Your idea is very interesting.

My readings about near-repdigit numbers has made me fascinated by

Sierpinski and Riesel numbers and especially their covering sets.

If you look at the search of Payam Samidoost, can we prove any of the

sixty-three or so possible candidates below the smallest provable

Riesel number 509203 are not Riesel numbers. I would be especially

interested in 2293 and 9221 because they are so small.

--- In

primenumbers@yahoogroups.com, Lélio Ribeiro de Paula

<lelio73@...> wrote:

>

> Each Sierpinski (and Riesel) number and the dual of it always have the

> same covering set as it is easy to see.

>

> So we only need to find a prime for a candidate in any one of the

> forms to eliminate it from the other side.

>

> Looking at the remaining candidates in SoB and in the dual Sierpinski

> search of Payam Samidoost we see that there is no number belonging to

> both lists, so no one of the 6 remaining candidates at SoB can be a

> solution to the problem, and the same to Payam's as well.

>

> In fact, the only two common candidates when Payam launched his

> project were 19249 and 28433.

>

> Payam found a prime for the dual of 19249 on August 17, 2002 so when

> an anonymous member of TeamPrimeRib submitted a prime for 28433 on

> December 30, 2004 to SoB, the search could have been called quits.

>

> Lélio

>