new idea?

This isn't really a new idea, but I would like to have it reconsidered.

I think that we should try skipping a range of 0.3 G or so every time we find a factor. Yes, I've heard all of the arguments against it last year about how all factors are distributed randomly, that skipped ranges will be very hard to keep track of, etc. However, I think that we should apply this method, and here is why:

First, skipping ranges after a factor is found will increase the rate that factors are found. Besides, how often do you find 2 factors within 0.3 G's of each other? Most likely, you haven't found those factors in the past month. Skipping ranges after a factor is found will make people sieve a range faster, with a very small percentage of factor loss.
However, many say that factors are distributed randomly, and that the chance of one factor being found very close to another is the the same as the chance that one factor is far apart from another. But while this is true theoretically, it isn't true in practice. In the range of 61-62T, where the factors were over 4x as dense as they are now, skipping a range of 0.3G will result in just a 5% factor loss, but over 9.2% of the range will be skipped.

Secondly, skipping ranges not only increase the rate at which factors are found but will also eliminate many PRP tests. Even though some may say that skipped ranges are hard to keep track of, we don't need to keep track of them. That's because, at the current p value of 300T, the factor density is so low that sieving is no longer beneficial unless a way of increasing the rate at which factors are found is used.

Without a way to increase the rate at which factors are found, sieving will probably die off at around 400T instead of a possibly higher value at 600T. Considering these things, we should give this method a try :)

You may (or may not) be right.

But I think there is one more important issue.

Is it worth it?

Here's a quick calculation.

Roughly speaking, we expect 12,000 factors up to 600T (give or take 1,000 factors, will not change the result much).

If we skip 0.3G everytime we find a factor, all we'll gain is 4-5 days of sieving effort (i.e. 0.3G * 12,000 = 3,600G = 3.6T ==> 3,600G / 800G per day).

As Nuri says, getting the whole range will not only get all possible factors, but won't take that much of a different amount of time.

Also, in regard to sieving not being beneficial:

In the amount of time that it takes me to do one test, I can almost guarantee a new factor. So it's like I did a test. Only sometimes I get more than that. So if I eliminate 6 tests in the time it takes me to do two, then I get four free tests. Sounds beneficial...

you must be kidding one factor in the time it takes to do a prp test? Are you faactoring or sieving? I have some of the highest reservd ranges adn i find at least 10 factors for every test i could have completed in the same amount of time. And some of these tests saved are for tests that will take alot more time than the current ones.

On my P-III 1000, I get 1.5 factors a day.

Assuming that the factors within +400k of leading edge are very important, and others less important to varying degrees, I get;

1 (one) very important factor a month. (1.5 per day * 0.4m/19m)

30 significantly important factors a month (i.e. factors above leading edge)

14 less important factors a month (i.e. factors below leading edge)


These are rough numbers of course.

And they will drop as p increase. (but not very fast going forward)

And there is also the issue of finding new primes, so the "significantly important factors" might worth less. (still, how many primes do we expect up to 20m, and at which n? I feel like, more than 80% of the factors we find above the leading edge will prove useful. Anyways, time will show.)

most likely 70-80% will count as refering to the "above the leading edge" factors. It is also important to remember that these factors save tests that will take 4-16 times as long as the currect tests. Most of the factors found in the 19-20 million range, even if some don't end up being worth anything, are worth much more than ones found in the 6-7 milion range.