The set of prime numbers¶
AUTHORS:
William Stein (2005): original version
Florent Hivert (200911): 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)

class
sage.sets.primes.
Primes
(proof)¶ 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) 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) 7

unrank
(n)¶ Return the nth prime number.
EXAMPLES:
sage: P = Primes() sage: P.unrank(0) 2 sage: P.unrank(5) 13 sage: P.unrank(42) 191
