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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 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 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.
Number of printable ASCII characters. [65] 96: Total number of character codes in the (six) ASCII sticks containing printable characters. 97: Smallest base which is not perfect odd power (where generalized Wagstaff numbers can be factored algebraically) for which no generalized Wagstaff primes are known. 100: Centesimal: As 100=10 2, these are ...
A factorial x! is the product of all numbers from 1 to x. The first: 1, 2, 6, 24, 120, 720, 5040, 40320, 362880, 3628800, 39916800, 479001600 (sequence A000142 in the OEIS). 0! = 1 is sometimes included. A k-smooth number (for a natural number k) has its prime factors ≤ k (so it is also j-smooth for any j > k).
All prime numbers are odd, with one exception: the prime number 2. [14] All known perfect numbers are even; it is unknown whether any odd perfect numbers exist. [15] Goldbach's conjecture states that every even integer greater than 2 can be represented as a sum
The number of binary rooted trees (every node has out-degree 0 or 2) with n endpoints (and 2n − 1 nodes in all). ... Number of odd entries in row n of Pascal's ...
If this factor p were in our list, then it would also divide P (since P is the product of every number in the list). If p divides P and q, then p must also divide the difference [3] of the two numbers, which is (P + 1) − P or just 1. Since no prime number divides 1, p cannot be in the list. This means that at least one more prime number ...