pracma (version 0.8.6)

primes: Prime Numbers

Description

Generate a list of prime numbers less or equal n, resp. between n1 and n2.

Usage

primes(n)
  primes2(n1, n2)
  nextPrime(n)
  twinPrimes(n1, n2)

Arguments

n

nonnegative integer greater than 1.

n1, n2

natural numbers with n1 <= n2<="" code="">.

Value

• vector of integers representing prime numbers

Details

The list of prime numbers up to n is generated using the "sieve of Erasthostenes". This approach is reasonably fast, but may require a lot of main memory when n is large.

primes2 computes first all primes up to sqrt(n2) and then applies a refined sieve on the numbers from n1 to n2, thereby drastically reducing the need for storing long arrays of numbers.

nextPrime finds the next prime number greater than n. In general the next prime will occur in the interval [n+1,n+log(n)].

twinPrimes uses primes2 and uses diff to find all twin primes in the given interval.

In double precision arithmetic integers are represented exactly only up to 2^53 - 1, therefore this is the maximal allowed value.

See Also

isprime, factorize

Examples

primes(1000)
  primes2(1949, 2011)

  nextPrime(1e+6)
  twinPrimes(1e6+1, 1e6+1001)
  length(primes(1e6))  # there are 78498 prime numbers less than 1,000,000.