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"Conjecture. The sum of a twin prime pair greater than or equal to 24 can be expressed as the sum of two twin prime pairs."

Examples:

24 = 12 + 12
36 = 12 + 24
60 = 24 + 36
84 = 24 + 60
120 = 36 + 84 = 60 + 60
144 = 24 + 120 = 60 + 84
204 = 60 + 144 = 84 + 120
...

to be more precise:

(11+13) = 24 = 12 + 12 = (5+7) + (5+7)
(17+19) = 36 = 12 + 24 = (5+7) + (11+13)
(29+31) = 60 = 24 + 36 = (11+13) + (17+19)
(41+43) = 84 = 24 + 60 = (11+13) + (29+31)
(59+61) = 120 = 36 + 84 = (17+19) + (41+43) = 60 + 60 = (29+31) + (29+31)
...

Is it always true or are there counterexamples? Is it a known conjecture?

There are no exceptions it works for all sum of twin prime pairs less than 19.999.944.

For example, for (197,199)

15-th 396

396=12+384
396=36+360
396=120+276

Further details can be found in our post: https://bhaxor.blog.hu/2019/03/03/batf41_haxor_stream_conjecture

I would like to know whether is it a known observation? Is it true for all sum of twin prime pairs greater than or equal to 24? I am curious for your opinion.

(When I was trying to check these I found the post: https://math.stackexchange.com/questions/1544221/twin-primes-sums-conjecture that contains a similar conjecture. My question originally was posted as a comment to this.)

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closed as off-topic by darij grinberg, RP_, Pace Nielsen, abx, Emil Jeřábek Mar 6 at 10:04

This question appears to be off-topic. The users who voted to close gave this specific reason:

  • "This question does not appear to be about research level mathematics within the scope defined in the help center." – darij grinberg, RP_, abx, Emil Jeřábek
If this question can be reworded to fit the rules in the help center, please edit the question.

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    $\begingroup$ Given that the twin prime conjecture is open, and overall we know next to nothing about twin primes,, do you really expect the answer to be known $\endgroup$ – Wojowu Mar 5 at 7:46
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    $\begingroup$ This is a cross-post of a Math.SE question (math.stackexchange.com/questions/3134627/…) that you asked yesterday. We usually recommend against cross-posting, since one may end up with unnecessary duplication of effort. $\endgroup$ – S. Carnahan Mar 5 at 8:51
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    $\begingroup$ You were very lucky to stumble across your own post from yesterday. Oh, and naming a conjecture after yourself is bound to create a very bad impression. $\endgroup$ – Gerry Myerson Mar 5 at 12:09
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    $\begingroup$ @GerryMyerson FWIW I think the OP meant to link to math.stackexchange.com/questions/1544221/… $\endgroup$ – Yemon Choi Mar 5 at 22:07
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    $\begingroup$ I have no idea what a "Twitch channel" is, but whatever it may be, you have named yours after yourself, which means you have named the conjecture after yourself, which etc. etc. Why not call it the Iterated Twin Prime conjecture? $\endgroup$ – Gerry Myerson Mar 6 at 11:43

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