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A prime number is a natural number that has exactly two distinct natural number divisors: the number 1 and itself. To find all the prime numbers less than or equal to a given integer n by Eratosthenes' method: Create a list of consecutive integers from 2 through n: (2, 3, 4, ..., n). Initially, let p equal 2, the smallest prime number.
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 ...
Rowland (2008) proved that this sequence contains only ones and prime numbers. 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 ...
No even number greater than 2 is prime because any such number can be expressed as the product /. Therefore, every prime number other than 2 is an odd number, and is called an odd prime. [10] Similarly, when written in the usual decimal system, all prime numbers larger than 5 end in 1, 3, 7, or 9. The numbers that end with other digits are all ...
Super-prime numbers, also known as higher-order primes or prime-indexed primes (PIPs), are the subsequence of prime numbers that occupy prime-numbered positions within the sequence of all prime numbers. In other words, if prime numbers are matched with ordinal numbers, starting with prime number 2 matched with ordinal number 1, then the primes ...
For example, addition and division, the factorial and exponential function, and the function which returns the nth prime are all primitive recursive. [1] In fact, for showing that a computable function is primitive recursive, it suffices to show that its time complexity is bounded above by a primitive recursive function of the input size. [2]
This is a list of articles about prime numbers. A prime number (or prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself. 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.