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A cluster prime is a prime p such that every even natural number k ≤ p − 3 is the difference of two primes not exceeding p. 3, 5, 7, 11, 13, 17, 19, 23, ... (OEIS: A038134) All odd primes between 3 and 89, inclusive, are cluster primes. The first 10 primes that are not cluster primes are: 2, 97, 127, 149, 191, 211, 223, 227, 229, 251.
This is due to the Euclid–Euler theorem, partially proved by Euclid and completed by Leonhard Euler: even numbers are perfect if and only if they can be expressed in the form 2 p−1 × (2 p − 1), where 2 p − 1 is a Mersenne prime. In other words, all numbers that fit that expression are perfect, while all even perfect numbers fit that form.
The first: 4, 6, 8, 9, 10, 12 ... An even number has the prime factor 2. The first: 2, 4 ... A factorial x! is the product of all numbers from 1 to x. The first: 1, 2 ...
A list of articles about numbers (not about numerals). Topics include powers of ten, notable integers, prime and cardinal numbers, and the myriad system.
Even numbers are always 0, 2, or 4 more than a multiple of 6, while odd numbers are always 1, 3, or 5 more than a multiple of 6. ... The 10 carry-on essentials that make for a first-class ...
The first few prime numbers are 2, 3, 5, 7, and 11. There is no such simple formula as for odd and even numbers to generate the prime numbers. The primes have been widely studied for more than 2000 years and have led to many questions, only some of which have been answered. The study of these questions belongs to number theory.
Even and odd numbers: An integer is even if it is a multiple of 2, and is odd otherwise. Prime number : A positive integer with exactly two positive divisors : itself and 1. The primes form an infinite sequence 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, ...
A factorial prime is a prime number that is one less or one more than a factorial (all factorials greater than 1 are even). [1] The first 10 factorial primes (for n ...