## Every Prime Number > 5 can be expressed as the sum of . . .

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• I think it was Hardy or Littlewood who stated that any fool can come up with an unprovable Conjecture. So here s mine Every prime number 5 can be expressed
Message 1 of 3 , Aug 24, 2014
I think it was Hardy or Littlewood who stated that any fool can come up with an unprovable Conjecture.

So here's mine

Every prime number > 5 can be expressed as the sum of ( ( a pair of twin primes ) / 2 ) + a prime number.

Examples:

7 = 4 + 3
11= 6 + 5
13 = 6 + 7
17 = 12 + 5
19 = 12 + 7
23 = 12 + 11
29 = 18 + 11
31 = 18 + 13
37 = 30 + 7
41 = 30 + 11
43 = 30 + 13
47 = 42 + 5
53 = 42 + 11
59 = 42 + 17
61 = 42 + 19
67 = 60 + 7
71 = 60 + 11
73 = 60 + 13
79 = 60 + 19
83 = 60 + 23
89 = 60 + 29
97 = 60 + 37
101 = 72 + 29

etc . . .

I am sure my Conjecture cannot be original ( but I wish! ), and perhaps someone knows of counter examples and previous investigations into the subject.

Thanks as always

Bob
• Sure. There are sufficient differences between primes to be pairing with the  even numbers resulting from the mean of two twin primes. The list of means of
Message 2 of 3 , Aug 25, 2014
Sure. There are sufficient differences between primes to be pairing with the  even numbers resulting from the mean of two twin primes.
The list of means of two twin primes are:
4,6,12,18,30,42,50,72,102,....
Its impossible that never we will find a difference between two primes that cannot be one of that list.
Ludovicus

• Here is an heuristic argument in behalf of the conjecture: The twin primes results from the pairing of the following A.P. 6n  - 1 = 5   11  17  23  29
Message 3 of 3 , Aug 25, 2014
Here is an heuristic argument in behalf of the conjecture:

The twin primes results from the pairing of the following A.P.
6n  - 1 = 5   11  17  23  29  35  41  47  53  59  65 .....
6n + 1 = 7   13  19  25  31  37  43  49  55  61  67 .....

Mean  = 6   12  18        30        42              60  ...

Also with the mean (3 + 5) / 2 = 4 , I have the available differences:
4 , 6 , 12 , 18 ,  30 , 42 , 60 ,  72 ... (4 & Multiples of 6)

The prime numbers >= 5  are contained in the sequence:
5  7  11  13  17  19   23   25  29  31  35  37  41  43  47  49  ...
(With differences: 2 , 4 , 2 , 4 , 2 , 4 ....)

That is: With this differences I can compose the available differences  and summing it, from each prime , I can reach another prime. So:
5  + 6  = 11
7  + 4  = 11
11 + 6  = 17
13 + 4  = 17
17 + 6  = 23
19 + 4  = 23
23 + 6  = 29
29 +12 = 41
31 + 6  = 37
. . . . . . . . .
113 + 18  = 131
. . . . . . . . .

El Lunes 25 de agosto de 2014 8:36, Luis Rodriguez <luiroto@...> escribió:

Sure. There are sufficient differences between primes to be pairing with the  even numbers resulting from the mean of two twin primes.
The list of means of two twin primes are:
4,6,12,18,30,42,50,72,102,....
Its impossible that never we will find a difference between two primes that cannot be one of that list.
Ludovicus

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