User TJAOI

[Uncwilly]

Originally Posted by LaurV

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...

Would this not form large dips repeatedly?
Try pulling some factor data for some other random ranges and see if it the same.

[LaurV]

Originally Posted by Uncwilly

Would this not form large dips repeatedly?
Try pulling some factor data for some other random ranges and see if it the same.

No, it will not. Because you "cut" the interval on both sides. If the interval is not "cut" on the left, i.e. pick any bit level, it will contain all 3 types of factors, for k=0, 1, 2, 3, (mod 4) in proportions 50%, 25%, 0%, 25%. But for you, the interval is limited. Where the factors in the second bar can come from? The most factors are always small (i.e. 2p+1, 6p+1, 8p+1). Say we take 70M exponents, the factors in the 1st bar are in the range 140M, and they come only from 2p+1. Because higher factors (4p+1 and higher) are excluded on the left. For q=4p+1 be in the 140M, then p would be in 35M, limited by your interval. The factors in the 2nd bar are double, i.e. 280M, one more bit, where they can come from? The 2p+1 factors should be 140M (limited by your interval in the right), the 4p+1 factors do not exist, the 6p+1 factors... ??
etc.
In fact, yes, the effect is seen on all bars, if your interval has the right "size". In your second graphic you can see the bar 6 and bar 8 being taller than bar 5 and bar 7.

[bloodIce]

Originally Posted by Uncwilly

For the sake of simplicity, I am binning them by the integer portion of the number.

If you do not truncate, but round the factors size in 70M-71M range you would see that your 28bit bar will disappear completely. To me this is normal, because Kmod4!=2. 70M-71M will have factors with K=1 in between 27.06 to 27.08 bits (27 bits bar) and with the next available K=3 between 28.65 and 28.67 bits (29 bits bar). Anything from approx. 27.08 and 28.65 bits will not be possible in this range of exponents. LaurV explained very nicely why you would see this as a general pattern in a limited range.

[LaurV]

To make Uncwilly happy, I scheduled 332M to 333M from 0 to 67 bits, in case some factors were missing in the past, they should be ready by tomorrow evening to 64 bits, then two more days for 64-67.

[Uncwilly]

Originally Posted by LaurV

To make Uncwilly happy, I scheduled 332M to 333M from 0 to 67 bits, in case some factors were missing in the past, they should be ready by tomorrow evening to 64 bits, then two more days for 64-67.

TJAOI has already been there to 58.

[tha]

I made a graph of the 53.000+ factors in the 12M range. I made a distinction between the lowest factor of an exponent and successive factors of each exponent found. I'd like to hear comments on the drop from 55 bits to 57 bits, the blue bars in the graph.

[The number of bits are rounded up, so ²log(exponent)=33.1 is counted as 34 bits]

[petrw1]

Originally Posted by LaurV

To make Uncwilly happy, I scheduled 332M to 333M from 0 to 67 bits, in case some factors were missing in the past, they should be ready by tomorrow evening to 64 bits, then two more days for 64-67.

Finding any?

[casmith789]

Originally Posted by tha

I made a graph of the 53.000+ factors in the 12M range. I made a distinction between the lowest factor of an exponent and successive factors of each exponent found. I'd like to hear comments on the drop from 55 bits to 57 bits, the blue bars in the graph.

[The number of bits are rounded up, so ²log(exponent)=33.1 is counted as 34 bits]

Presumably that drop comes because people stopped checking for factors after 55-57 bits in the 12 million range, presumably because (at the time) doing an LL test was more worthwhile than trial factoring further?

[Uncwilly]

Originally Posted by tha

I made a graph of the 53.000+ factors in the 12M range. I made a distinction between the lowest factor of an exponent and successive factors of each exponent found. I'd like to hear comments on the drop from 55 bits to 57 bits, the blue bars in the graph.

That looks like the same pattern that I pointed out.

[LaurV]

Originally Posted by petrw1

Finding any?

Few thousands already (new). Unfortunately, nothing "first" yet. Still going.

[LaurV]

Originally Posted by tha

I made a graph of the 53.000+ factors in the 12M range. I made a distinction between the lowest factor of an exponent and successive factors of each exponent found. I'd like to hear comments on the drop from 55 bits to 57 bits, the blue bars in the graph.

[The number of bits are rounded up, so ²log(exponent)=33.1 is counted as 34 bits]

Originally Posted by casmith789

Presumably that drop comes because people stopped checking for factors after 55-57 bits in the 12 million range, presumably because (at the time) doing an LL test was more worthwhile than trial factoring further?

Exactly. In fact, they stopped much earlier than 57 bits, at the time there were no GPUs and LL-ing a 12M was most profitable after 52 bits (on the CPU) or so. Only in the last years due to GPUs we "advanced" the small expos to 60-63 bits -- and only the one with no known factors. What you see on the graphic is TJAOI and others like him TF-ing everything (dc-ed or not, known factors or not) to 57 bits. Is where the front of "TF-doublecheck" actually is, currently.