Check if prime number

Determine prime decomposition

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A few details about what represent prime numbers and prime decomposition (factorization)

Prime Numbers

A prime number is a natural number greater than 1 that has exactly two distinct positive divisors: 1 and itself. In other words, a prime number can only be divided evenly (without a remainder) by 1 and the number itself. For example:

  • 2 is a prime number because its only divisors are 1 and 2.
  • 3 is a prime number because its only divisors are 1 and 3.
  • 4 is not a prime number because it can be divided evenly by 1, 2, and 4.

Prime numbers are fundamental in mathematics, especially in number theory, because they serve as the "building blocks" of all natural numbers. Any natural number greater than 1 can be expressed as a product of prime numbers, a concept known as the prime factorization theorem.

Prime Factor Decomposition

Prime decomposition (also known as prime factorization) is the process of breaking down a natural number greater than 1 into a product of prime numbers. These prime numbers are the "building blocks" of the original number, and the decomposition is unique for each number (apart from the order of the factors), as guaranteed by the Fundamental Theorem of Arithmetic. For example:

  • the prime decomposition of 12 is 12=2×2×3 (or 12=22×3).
  • the prime decomposition of 30 is 30=2×3×5.

This method is widely used in mathematics for tasks like finding the greatest common divisor (GCD), least common multiple (LCM), and understanding the properties of numbers.

Mobile Application

An application developed for a similar purpose, with extended features

Prime Numbers - primeN

Prime Numbers - primeN application allows you:

  • to check if a number is a prime number. If the number is not prime, it will be displayed its prime factor decomposition.
  • to search for the prime numbers into a range.
  • to view in list format the set of first prime numbers.
  • to view in grid format a set of numbers with the prime numbers marked accordingly.

List of Prime Numbers

The prime numbers smaller than 1000

Table of Prime Numbers

The prime numbers distribution in the first 100 numbers