# Prime Numbers from 1 to 1000

Prime numbers from 1 to 1000 will include the list of primes, that have only two factors, i.e. 1 and the number itself. To find the prime numbers from 1 to 1000, we need to check if the number is a natural number and has no positive divisor other than 1 and itself. We do not consider 1 as a prime number, as it has only one factor but other prime numbers have two factors.

For example, 5 is a prime number, because it has only two factors, 1 and 5, such as;

• 5 = 1 x 5

But 4 is not a prime number, as it has more than two factors, 1, 2, and 4, such as,

• 1 x 4 = 4
• 2 x 2 = 4

Here, 4 is said to be a composite number. These factors can be determined with the help of the prime factorisation method.

## List of Prime Numbers 1 to 1000

Now, let us see here the list of prime numbers starting from 1 to 1000. We should remember that 1 is not a prime number, as it has only one factor. Thus, the prime numbers start from 2.

 Numbers Number of prime numbers List of prime numbers 1 to 100 25 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, 97 101-200 21 prime numbers 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199 201-300 16 prime numbers 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293 301-400 16 prime numbers 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397 401-500 17 prime numbers 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499 501-600 14 prime numbers 503, 509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599 601-700 16 prime numbers 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691 701-800 14 prime numbers 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797 801-900 15 prime numbers 809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887 901-1000 14 prime numbers 907, 911, 919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997 Total number of prime numbers (1 to 1000) = 168

From the above list of prime numbers, we can find that each of the primes has only two factors.

## How to Find Prime Numbers From 1 to 1000?

By the definition of prime numbers, we know that the prime number will have only two factors. In the above-given list, the numbers provided are all prime numbers. We can cross-check with any of these numbers to know if they are prime or not, by prime factorising them.

For example:

• 709 = 1 x 709, only two factors
• 911 = 1 x 911, only two factors
• 401 = 1 x 401, only two factors

But if we check with any other, let us say, 15, then the factors of 15 are:

• 1 x 15 = 15
• 3 x 5 = 15

Thus, there is a total of four factors: 1, 3, 5, and 15. So, 15 is not a prime number.

Therefore, this way we can find all the prime numbers. Let us see some of the properties of prime numbers, to make it easier to find them.

### Properties of Prime Numbers

• A prime number will have only two factors, 1 and the number itself
• 2 is the only even prime number
• All the even numbers greater than 2, are the product of two or more prime numbers

## Solved Examples

Q.1: From the list of prime numbers 1 to 1000 given above, find if 825 is a prime number or not?

Solution: The list of prime numbers from 1 to 1000 does not include 825 as a prime number. It is a composite number since it has more than two factors. We can confirm this by prime factorisation of 825 also.

Prime Factorization of 825 = 31 × 52 × 111

Hence, 825 includes more than two factors.

Q.2: Find if 911 is a prime number or not?

Solution: Since, 911 has only two factors, 1 and 911. Therefore, 911 is a prime number.

911 = 1 x 911

Q.3: What are the factors of 443?

Solution: Since 443 is a prime number, therefore, it has only two factors 1 and 443.

Q.4: What are the prime numbers from 1 to 300? How many are they?

Solution: The prime numbers from 1 to 300 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.

Therefore, there is a total of 62 prime numbers between 1 to 300.

## Practice Questions

1. Which of the following statements are true or false?
• 1 is a prime number – ______
• 2 is the only even prime number – ______
• 1000 is not a prime number – ______
• A prime number has more than two factors – ______
2. Find if 221 is a prime number or not.

## Frequently Asked Questions on Prime Numbers 1 to 1000

Q1

### How many prime numbers are there in between 1 to 1000?

There are a total of 168 prime numbers in between 1 to 1000.
Q2

### What are the prime numbers from 1 to 200?

The prime numbers from 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.
Q3

### How to find if a number is prime?

First, find the factors of the given number. If the number of factors is more than two, then the number is not a prime number otherwise it is a prime number.
Q4

### Why 11 is a prime number?

11 has only two factors, 1 and 11, therefore it is a prime number.
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