What is a prime number?
A prime number is a natural number greater than 1 that is not a product of two
smaller natural numbers.
A prime number is a whole number greater than 1 whose only factors are 1 and
itself. A factor is a whole number that can be divided evenly into another
number.
For example, 5 is a prime number because the only ways of writing it as a
product, 1 × 5 or 5 × 1, involve 5 itself.
The first few prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, and 29.
Numbers that have more than two factors are called composite numbers. The
number 1 is neither prime nor composite.
A natural number greater than 1 that is not prime is called a composite
number. For example, 4 is a composite because it is a product (2 x 2) in which
both numbers are smaller than 4.
The property of being prime is called primality.
There are infinitely many primes, as demonstrated by Euclid around 300 BC. No
known simple formula separates prime numbers from composite numbers. However,
the distribution of primes within the natural numbers in the large can be
statistically modeled. 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.
