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drummers-lowrise
1) Message boards : General discussion : Duh, what am I missing here? (Message 151515)
Posted 6 days ago by Profile composite
The reviewer didn't understand it. He thinks I used some incorrect logic with upper bounds. At first blush I took him at his word. Then I realized it's my fault for not explaining clearly enough that what I did concerns partitioning the conjecture to prove the parts separately. I clarified and told him not to bother rereading it with the new understanding, wait for the rewrite.

While waiting for that feedback on ideal Waring's conjecture, I took a first stab at proving the Collatz conjecture, it looks related (both conjectures involve multiplications by 3 and divisions by 2). It would be a gangbuster of a paper to prove both conjectures with one blow. I'd like to stop the waste of compute cycles and energy trying to find a counterexample to the Collatz conjecture (one click and you'll see I was guilty of that). A couple of interesting lemmas came out the first day of work, like: there are no length-1 cycles except the trivial cycle, and there are no length-2 cycles. Of course the state of the art says there are no non-trivial cycles of length less than 268 (based on the state of the Collatz search). I'm not peeking at prior art so that I can continue thinking outside the box - actually, I don't even know where the box is because I haven't looked. But I'll pause for a while, there are other demands for my time.
2) Message boards : General discussion : Duh, what am I missing here? (Message 151420)
Posted 13 days ago by Profile composite
The approach I took always ended in an insurmountable block one way or another whenever an error was corrected. So I've abandoned that approach and tried a different one, very different. Submitted for review. Let's see if this one sticks.
3) Message boards : Number crunching : Once in a Blue Moon Challenge (Message 151247)
Posted 28 days ago by Profile composite
I only had a look at htop output.

1-second sampling htop doesn't gives you the whole picture.
You can adjust the sampling rate with a command line flag to get a better idea.
You typically won't see fleeting tasks like interrupt handlers running, which will take over a logical core and kick off whatever is running there for less time than it takes to render the window. That's why tasks randomly switch logical cores. If the scheduler is smart enough, it should realize that tasks with lots of cache still loaded on a particular core would be better off returning to the same core instead of trying to run the task earlier on another core and causing a spike in RAM accesses. It depends on how busy the system is.
4) Message boards : General discussion : Duh, what am I missing here? (Message 150993)
Posted 51 days ago by Profile composite
But space that pushes?

It's good to imagine possibilities, however theories have to be consistent with everything that we observe. That's science. The theory of special relativity accounted for results of experiments that didn't agree with the predictions of Newtonian (classical) mechanics, but the power of special relativity was confirmed by the accuracy of predictions it made for future measurements.

Two identical fermions (particles of half-integer spin, like protons or electrons) have distinct quantum states (the Pauli exclusion principle) so they can't occupy the same position. That would be degenerate in Quantum Mechanics (QM) - multiple linearly independent eigenvectors having the same eigenvalue. One way of thinking of this is a "degeneracy pressure" that keeps them apart. In simple terms, particles which have different quantum states can't be merged together under normal circumstances.

There is one exception - black holes. They are an enigma from the point of view of QM because fermions appear to be compressed down to a single point in space, which is degenerate - the extreme gravity overcomes the quantum force that keeps them apart. But it's only degenerate from the point of view of 3 spacial dimensions. If other spacial dimensions are accessible in a black hole, QM may hold so that fermions retain their distinct quantum states in those other dimensions. Since we have no way of getting information from inside a black hole and this explanation doesn't arise from some theory that explains other things, this idea would not be considered seriously. Another imaginative idea, that black holes are a "gateway to another universe" isn't credible - the matter and energy that disappear into a black hole measurably exert their gravitational effect here in our 4-dimensional spacetime. And actually, we don't have evidence that the contents of a black hole are concentrated at a single point; there could be a hard core of material well within the Schwarzschild radius. Gravitationally, they look the same from the outside.

In contrast to fermions, a Bose-Eintein Condensate (BEC) has multiple identical bosons (particles of integer spin, like helium nuclei) acquiring the same (lowest) quantum state by extreme cooling, so you can't tell where one gas particle starts and another ends - the collection of gas particles behaves statistically as if it's one particle. The Riemann Zeta function of (3/2) appears in the calculation of the critical temperature at which the collection of gas particles becomes a BEC.

Guess where else the Riemann Zeta function appears. The zeroes of the Zeta function have a connection with the distribution of prime numbers. If you can prove that the non-trivial zeroes all lie on the line in the complex plane with real part = 1/2, there's a million dollar prize waiting for you at the Clay Mathematics Institute.
5) Message boards : General discussion : Idea of "All-Teams"-Events... (Message 150987)
Posted 52 days ago by Profile composite
One way to motivate people work on a focus project is to assign extra credit to the focus project, say 10%. Given a set of otherwise equal choices, I'll work on the project that has an incremental benefit for working on the indicated project NOW.
6) Message boards : General discussion : Duh, what am I missing here? (Message 150916)
Posted 60 days ago by Profile composite
The reviewer is busy organizing a conference. That explains the delay.

