## A goldbach conjecture for triplet-middle primes

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• ... Phil used his fingers and toes ... Err, what have you got against 2 mod 30, Phil? Example: take 13 from {11, 13, 17} and 19 from (17, 19, 23) to make 13 +
Message 1 of 3 , Dec 1, 2001
I wrote:

> Phil: As for "triplet middles": try the analyis mod 30.

Phil used his fingers and toes
(and perhaps some, but not enough, of Anna's):

> Therefore the gamut of sums is
> 30n + { 0, 4, 6, 8, 22, 24, 26, 28 }

Err, what have you got against 2 mod 30, Phil?

Example: take 13 from {11, 13, 17}
and 19 from (17, 19, 23)
to make 13 + 19 = 32 = 2 mod 30

Also sprach Rosinante:

failed mod 30

5700010 10
5700012 12
5700014 14
5700016 16
5700018 18
5700020 20
5700040 10
5700042 12
5700044 14
5700046 16
5700048 18
5700050 20
5700070 10
5700072 12
5700074 14
5700076 16
5700078 18
5700080 20
....... ..

Conjecture: The largest even number n whose residue mod 30
is not in [10,20], with n not expressible as the sum of 2
triplet-middles, is 12010144.

David (stopped at 10^8)
• ... Exponentials are wonderful; they cut off real fast. Also sprach Rosinante failed 5751472 5823812 5950106 5972786 6025984 6112688 6168926 6246668 7226486
Message 2 of 3 , Dec 1, 2001
> Conjecture: The largest even number n whose residue mod 30
> is not in [10,20], with n not expressible as the sum of 2
> triplet-middles, is 12010144.

Exponentials are wonderful; they cut off real fast.
Also sprach Rosinante

failed

5751472
5823812
5950106
5972786
6025984
6112688
6168926
6246668
7226486
7310302
7400392
8267876
8521976
11078306
11814566
12010144

[the rest is silence]
• ... I do, don t I :-) ... I find fingers and toes far superior to programs like Mathematica, but just this once Mathematica is capable of doing this vast
Message 3 of 3 , Dec 2, 2001
On Sat, 01 December 2001, d.broadhurst@... wrote:
> I wrote:
>
> > Phil: As for "triplet middles": try the analyis mod 30.
>
> Phil used his fingers and toes
> (and perhaps some, but not enough, of Anna's):
>
> > Therefore the gamut of sums is
> > 30n + { 0, 4, 6, 8, 22, 24, 26, 28 }
>
> Err,

I do, don't I :-)

> what have you got against 2 mod 30, Phil?
> Example: take 13 from {11, 13, 17}
> and 19 from (17, 19, 23)
> to make 13 + 19 = 32 = 2 mod 30

I find fingers and toes far superior to programs like Mathematica, but just this once Mathematica is capable of doing this vast computational feet better than my own digits. How bizarre.

(sic, above, for reference)

In[24]:=
r30 = {11, 13, 17, 19}

Out[24]=
{11, 13, 17, 19}

In[25]:=
Union[Flatten[Outer[Mod[#1 + #2 , 30] &, r30, r30]]]

Out[25]=
{0, 2, 4, 6, 8, 22, 24, 26, 28}

Shall we just say it was an off day...

I'm glad that there's a post-processing filter which is able to extract some sense out of my gibberings. Ta muchly.

Phil

Don't be fooled, CRC Press are _not_ the good guys.
They've taken Wolfram's money - _don't_ give them yours.
http://mathworld.wolfram.com/erics_commentary.html

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