How do you construct prime numbers in Sage?
The class Primes
allows for primality testing:
sage: 2^(2^12)+1 in Primes() False sage: 11 in Primes() True
The usage of next_prime
is self-explanatory:
sage: next_prime(2005) 2011
The Pari command primepi
is used via the Sage command
pari(x).primepi()
. This returns the number of primes
,
for example:
sage: pari(10).primepi() 4
Using primes_first_n
or primes
one can check that, indeed, there
are
primes up to
:
sage: primes_first_n(5) [2, 3, 5, 7, 11] sage: list(primes(1, 10)) [2, 3, 5, 7]
See About this document... for information on suggesting changes.