A song? This is starting to sound like the lyrics. Here's the latest verse.

Setting aside the proof a week, I looked at it again.
Some minor fixes and clearer speak, good so far, my friend.
Were mathematics so water-tight, the proof I thought was true?
I cast the doubt and checked it out, then shot a hole clean through!

I saved the reviewer the trouble this time, the claim of proof - withdrew.
7) Message boards : General discussion : Duh, what am I missing here? (Message 150905)
Posted 60 days ago by Profile composite

On Google Maps, line up Dallas, TX with the right edge of the browser window. Then follow that window edge northward, waaayyy up North. Zoom in on that highway East of Winnipeg. You'll see the sign on Highway #1 that says "Longitudinal Centre of Canada" at 96 degrees 48 minutes 35 seconds West. Wikipedia has Dallas at 96 degrees 48 minutes 32 seconds West. That's a difference of about 40 metres at the latitude of the highway. In Dallas, that line would run through the Hyatt Regency's Reunion Ballroom, about 70 metres West of the Reunion Tower.

I read 'Dallas'
Proper above 'Middle East'
I need to get to a map.
It is much simpler here in Australia.
And less metrics to explain where you are.
Crocodiles? Heat? Sand? Politicians?

Ah, sorry 'bout the confusion, mate - has Google localized maps for Australians with South at the "top"? LOL
8) Message boards : General discussion : Duh, what am I missing here? (Message 150902)
Posted 60 days ago by Profile composite

74.9 C temperature range this year (annual low -38.4 C Feb 13; annual high +36.5 C June 5).
Last winter had 30 days with daily low temperature below -20 C, for 11 of those days below -30 C.

I just re-read that - 75 degrees C difference between cold and hot?
I'll take my chances with ANY weather in Australia compared to that.

I am going to take a guess here - upper mid west?
Or in Anchor-man 2 - middle east?
Stay Classy!

Edit: You are in Canada - I thought I should see where you might be - very a lot upper mid west!

On Google Maps, line up Dallas, TX with the right edge of the browser window. Then follow that window edge northward, waaayyy up North. Zoom in on that highway East of Winnipeg. You'll see the sign on Highway #1 that says "Longitudinal Centre of Canada" at 96 degrees 48 minutes 35 seconds West. Wikipedia has Dallas at 96 degrees 48 minutes 32 seconds West. That's a difference of about 40 metres at the latitude of the highway. In Dallas, that line would run through the Hyatt Regency's Reunion Ballroom, about 70 metres West of the Reunion Tower.
9) Message boards : General discussion : Duh, what am I missing here? (Message 150852)
Posted 64 days ago by Profile composite
It could be a while before I get the reviewer's response. Summertime is premium here.
So far 18 days with daily high temperature exceeding +30 C and we are still a month before the usual hottest period.

74.9 C temperature range this year (annual low -38.4 C Feb 13; annual high +36.5 C June 5).
Last winter had 30 days with daily low temperature below -20 C, for 11 of those days below -30 C.

There's also a drought happening in the prairies. Expect higher food prices.
Some immature crops have been salvaged as fodder with an early cut to prevent the grasshoppers from taking it all.
10) Message boards : General discussion : an idea for speeding up LLR testing (Message 150846)
Posted 64 days ago by Profile composite
How about testing 2 candidate primes at the same time for most of the LLR iterations?

Since we are repeating the same calculations for different candidates, say X and Y, just with different modulii and different numbers of iterations, then use a common calculation for (X-1) iterations with the modulus which is the product of the candidates (X*Y).
At iteration X compute the LLR residue for candidate X as A (mod X), and replace the intermediate result A with A (mod Y), then continue as normally until iteration Y with A (mod Y).

Of course, we will be doing (X-1) iterations with a modulus twice as long, plus 1 additional (normal length) modulus operation.
But if the modulus code is faster than the rest of the code in each iteration, then we have a speedup by using the slower code just Y times for each 2 candidates instead of (X+Y) times.
There's a net speedup if the overhead of multiplying the candidates X and Y together, plus 1 additional normal length modulus operation, plus the extra time of using the longer modulus for (X-1) iterations,
is less than the time saved by not repeating the first X iterations of the slower code for candidate Y.

i.e.
A(n+1) = An2-2 (mod X*Y)
At iteration X instead taking AX (mod X*Y)
compute LLR residue for candidate X = AX (mod X)
and replace AX with AX (mod Y)
then continue as normal until iteration Y with
A(n+1) = An2-2 (mod Y)


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