[seqfan] Re: [math-fun] prime ladders

[Edwin Clark]

On Wed, 11 Mar 2009, Warut Roonguthai wrote:

> I found that all the 4-digit primes are connected even under the
> restriction, and this is also true for the 5-digit case.
>
> Too lazy for larger cases ...
>
> Warut

Also being lazy, but having no free will, I found the connected components 
of the 6-digit primes and the 7-digit primes. (primes p and q are adjacent 
if they differ in one digit);

For the 6 digit primes there are 7 connected components:
Six singletons corresponding to the 6 weak primes:
294001, 505447, 584141, 604171, 929573, 971767
and one large component containing the rest.

For the 7-digit primes there are 38 connected components:
37 singletons corresponding to the 37 weak primes:
1062599, 1282529, 1524181, 2017963, 2474431, 2690201, 3070663, 3085553, 
3326489, 4393139, 5152507, 5285767, 5564453, 5575259, 5974249, 6173731, 
6191371, 6236179, 6463267, 6712591, 7204777, 7469789, 7469797, 7810223, 
7858771, 7982543, 8090057, 8353427, 8532761, 8639089, 9016079, 9262697, 
9537371, 9608189, 9663683, 9700429, 9931447
and one large component containing the rest.

--Edwin

PS I have submitted the 4 sequences suggested by Neil for this problem to 
the OEIS as A158576-A158579