- --- In primenumbers@yahoogroups.com, "David Broadhurst" <d.broadhurst@...> wrote:
>

Thank you David. At least I go into Good Friday with one less potential illusion. :)

> Mark Underwood's most interesting sequence for the OEIS

> might be the cases for which his conjecture fails, namely

>

> "Numbers n such that there are no primes of the forms

> 2^m+3^n or 2^n+3^m for m < n"

>

> This sequence begins with

>

> n = 1679, 1743 ...

>

> but Mark would need two more entries to satisfy Neil Sloane.

> PFGW records that there are no more with n < 2500.

> Heuristics suggest that more exist, beyond that paltry limit.

>

And that 1679,1743, .. sequence, it is not only hard computing, but psychologically

difficult as well, to find a *lack* of primes. Actually finding primes (especially unique

ones) is so much more fun!

On that note, some 2-3 prime time fun, where a,b are 2-3 numbers and

both 2^a + 3^b and 3^b + 2^a are prime.

2^1 + 3^1

2^1 + 3^2 and 2^2+3^1

2^2 + 3^2

2^3 + 3^1 and 2^1 + 3^3

2^3 + 3^2 and 2^2 + 3^3

2^4 + 3^1 and 2^1 + 3^4

2^4 + 3^4

2^6 + 3^2 and 2^2 + 3^6

2^8 + 3^3 and 2^3 + 3^8

2^8 + 3^4 and 2^4 + 3^8

2^9 + 3^2 and 2^2 + 3^9

2^9 + 3^4 and 2^4 + 3^9

2^12 + 3^4 and 2^4 + 3^12.

Mark - --- In primenumbers@yahoogroups.com, "David Broadhurst" wrote:
> --- In primenumbers@yahoogroups.com, "Mike Oakes" wrote:

(Thanks, Mike !)

> > I have today uploaded a file containing the results of my search

> > for all primes of this form for 2<=b<=1000, 2<=p<10000, done in

> > the years 2000-2008.

> Here is a simple link to Mike's interesting table:

Thanks, David!

> http://tinyurl.com/d3nf9w

(Remark: These tiny urls are nice, but can be quite annoying when they point to a website that re-arranged its directory structure - with tinyurls ultra-efficient and discreet forwarding system you sometimes can't get the slightest info about where/what you had been pointed to and try to find it "by hand"...Â [this happened to me a few days ago - but I forgot where & what is was about...])

OTOH:

p=2 : A006254 Numbers n such that 2n-1 is prime.

p=3 : A002504 numbers such that 1+3x(x-1) is (a "cuban") prime.

p=5 : A121617 Nexus numbers of order 5 (or A022521[n-1] = n^5 - (n-1)^5) are primes.

p=7 : A121619 Nexus numbers of order 7 (A022523[n-1] = n^7 - (n-1)^7) are primes

p >= 11 seems not yet there, so Mike could enter his numbers into OEIS, starting there !

Maximilian, per proxy SOSR

(Society for On-line Sequence Recovery)