The set of prime numbers#
AUTHORS:
William Stein (2005): original version
Florent Hivert (2009-11): adapted to the category framework.
- class sage.sets.primes.Primes(proof)#
Bases:
Set_generic
,UniqueRepresentation
The set of prime numbers.
EXAMPLES:
sage: P = Primes(); P Set of all prime numbers: 2, 3, 5, 7, ...
We show various operations on the set of prime numbers:
sage: P.cardinality() +Infinity sage: R = Primes() sage: P == R True sage: 5 in P True sage: 100 in P False sage: len(P) Traceback (most recent call last): ... NotImplementedError: infinite set
- first()#
Return the first prime number.
EXAMPLES:
sage: P = Primes() sage: P.first() 2
- next(pr)#
Return the next prime number.
EXAMPLES:
sage: P = Primes() sage: P.next(5) # needs sage.libs.pari 7
- unrank(n)#
Return the n-th prime number.
EXAMPLES:
sage: P = Primes() sage: P.unrank(0) # needs sage.libs.pari 2 sage: P.unrank(5) # needs sage.libs.pari 13 sage: P.unrank(42) # needs sage.libs.pari 191