GAPS BETWEEN PRIME PAIRS (Twin Primes)

[storm5510]

I will run 7.0e15 to 7.05e15. These do not appear to be spoken for...

[storm5510]

Originally Posted by storm5510

I will run 7.0e15 to 7.05e15. These do not appear to be spoken for...

I am going to stop with this until everyone gets sorted out as to what they want to run!

[storm5510]

Reserved: 85e15 to 85.999999999999999e15.

[mart_r]

Originally Posted by storm5510

Reserved: 85e15 to 85.999999999999999e15.

Did you mean prime twins between 85e15 and 86e15? That would be k=14.166666666666667e15 to 14.333333333333333e15 for the program.
But why aiming so high? I mean, it's okay to search a higher range, but the search is easier to handle if k is a multiple of, say, 1e13.
On the other hand, a range of 1e15 in terms of k is quite a bite. Just wanted to make sure we are talking about the same numbers.

[Bobby Jacobs]

Originally Posted by robert44444uk

Not the case as defined. For a gap of 10 or less, the record merit is 2.06 for the gap following 77. However it is not a maximal gap because the gap of 12 at 58 is.

1      6  FMR  R.Rathbun   1998   1.78    0                 1
    2     12  FM   R.Rathbun   1998   1.61    1                 3
    3     18  FM   R.Rathbun   1998   1.55    2                 7
    4     24  F    R.Rathbun   1998   0.76    1               103
    5     30  FMR  R.Rathbun   1998   2.00    4                12
    6     36  FM   R.Rathbun   1998   1.41    3                52
    7     42  F    R.Rathbun   1998   0.93    5               378
    8     48  F    R.Rathbun   1998   1.60    4                87
    9     54  F    R.Rathbun   1998   1.25    4               313
   10     60  F R  R.Rathbun   1998   2.06    7                77
   11     66  F    R.Rathbun   1998   1.56    7               287
   12     72  FMR  R.Rathbun   1998   2.69   10                58

Actually, the definition of a gap with record merit is that it has higher merit than any gap before it. Since the gap of 72 with merit 2.69 occurs before the gap of 60 with merit 2.06, then the gap of 60 is not a gap with record merit.

[storm5510]

Originally Posted by mart_r

Did you mean prime twins between 85e15 and 86e15? That would be k=14.166666666666667e15 to 14.333333333333333e15 for the program.
But why aiming so high? I mean, it's okay to search a higher range, but the search is easier to handle if k is a multiple of, say, 1e13.
On the other hand, a range of 1e15 in terms of k is quite a bite. Just wanted to make sure we are talking about the same numbers.

I didn't write it correctly. You are correct. It is 85e15 to 86e15. I tried to express the -1 where it was not really needed.

Why so high? I want to stay out of everyone's way because it sometimes is difficult to determine where everyone is.

This will take a while. I have it spread across three machines. I hate to guess, but if I had to, late March or early April before this is done. Then again, it may take longer. I am using TwinGaps2. I am unaware of anything more recent.

Thank you for your interest, and your reply. .

[robert44444uk]

Originally Posted by Bobby Jacobs

Actually, the definition of a gap with record merit is that it has higher merit than any gap before it. Since the gap of 72 with merit 2.69 occurs before the gap of 60 with merit 2.06, then the gap of 60 is not a gap with record merit.

Can you send me the specific paper in which this is defined as such? When I Google the phrase you use, the only reference is your own Mersenneforum post.

It sounds as if what you are defining is something that we can name as "maximal merit".

I repeat what I said earlier. The definition is, I think, clear. It is not the definition of "maximal merit". What is being described here is,[B] for a prime gap of length x, there is no prime gap of length x or less with a higher merit. [/B}.

For a gap of 10 or less, the record merit is 2.06 for the gap following 77. However it is not a "maximal merit" because the gap of 12 at 58 is.

[storm5510]

I thought I understood the premise of this, but now I do not think so.

19 - 17 = 2 and 31 - 29 = 2. The gap between 31 and 19 is 12. I tried to write a Perl script to do this, but after looking at some robert44444uk posted, I knew I was way off. The script ran without errors, but the results were simply not correct. Oh, well.

[rudy235]

Originally Posted by storm5510

I thought I understood the premise of this, but now I do not think so.

19 - 17 = 2 and 31 - 29 = 2. The gap between 31 and 19 is 12. I tried to write a Perl script to do this, but after looking at some robert44444uk posted, I knew I was way off. The script ran without errors, but the results were simply not correct. Oh, well.

Well sure it is 12 but being that 17–19 =3*6+/-1 and 29–31 =5*6+/-1
The gap is defined as the difference of the coefficients 3 and 5, Thus it is a gap of 2. Makes sense?

[storm5510]

Originally Posted by rudy235

Well sure it is 12 but being that 17–19 =3*6+/-1 and 29–31 =5*6+/-1
The gap is defined as the difference of the coefficients 3 and 5, Thus it is a gap of 2. Makes sense?

It would appear you are creating negative numbers by subtracting the larger from the smaller. Robert used multiplications and divisions by 6 in his Perl scripts "Difference of the coefficients." I knew I was way off somewhere.

Thank you for the reply!

[mart_r]

Reserving 7.0e15 to 7.5e15.

Originally Posted by storm5510

Why so high? I want to stay out of everyone's way because it sometimes is difficult to determine where everyone is.

It appears that, apart from you, I'm currently the only person in the world looking for gaps between prime twins.