--- In

primenumbers@yahoogroups.com, Alan Eliasen <eliasen@...> wrote:

>

> On 11/08/2010 04:03 PM, djbroadhurst wrote:

> > Videlicet: How many 7's are there in the largest known prime,

> > when the latter is written in base 137?

> >

> > David (who has no idea, but might be told, eventually)

>

> It would be nice to get an answer to this, and edifying to people

> interested in the problem to see what the bottlenecks are. The number

> itself, 2^42643801-1, can be calculated with Java (with my patches)

Expletive!

I've been running a pfgw script to answer David's question using the above 2^42643801-1 for the past 24 hours.

I just noticed I should instead be using 2^43112609-1.

As it appears Kevin will soon have the answer I will not start a second attempt, at least for the time being.

cheers

Ken

> milliseconds (without my patches, several days. It's only a left-shift

> and a subtract, both of which can be done in small O(n) time.)

>

> Converting the radix in native Java will take days and days. Even

> though it has fast operations for bitCount, that's not much help here.

> (Even I can do in my head that there will be 42643801 ones and no

> zeroes, if we only want the binary digits). Scanning the final number

> for sevens can be done in milliseconds.

>

> (My wild estimate, which I may have bungled, is 43853 sevens in the

> number.)

>

> --

> Alan Eliasen

> eliasen@...

> http://futureboy.us/

>