"**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.)