 List Of Prime Numbers

## List Of Prime Numbers, Prime Numbers 1 to 100, How To Find Prime numbers

List Of Prime Numbers: A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers. And a natural number greater than 1 that is not prime is called a composite number. Hence, For example, 5 is prime because the only ways of writing it as a product, 1 × 5 or 5 × 1, involve 5 itself. However, 4 is composite because it is a product (2 × 2) in which both numbers are smaller than 4. The Primes are central in number theory because of the fundamental theorem of arithmetic: every natural number greater than 1 is either a prime itself or can be factorized as a product of primes that is unique up to their order. So the property of being prime is called primality.

From the very beginning, there are infinitely many primes, as demonstrated by Euclid around 300 BC. Hence, there is no known simple formula that separates prime numbers from composite numbers. So, the distribution of primes within the natural numbers in the large can be statistically modelled. However, the first result in that direction is the prime number theorem, proven at the end of the 19th century, which says that the probability of a randomly chosen large number being prime is inversely proportional to its number of digits, that is, to its logarithm.

## Definition And Examples

Few Facts: A natural number (1, 2, 3, 4, 5, 6,) etc is called a prime number (or a prime) if it is greater than 1 and cannot be written as the product of two smaller natural numbers. So the numbers greater than 1 that are not prime are called composite numbers. Hence, For example, among the numbers 1 through 6, the numbers 2, 3, and 5 are the prime numbers, as there are no other numbers that divide them evenly (without a remainder). So 1 is not prime, as it is specifically excluded in the definition. 4 = 2 × 2 and 6 = 2 × 3 are both composites.

### Some Facts

Demonstration, with Cuisenaire rods, that 7 is prime, because none of 2, 3, 4, 5, or 6 divide it evenly
Demonstration, with Cuisenaire rods, that 7 is prime, because none of 2, 3, 4, 5, or 6 divide it evenly
Every natural number has both 1 and itself as a divisor. So if it has any other divisor, it cannot be prime. Therefore this idea leads to a different but equivalent definition of the primes: they are the numbers with exactly two positive divisors, 1 and the number itself.
Here are the first 25 prime numbers (all the prime numbers less than 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 Therefore, every prime number other than 2 is an odd number and is called an odd prime. Similarly, when written in the usual decimal system, all prime numbers larger than 5 ends in 1, 3, 7, or 9. So the numbers that end with other digits are all composite: decimal numbers that end in 0, 2, 4, 6, or 8 are even, and decimal numbers that end in 0 or 5 are divisible by 5.

## Prime Number In Details

We can say Prime numbers are natural numbers that are divisible by only 1 and the number itself. So in other words, prime numbers are positive integers greater than 1 with exactly two factors, 1 and the number itself. Hence some of the prime numbers include 2, 3, 5, 7, 11, 13, etc. So always remember that 1 is neither prime nor composite. Hence, we can say that except for 1, the remaining numbers are classified as prime and composite numbers. Therefore 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, a list of prime numbers from 1 to 1000, a chart, differences between prime numbers and composite numbers, how to find the prime numbers using formulas, along with video lesson and examples.

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## History of Prime Numbers

The prime number was discovered by Eratosthenes (275-194 B.C., Greece). Once 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.

You can practise this method by writing the positive integers from 1 to 100, circling the prime numbers, and putting a cross mark on composites. Though this kind of activity refers to the Sieve of Eratosthenes.

## Some Properties of Prime Numbers

So every number greater than 1 can be divided by at least one prime number.
And every even positive integer greater than 2 can be expressed as the sum of two primes.
Hence except for 2, all other prime numbers are odd. So in other words, we can say that 2 is the only even prime number.
So every two prime numbers are always coprime to each other.
So each composite number can be factored into prime factors and individually all of these are unique in nature.

## FAQ Of Prime Numbers

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### What are Prime Numbers?

A prime number is a positive integer having exactly two factors, i.e. 1 and the number itself. So if p is a prime, then its only factors are necessarily 1 and p itself. Therefore any number that does not follow this is termed a composite number, which can be factored into other positive integers. Hence 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.

### 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.