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By Euclid's theorem, there are an infinite number of prime numbers. Subsets of the prime numbers may be generated with various formulas for primes. The first 1000 primes are listed below, followed by lists of notable types of prime numbers in alphabetical order, giving their respective first terms. 1 is neither prime nor composite.
The tables contain the prime factorization of the natural numbers from 1 to 1000. When n is a prime number, the prime factorization is just n itself, written in bold below. The number 1 is called a unit. It has no prime factors and is neither prime nor composite.
In mathematics, the prime-counting function is the function counting the number of prime numbers less than or equal to some real number x. [1] [2] It is denoted by π(x) (unrelated to the number π). A symmetric variant seen sometimes is π 0 (x), which is equal to π(x) − 1 ⁄ 2 if x is exactly a prime number, and equal to π(x) otherwise.
4.2 Number of primes below a given bound. ... every prime number other than 2 is an odd number, ... is still used to construct lists of primes. [16] [17] Around 1000 ...
Besides, 491 is the only prime below 1000 with weak irregular index 4, and all other odd primes below 1000 with weak irregular index 0, 1, or 2. ( Weak irregular index is defined as "number of integers 0 ≤ n ≤ p − 2 such that p divides a n .)
For example, 3 is a Mersenne prime as it is a prime number and is expressible as 2 2 − 1. [1] [2] The exponents p corresponding to Mersenne primes must themselves be prime, although the vast majority of primes p do not lead to Mersenne primes—for example, 2 11 − 1 = 2047 = 23 × 89. [3]
In number theory, cousin primes are prime numbers that differ by four. [1] Compare this with twin primes, pairs of prime numbers that differ by two, and sexy primes, pairs of prime numbers that differ by six. The cousin primes (sequences OEIS: A023200 and OEIS: A046132 in OEIS) below 1000 are:
As a consequence of the prime number theorem, one gets an asymptotic expression for the n th prime number, denoted by p n: p n ∼ n log n . {\displaystyle p_{n}\sim n\log n.} [ 39 ] A better approximation is by Cesàro (1894): [ 40 ]