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## #26 2017-06-29 17:31:10

Luca Ravioli
Member
Registered: 2017-06-29
Posts: 5

### Re: Strange Prime number pattern

Correction,  the first difference is not 1 except between the 2 and 3 primes.

prime, 1st. diff., 2nd. diff., 3rd. diff.
2,1,1,
3,2,0,2
5,2,2,-4
7,4,-2,4
11,2,2,-4
13,4,-2,4
17,2,2,0
19,4,2,-6
23,6,-4,8
29,2,4,-6
.....

So the point for 2 is out of place, because the first difference is 1, unlike for the other primes.  I cant figure out how to upload the image.

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## #27 2017-06-29 17:45:51

Luca Ravioli
Member
Registered: 2017-06-29
Posts: 5

### Re: Strange Prime number pattern

Canceled comment.

Last edited by Luca Ravioli (2017-06-29 17:54:50)

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## #28 2017-06-29 17:59:46

Luca Ravioli
Member
Registered: 2017-06-29
Posts: 5

### Re: Strange Prime number pattern

``````                                                                                    Prime nubers

80 ++-------------------+---------------------+--------------------+---------------------+--------------------+--------------------+---------------------+-------------------++
+                    +                     +                    +                     +                    +                    +                     +                    +
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60 ++                                                                                                                                                                        ++
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|            M                                                                                                                                                             |
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|   M    M   M   M        M                                                                                                                                                |
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40 ++  M    M   M   M            M                                                                                                                                           ++
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|   M    M   M   M   M    M                    M                                                                                                                           |
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|            M                                                                                                                                                             |
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|   M    M   M       M    M       M   M                                                                                                                                    |
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|   M    M   M   M   M        M       M                                                                                                                                    |
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|   M    M   M   M   M    M                                                                                                                                                |
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|   M    M   M   M   M    M   M   M        M                                                                                                                               |
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|            M            M           M                                                                                                                                    |
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|   M    M   M   M   M    M   M   M   M                                                                                                                                    |
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20 ++  M    M   M   M   M    M   M   M   M    M                                                                                                                              ++
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|            M            M           M            M                                                                                                                       |
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|   M    M   M   M   M    M   M   M   M    M       M                                      M                                                                                |
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|   M    M   M   M   M    M   M   M   M    M   M                                                                                                                           |
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|            M            M           M            M                                                                                                                       |
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|   M    M   M   M   M    M   M   M   M        M   M    M   M   M                                                                                                          |
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|   M    M   M   M   M    M   M   M   M    M   M   M        M                                                                                                              |
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|            M            M           M            M            M                                                                                                          |
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|   M    M   M   M   M    M   M   M   M    M   M   M        M   M                                                                                                          |
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|   M    M   M   M   M    M   M   M   M    M   M            M                         M                                                                                    |
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0 ++  M        M            M           M            M            M                                                                                                         ++
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|        M   M   M   M    M   M   M   M    M   M   M    M                                                                                                                  |
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|            M   M   M    M   M   M   M    M   M   M    M   M   M                                                                                                          |
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|                         M           M            M            M                                                                                                          |
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|                    M    M   M   M   M    M   M   M    M   M   M   M    M   M                                                                                             |
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|                         M   M   M   M    M   M   M    M   M   M   M                                                                                                      |
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|                                     M            M            M                                                                                                          |
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|                                 M   M    M   M   M    M   M   M   M                 M                                                                                    |
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|                                     M    M   M   M    M   M   M   M    M   M   M    M                                                                                    |
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|                                                  M            M            M            M                                                                                |
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-20 ++                                             M   M    M   M   M   M    M   M        M   M                                                                               ++
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|                                                  M    M   M   M   M    M   M   M    M   M                                                                                |
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|                                                           M   M   M    M   M   M    M   M   M                                                                            |
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|                                                               M   M    M   M   M    M   M       M                                                                        |
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|                                                                        M   M   M    M   M                    M                                                           |
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-40 ++                                                                                        M   M                                                                           ++
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-60 ++                                                                                                                                                                        ++
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+                    +                     +                    +                     +                    +                    +                     +                    +
-80 ++-------------------+---------------------+--------------------+---------------------+--------------------+--------------------+---------------------+-------------------++
0                    10                    20                   30                    40                   50                   60                    70                   80
1st difference``````

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## #29 2017-06-29 20:15:32

Luca Ravioli
Member
Registered: 2017-06-29
Posts: 5

### Re: Strange Prime number pattern

pi man wrote:

You won't ever have a pair of 4's in a row.   Let's say X is a prime number.   We know it's odd as they all are except for 2.     Every odd number is going to be either:

A) divisible by 3 (x mod 3 = 0);
B) have a remainder of 1 when divided by 3 (x mod 3 = 1);
C) have a remainder of 2 when divided by 3 (x mod 3 = 2).

Let's consider X, X+4 and X + 8 when X is prime:

A) X is divisible by 3 - can't happen when X is prime
B) X mod 3 = 1
Then (X+4) mod 3 = 2
and (X+8) mod 3 = 0.
Therefore X+8 is divisible by 3 and is not prime.
C) X mod 3 = 2
Then (X+4) mod 3 = 0
Therefore X+4 is divisible by 3 and is not prime.

So for any prime number X, either X+4 or X+8 will be divisible by 3.

Is that the reason for all the holes in the graph accept the stripes due to even numbers not being prime?

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