AUTHORS:
William Stein (2005): original version
Florent Hivert (2009-11): adapted to the category framework. The following methods were removed:
- cardinality, __len__, __iter__: provided by EnumeratedSets
- __cmp__(self, other): __eq__ is provided by UniqueRepresentation and seems to do as good a job (all test pass)
Bases: sage.structure.parent.Set_generic, sage.structure.unique_representation.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) # note: this used to be a TypeError
Traceback (most recent call last):
...
NotImplementedError: infinite list
Returns the first prime number.
EXAMPLES:
sage: P = Primes()
sage: P.first()
2
Returns the next prime number.
EXAMPLES:
sage: P = Primes()
sage: P.next(5)
7
Returns the n-th prime number.