NextPrime
Details
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- When used with a negative k value, NextPrime will give the previous
prime.
- Mathematical function, suitable for both symbolic and numerical manipulation.
- For positive x, NextPrime[x] is the (m+1)
prime number
where m is the number of primes less than or equal to x.
- NextPrime[x, k] is the (m+k)
prime number
where m is the number of primes less than or equal to x.
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Examples
open allclose allScope (9)
Numerical Evaluation (7)
Symbolic Manipulation (2)
Applications (15)
Basic Applications (6)
Highlight the sequence of primes using NextPrime:
Visualize the primes with a parabolic sieve:
Visualize the sieve of Eratosthenes for the first 5 primes:
Spiral of a NextPrime sequence:
Hexagonal prime spiral using NextPrime:
Find the lowest-divisor pair for an integer :
Number Theory (5)
NextPrime numbers modulo 10:
NextPrime numbers modulo :
Plot prime gaps around powers of 10:
Visualize the gaps between primes below 104:
Plot a histogram of the closest distances to a prime for a range of integers:
Compare the NextPrime sequence to PrimePi:
It is conjectured that for any integer , there is a prime
with
:
Properties & Relations (4)
Text
Wolfram Research (2007), NextPrime, Wolfram Language function, https://reference.wolfram.com/language/ref/NextPrime.html (updated 2020).
CMS
Wolfram Language. 2007. "NextPrime." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2020. https://reference.wolfram.com/language/ref/NextPrime.html.
APA
Wolfram Language. (2007). NextPrime. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/NextPrime.html