Stormer pairs collection by Warren D. Smith & Jim White

several files have been posted here

/tuning-math/files/WarrenDSmith/

which contain what I think currently
is the world's most extensive collection of "Stormer pairs" --
adjacent integers Q and Q+1 such that B=MaxPrimeDivisor((Q+1)*Q)
is small but Q is large.

These include putatively every Stormer pair with B<=p40=173,
as well as a collection of Qs of many different bitlengths up to 417 bits long
with widely varying Bs but always below P1000000=15485863.

--- In tuning-math@yahoogroups.com, "WarrenS" <warren.wds@...> wrote:
>
> several files have been posted here
>
> /tuning-math/files/WarrenDSmith/
>
> which contain what I think currently
> is the world's most extensive collection of "Stormer pairs" --
> adjacent integers Q and Q+1 such that B=MaxPrimeDivisor((Q+1)*Q)
> is small but Q is large.
>
> These include putatively every Stormer pair with B<=p40=173,
> as well as a collection of Qs of many different bitlengths up to 417 bits long
> with widely varying Bs but always below P1000000=15485863.

Also of relevance is this program:

http://www.ics.uci.edu/~eppstein/0xDE/stormer.py

that implements Stormer's algorithm.

I added all superparticular ratios up through the 13 limit to http://xenharmonic.wikispaces.com/List+of+Superparticular+Intervals

(For mathematicians, the "p limit" is the multiplicative group generated by the primes no greater than p. So the 13 limit is the set of all rational numbers whose prime factorizations include only 2, 3, 5, 7, 11, and 13.)

Keenan

--- In tuning-math@yahoogroups.com, "Keenan Pepper" <keenanpepper@...> wrote:

> I added all superparticular ratios up through the 13 limit to http://xenharmonic.wikispaces.com/List+of+Superparticular+Intervals

What are these goofy factorizations such as 81/80 = 34/(24*5)?

> I added all superparticular ratios up through the 13 limit to http://xenharmonic.wikispaces.com/List+of+Superparticular+Intervals
>
> (For mathematicians, the "p limit" is the multiplicative group generated by the primes no greater than p. So the 13 limit is the set of all rational numbers whose prime factorizations include only 2, 3, 5, 7, 11, and 13.)
>
> Keenan

--well, White's list is the same except it does not stop at P6=13, but rather at P40=173.
White's computer program is somewhat like Eppstein's but far superior.

On Sat, Mar 10, 2012 at 4:24 PM, genewardsmith
<genewardsmith@sbcglobal.net>wrote:

> **
>
>
> What are these goofy factorizations such as 81/80 = 34/(24*5)?
>

Gene,

I'd guess that the superscript indication for exponents have gotten
lost. 81/80 = 3^4/(2^4 * 5).

Dave *Bowen*