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# The set of prime numbers

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)

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)          # note: this used to be a TypeError
      Traceback (most recent call last):
      ...
      NotImplementedError: infinite list

  `first`()

    Returns the first prime number.

    EXAMPLES:

        sage: P = Primes()
        sage: P.first()
        2

  `next`(pr)

    Returns the next prime number.

    EXAMPLES:

        sage: P = Primes()
        sage: P.next(5)
        7

  `unrank`(n)

    Returns the n-th prime number.

    EXAMPLES::
      sage: P = Primes() sage: P.unrank(0) 2 sage: P.unrank(5) 13 sage: P.unrank(42) 191

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