User TJAOI

[petrw1]

Is this the end of it? Are all ranges done?

[Mark Rose]

Probably. I haven't heard if TheMawn finished 70M, but there was only 47 GHz-day in that range, so I imagine he finished a week ago.

Everyone else has checked in!

[TheMawn]

Originally Posted by Mark Rose

Probably. I haven't heard if TheMawn finished 70M, but there was only 47 GHz-day in that range, so I imagine he finished a week ago.

Everyone else has checked in!

Oh. I thought I mentioned that. It's been done for a while. There wasn't much there. One new factor, two or three missed but found by P-1.

[garo]

Would heat-maps like this be useful for figuring out where the holes are? I said earlier that GP2 did some great work on this in 2002/2003.

The x-axis is the bit size of the factor rounded down. y-axis is the exponent range in hundred of thousands. The cells show the number of factors found at each bit-level for each range.

[Uncwilly]

Originally Posted by garo

The x-axis is the bit size of the factor rounded down. y-axis is the exponent range in hundred of thousands. The cells show the number of factors found at each bit-level for each range.

This is a graph I have of the 332M range that shows the same issue that I see on your chart, namely, after the lowest bit, there is a drop-off on the next 2 bits, then it returns to a downward trend.
Is there and explanation for this?

[bloodIce]

Originally Posted by Uncwilly

This is a graph I have of the 332M range that shows the same issue that I see on your chart, namely, after the lowest bit, there is a drop-off on the next 2 bits, then it returns to a downward trend.
Is there and explanation for this?

What is the range (332M to 333M) or something else? How do you calculate the bitlevel of a factor? Do you round-up, like if a factor is 29.57 bits, this will be in 30 bitlevel in your graph?

[petrw1]

I took a few days off of regular DC-TF to refactor a couple ranges of sannerud's suspect work...(during which I did find the expected number of factors) ....

Prior to this I completed over 5,000 DC-TF assignments and had about a 1/70 ratio of factors found.

However since returning to DC-TF I have done 287 assignments without 1 single factor....

[LaurV]

Originally Posted by Uncwilly

This is a graph I have of the 332M range that shows the same issue that I see on your chart, namely, after the lowest bit, there is a drop-off on the next 2 bits, then it returns to a downward trend.
Is there and explanation for this?

How can you have 29 bits factors for 332M? The smallest factor is 664M (2p+1) which is well into 30 bits...
If you calculate them by truncation, as bloodIce already suggested (which would be somehow wrong, they all HAVE 30 bits at least, in their representation), then your problem (?) is at 31-32 and it may be related to a 32-bits word overflow or signed/unsigned math... (maybe this worth an investigation?)

[TheMawn]

Originally Posted by petrw1

I took a few days off of regular DC-TF to refactor a couple ranges of sannerud's suspect work...(during which I did find the expected number of factors) ....

Prior to this I completed over 5,000 DC-TF assignments and had about a 1/70 ratio of factors found.

However since returning to DC-TF I have done 287 assignments without 1 single factor....

On its own, if you have a 1 in 70 chance of getting a success, then you have roughly a 1.6% of not getting a success after 287 attempts. Not impossible, but quite unlikely.

However, you are missing the fact that these exponents have had P-1 done on them. Some factors will have been found, so the pool of unfactored exponents has been "diluted" because some of the factors have been picked out by P-1.

[Uncwilly]

Originally Posted by bloodIce

What is the range (332M to 333M) or something else? How do you calculate the bitlevel of a factor? Do you round-up, like if a factor is 29.57 bits, this will be in 30 bitlevel in your graph?

The graph is 332,192,831 to 332599979 (I have not extended it to the end of the range.)

Originally Posted by LaurV

How can you have 29 bits factors for 332M? The smallest factor is 664M (2p+1) which is well into 30 bits...
If you calculate them by truncation, as bloodIce already suggested (which would be somehow wrong, they all HAVE 30 bits at least, in their representation), then your problem (?) is at 31-32 and it may be related to a 32-bits word overflow or signed/unsigned math... (maybe this worth an investigation?)

Here is the lowest of all the factors in that I am seeing (I am not tracking the bit of the range below 332,192,831) http://www.mersenne.ca/exponent/332192879
For the sake of simplicity, I am binning them by the integer portion of the number.
But if you look at garo's chart, the number of factors drops in the same pattern. The 2nd & 3rd bit levels are lower than one might expect. Here is the chart for his range.

[LaurV]

Originally Posted by Uncwilly

The graph is 332,192,831 to 332599979 (I have not extended it to the end of the range.)


Here is the lowest of all the factors in that I am seeing (I am not tracking the bit of the range below 332,192,831) http://www.mersenne.ca/exponent/332192879
For the sake of simplicity, I am binning them by the integer portion of the number.
But if you look at garo's chart, the number of factors drops in the same pattern. The 2nd & 3rd bit levels are lower than one might expect. Here is the chart for his range.

This is interesting, can it be pure mathematical explanation? Like for example, all prime exponents p can result in mersenne numbers Mp with factors of the form q=2*(4k)p+1, therefore the third bar is higher (i.e. 8p+1), but there is no q=2*(4k+2)p+1 factors (i.e. 4p+1, those would result in 3 or 5 (mod 8), and they can not be factors for a mersenne with an odd exponent, prime or not, therefore the second bar is lower), and only exponents with p=3 (mod 4) can have a q=2*(4k+1)p+1 factors, i.e. 2p+1, and also only p=1 (mod 4) can have a q=2*(4k+3) factor, i.e. 6p+1. This would result (always? probabilistically?) in a "mid, deep, mid, high" pattern (?!?) for the bars...