Tool to search for prime numbers according to criteria. A prime number is a natural number whose divisors are 1 and itself (like 2, 3, 5, 7, 11, 13, 17, 19, etc.)

Prime Numbers Search - dCode

Tag(s) : Arithmetics

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⮞ Go to: Primality Test

⮞ Go to: Prime Factors Decomposition

Prime number finding is a field of mathematics that involves identifying and studying prime numbers, which are integers greater than 1 and having only two divisors: 1 and themselves.

There are an infinite number of prime numbers, but their distribution in the set of integers or the prediction that a number is prime remain important areas of research in mathematics.

To know if a number is prime, it is necessary to pass a primality test. A test that will verify mathematically and algorithmically, that the number is divisible by none other than itself.

The most basic method is to divide a number by all integers less than itself to check if it has any divisors other than 1 and itself.

__Example:__ `10` is divisible by 2 so is not prime

__Example:__ `11` is not divisible by 2, 3, 4, 5, 6, 7, 8, 9, or 10, so it's a prime.

There are various techniques to speed up this calculation a little, but there is no method that can find both exhaustively and quickly the list of prime numbers.

As for finding a number, it is necessary to test the primality of all numbers between a low limit and an upper limit (the beginning and the end of the list).

To list the first prime numbers, the Eratosthenes sieve is a method which consists of writing all the integers from 2 (the smallest) up to N. Then, delete all the multiples of 2, then the multiples of 3, and and so on. The remaining numbers are the first prime numbers.

Again, it has no foolproof technique to detect the next prime nor the previous prime, nor the nth prime. dCode will detect the first number (greater or lower) that will be a prime number.

Twin primes are pairs of prime numbers whose difference is 2.

__Example:__ (3, 5), (5, 7), and (11, 13) are twin primes.

It is conjectured that there are infinitely many twin prime numbers.

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Cite as source (bibliography):

*Prime Numbers Search* on dCode.fr [online website], retrieved on 2024-06-15,

prime,number,nth,list,search,lower,greater

https://www.dcode.fr/prime-numbers-search

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