted as a prime number. If a pair of numbers has no common factor apart from 1, then the numbers are called co-prime numbers.
Co-prime numbers can be prime or composite, the only criteria to be met is that the GCF of co-prime numbers is always 1.

Examples of co-prime numbers:

5 and 9 are co-primes.

6 and 11 are co-primes.

18 and 35 are co-primes.

Note: - Co-prime numbers need not necessarily be prime numbers.

### Prime Numbers and Composite Numbers

A prime number is a number that has exactly two factors i.e. '1' and the number itself. A composite number has more than two factors, which means apart from getting divided by 1 and the number itself, it can also be divided by at least one positive integer. A comparison between Prime Numbers vs Composite Numbers is given below.

## Prime Numbers- Solved Questions

Q1: What is the prime factorization of 23?

Answer: The prime factorization of 23 = 1 and 23. Since 23 is a prime number, therefore, it has only two factors.

Q2: Find out which of the following is a prime number?

78, 45, 61, 29, 93, 9.5, 64, 42

Answer: The prime number has only two factors. So, we have factors of

78= 1, 2, 3, 6, 13, 26, 39, and 78 .

45= 1, 3, 5, 9, 15, and 45.

61= 1 and 61

29= 1 and 29

93= 1, 3, 31 and 93.

9.5= It is a Decimal. A prime number must be a whole number.

64= 1, 2, 4, 8, 16, 32 and 64

42= 1, 2, 3, 6, 7, 14, 21 and 42.

So, after factorization, we have 61 and 29 as a prime number because they have only two factors one and itself.

Q3: Is 17 a prime number?

Answer: Yes, 17 is prime number because it only has two factors 1 and 17.

Q4: What is the formula for finding prime number?

Answer: Prime numbers other than 2 and 3, can be written in the form of

6n + 1 or 6n - 1.

So, any number apart from 2 and 3, can be checked if it is prime or not by trying to express it in the form of 6n + 1 or 6n - 1

So, If we put a whole number like 1 then the formula is

6n - 1 i.e   6(1) - 1 = 5

6n + 1 i.e   6(1) + 1 = 7

Again, If we put a whole number like 2 then the formula is

6n - 1 i.e  6(2) - 1 = 11

6n + 1 i.e  6(2) + 1 = 13

Hence, we can find if the given number is prime or not by simply, expressing it in form 6n ± 1.

Q5: Check if 83 and 88 are prime numbers or not.

The factors of 83 are 1 and 83.

The factors of 88 are 1, 2, 4, 8, 11, 22, 44, and 88 .

So, as we know that a prime number has only two factors.

Hence 83 is a prime number, whereas 88 is not a prime number as it has more than two factors.

Q6: Find out the smallest prime number between 10 to 20?

Answer: All prime numbers between 10 and 20 are 11, 13, 17, 19. There are 4 prime numbers between 10 and 20 and the smallest prime number between 10 and 20 is 11.

Q7: Which is the largest 3-digit prime number?

Answer: The largest three digit number we have is 999. After factoring 999 we get:

The factors of 999 is 1, 3, 9, 27, 37, 111, 333 and 999.

So although it is the largest three digit number but it is not a prime number.

Now, we have 998 as the number and The factors of 998 are 1, 2, 499, and 998.

So again 998 is not a prime number.

Now, we have 997 as the largest 3-digit number other than 999 and 998.

There are only 2 factors of 997, which are 1 and 997. Hence it is a prime number.

So, The largest 3-digit prime number is 997.

Q8: What is the sum of the first five prime numbers divided by four?

Answer: The first five prime numbers are 2, 3, 5, 7, and 11.

Now, the sum of first five prime numbers i.e

2 + 3 + 5 + 7 + 11= 28

So, the sum of first five prime numbers is 28 divided by four is

28 ÷ 4 =7

Hence, the sum of the first five prime numbers divided by four is 7

Q9: List all the prime numbers less than 60.

Answer: All the prime numbers from 1 to 60 are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, and  61.

So, The prime numbers less than 60 are :

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, and 59

Q10: How many prime numbers are there between 90 and 100?

Answer: 97 is the only prime number between 90 and 100 that have only two factors i.e. 1 and the number itself is 97.

Prime Numbers- FAQs

Numbers having only two factors i.e. 1 and the number itself are called prime numbers whereas numbers with more than 2 factors are composite numbers.

One of the easiest methods to find that a given number p, is a prime number, is to check the number of factors of the number p. If p has exactly two factors, 1 and p, then we say that p is a prime number.

No, the number 1 is neither a prime number nor a composite number. 1 is divisible by only itself, thus it has only 1 factor. As a result, it defies both the prime and composite number definitions. They both have more than two factors.

A prime number is a number that has only two factors, that is, 1 and the number itself. For example, 2, 3, 5, 7 are prime numbers. Co-prime numbers are the numbers whose highest common factor is 1. For example, 2 and 3 are co-prime numbers.

The smallest number which has exactly two factors 1 and itself is 2. Therefore, the smallest prime number is 2.

The answer to this question is 25. There are 25 prime numbers between 1 to 100 which 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 answer to this question is no. All prime numbers belong to the set of natural numbers or positive integers.

Yes, 2 a prime number and it is the smallest and only even prime number.

No, 91 is not a prime number because It has more than 2 factors which are 1, 7, 13 and 91.

The first five prime numbers are 2, 3, 5, 7 and 11.

The prime numbers between 1 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.

Yes, 23 is a prime number because it has only two factors i.e. 1 and 23 itself.

Yes, 29 is a prime number because it is only divisible by 1 and 29 itself.

2 is the smallest and only even prime number.