Prime Number Calculator

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What is meant by prime number?

Essentially, prime number or the word prime is stated to be the natural number which is greater than 1 & that does not have positive divisors except 1 & itself. Moreover, a natural number which is not greater than 1 & which does not happen to be a prime number is known as a composite number.

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5  is  prime number because 1 &  5 are its only positive  integer factors

while 6 is stated to be a composite number for the fact  that it has divisors 2 & 3 apart from 1 & 6

Fundamental theorem of arithmetic

This fundamental theorem of arithmetic states that any integer which is greater than 1 will be able to be expressed in the form of a product of primes (which is unique) & this is done up to ordering. However, the aspect that makes this theorem quite different is the fact that 1 is to be excluded as prime. The reason behind this exclusion is that an individual will be in a position to include numerous instances of 1 & this is possible in any factorization like the one mentioned below –

\( e.g.,\, 3\, ,1 \cdot 3 ,1 \cdot 1 \cdot 3,etc.\)

\( here \,are\, all \,valid\, factorizations\, of \,the\, number\, 3\)

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What is primality?

The fact about a property being known as either a prime or not a prime is said to be primality. While trial division is stated to be a quite simple but a slow method to know or to verify primality of a number. However, there are other kinds of tests which are put in to use to know the primality of the large numbers. And one of them is the Miller – Rabin primality test. This test is though fast still has small probability of error.

While on the other hand, AKS primality test comes up with the correct answer that too in the polynomial time. However, at the end, it is stated to be a little slow to be practical enough. An individual will be able to find the possible solution to this question in the form of Mersenne numbers. While the largest prime number to be ever known or at the least till January of 2016 is stated to be 22,338,618  decimal digits.

What is the use of a prime number?

Basically, prime numbers or simply primes are put in to use in the following fields, information technology in general & public – key cryptography in specific as this makes use of the properties like that of the difficulties faced when factoring large numbers especially to their prime factors. Additionally, these prime numbers come up with several different generalizations in some or the other mathematical domains like that of algebra & especially for prime elements besides the prime ideals.

How to use online prime number calculator?

Individuals who wish to make use of the prime number calculator will have to first enter the number in the field marked for it before they click on calculate tab to know the answer.