## 25599Re: Every Prime Number > 5 can be expressed as the sum of . . .

Expand Messages
• Aug 25, 2014
• 0 Attachment
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@...> escribiÃ³:

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

• Show all 3 messages in this topic