# [seqfan] Re: Sums of three Mersenne primes, and prime sums of three Mersenne primes

Jonathan Post jvospost3 at gmail.com
Fri Mar 5 08:25:24 CET 2010

```Sums of five Mersenne primes can also be prime (though, obviously sums
of an even number of Mersenne primes are even).

3 + 3 + 3 + 3 + 7 = 19
3 + 3 + 3 + 7 + 7 = 23
3 + 7 + 7 + 7 + 7 = 31
3 + 3 + 3 + 3 + 31 = 43
3 + 3 + 3 + 7 + 31 = 47
7 + 7 + 7 + 7 + 31 = 59
3 + 3 + 3 + 31 + 31 = 71
3 + 7 + 7+ 31 + 31 = 79

This sequence 19, 23, 31, 43, 47, 59, 71, 79, ...
is not in OEIS.

Hence it was not arbitrary to first look at sums of three Mersenne
Primes, and the subsequence of primes within that.

I neglected to mention the analogy to:
A155877  	Sums of three Fermat numbers.
A166484  	Prime sums of three Fermat numbers.

On Thu, Mar 4, 2010 at 4:05 PM, Jonathan Post <jvospost3 at gmail.com> wrote:
> This was crudely drafted by hand.  But if I did it right, it's not in OEIS.
>
> Sums of three Mersenne primes = A000668(i) + A000668(j) + A000668(k),
> i,j,k integers not necessarily distinct
>
> 9, 13, 17, 21, 37, 41, 45, 65, 69, 93, 133, 137, 141, 161, 165, 189,
> 257, 261, 285, 381, 8197, 8201, 8225, ...
>
> Prime sums of three Mersenne primes = A000040 INTERSECTION {A000668(i)
> + A000668(j) + A000668(k), i,j,k integers not necessarily distinct}
>
> 13, 17, 37, 41, 137, 257, ...
>
> The first of these seqs is a subset of sums of three odd primes; the
> second of these is a subset of prime sums of three primes -- but where
> are these in OEIS?
>
> I also would xref A066615  Numbers which are not the sum of two or
> three distinct primes.
>
> Would anyone like to correct me, ore extend these?
>
> And are there any strong feelings as to whether these are worth
> submitting or not?
>
> Thank you,
>
> Jonathan Vos Post
>

```