>
> We were lucky, for Sage contains a twinprimes object.
>
> sage: twinprime
> twinprime
> sage: twinprime(4)
> /home/ncohen/.Sage/local/lib/python2.7/site-packages/IPython/core/interactiveshell.py:2883:
>  
> DeprecationWarning: Substitution using function-call syntax and unnamed 
> arguments is deprecated and will be removed from a future release of Sage; 
> you can use named arguments instead, like EXPR(x=..., y=...)
> See http://trac.sagemath.org/5930 for details.
> ...
> ValueError: the number of arguments must be less than or equal to 0
> sage: twinprime()
> twinprime
> sage: twinprime()()()()()()()()()()()()()
> twinprime
> sage: twinprime()==twinprime
> twinprime == twinprime
>
> As you can see, it is not immediately obvious what this object is. And 
> Sage's doc for "twinprime?" is not exactly... Explicit.
>
> Explanation: it turns out that for Sage, "twinprimes" is a constant, like 
> pi, e, gamma, ...
>

Indeed.  I'm not sure how to fix this, though.

http://git.sagemath.org/sage.git/tree/src/sage/symbolic/constants.py#n1149

In this class, we don't quite instantiate the nice documentation we 
actually have for TwinPrime
    r"""
    The Twin Primes constant is defined as
    `\prod 1 - 1/(p-1)^2` for primes `p > 2`.

    EXAMPLES::

        sage: float(twinprime)
        0.6601618158468696
        sage: twinprime.n(digits=60)
        0.660161815846869573927812110014555778432623360284733413319448

    """
but instead do 
TwinPrime().expression()
which gets rid of all that useful info.  Same for most such constants, I 
believe, so that they are in the symbolic ring/Ginac.

Does anyone have a quick way to fix this?  (Maybe even by getting rid of 
.expression() ?)  I have wondered about this too but I knew what the twin 
prime constant was so I didn't run into it... but of course Nathann is 
right that this is not that helpful currently.

- kcrisman

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