[seqfan] Re: A051501

[Rick Shepherd]

Hello all.  (I used to be on this list a few years ago and I'm back now,
mostly reading appreciatively.).

One way to fix part of this would be to state how many digits the next prime
has.

If the formula in A034887 is correct, then A034887(A051501(4))=A034887
(137438953481)
=41373247571, so A051501(5) is at least a 41,373,247,571-digit number
(and has at most 41,373,247,572 digits).  (Just!) by finding the leading
digit
of 2^137438953481, one may be able to state definitively that it's the
smaller
number of digits (by Bertrand's Postulate).

(I was just about to click send as Joerg Arndt's message arrived.).

Regards,
Rick

On Thu, Jul 30, 2009 at 10:05 PM, <franktaw at netscape.net> wrote:

> I have a couple of problems with
> http://www.research.att.com/~njas/sequences/A051501
> I'm not sure how to fix them.
>
> First, the comment from T. D. Noe; specifically the statement that the
> largest known prime ... is only 2^32582657-1.  This statement is out of
> date; as far as I can tell, the largest known prime is currently
> 2^43112609-1.  This could obviously be corrected; but, it will likely
> become out of date again.  I guess what is needed is a reference to a
> web site with the largest known primes.
>
> Second, the "Extension": "The next term is too large to display and in
> any case b is not known sufficiently accurately to compute it."  This
> suggests that one would compute more terms of the sequence by getting a
> sufficiently accurate value of b, and plugging it into the formula.  In
> fact, just the opposite is the case: one would get a more accurate
> value of b by determining the next term of the sequence, and working
> backwards to determine what value of b that corresponds to.  (Not that
> anyone is likely to do that anytime soon.)  I'm not sure how to reword
> this so that it is less misleading.
>
> Franklin T. Adams-Watters
>
>
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