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However, it does not contain all the prime numbers, since the terms gcd(n + 1, a n) are always odd and so never equal to 2. 587 is the smallest prime (other than 2) not appearing in the first 10,000 outcomes that are different from 1. Nevertheless, in the same paper it was conjectured to contain all odd primes, even though it is rather inefficient.
A prime sieve or prime number sieve is a fast type of algorithm for finding primes. There are many prime sieves. The simple sieve of Eratosthenes (250s BCE), the sieve of Sundaram (1934), the still faster but more complicated sieve of Atkin [1] (2003), sieve of Pritchard (1979), and various wheel sieves [2] are most common.
⎕CR 'PrimeNumbers' ⍝ Show APL user-function PrimeNumbers Primes ← PrimeNumbers N ⍝ Function takes one right arg N (e.g., show prime numbers for 1 ... int N) Primes ← (2 =+ ⌿ 0 = (⍳ N) ∘. |⍳ N) / ⍳ N ⍝ The Ken Iverson one-liner PrimeNumbers 100 ⍝ Show all prime numbers from 1 to 100 2 3 5 7 11 13 17 19 23 29 31 37 41 43 ...
The progressions of numbers that are 0, 3, or 6 mod 9 contain at most one prime number (the number 3); the remaining progressions of numbers that are 2, 4, 5, 7, and 8 mod 9 have infinitely many prime numbers, with similar numbers of primes in each progression.
C, The Complete Reference [1] is a book on computer programming written by Herbert Schildt. The book gives an in-depth coverage of the C language and function libraries features. [2] [3] The first edition was released by Osbourne in 1987. The current version is 4th. Last revision: January 13th, 2018. [4]
APL (named after the book A Programming Language) [3] is a programming language developed in the 1960s by Kenneth E. Iverson. Its central datatype is the multidimensional array. It uses a large range of special graphic symbols [4] to represent most functions and operators, leading to very concise code.
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A snippet of C code which prints "Hello, World!". The syntax of the C programming language is the set of rules governing writing of software in C. It is designed to allow for programs that are extremely terse, have a close relationship with the resulting object code, and yet provide relatively high-level data abstraction.