I need a cost estimate for some data.

[CRGreathouse]

Originally Posted by Kathegetes

America has a atom clock for time synchronous many lands and GPS dateliyes in space. Does she have same asfor primes in order and time? Try again. Who do you look to for primes in count and order?

Well, up to 10^17, there's http://primes.utm.edu/nthprime/

[CRGreathouse]

Originally Posted by danaj

I do as well, but I was nervous about C libraries (logl) and floating point accuracy on random machines. Admittedly I'm probably not nearly paranoid enough for that, so I should just do the calculations assuming reasonable double-precision. It just makes my numbers one too far, which I viewed as a reasonable sacrifice at the time. Most of my effort was spent on tightening the bounds for smaller inputs.

I just used excessive precision in gp.

Originally Posted by danaj

Some of it is my using a fast machine (4.3GHz i4770K), some is how sensitive his code is to all the myriad tuning factors.

Yes, I just have everything using the defaults.

[CRGreathouse]

Hmm. I installed and tested Math::Prime::Util::prime_count and it actually seems to be slower than the Bau's program:

> ./count 1000000000000000000
pi(1000000000000000000) ~ 24739954284265752 (about 37.5 min)
pi(1000000000000000000) = 24739954287740860; 2771.51 seconds.
> time perl -MMath::Prime::Util -e 'print Math::Prime::Util::prime_count("1000000000000000000")'
24739954287740860
real	58m30.056s
user	57m41.044s
sys	0m2.040s

46 minutes vs. 58 minutes. (Ignore my wrapper program...!)

[Kathegetes]

Originally Posted by Uncwilly

Do you mean:
↑↑↓↓←→←→BA?

up up down. First I am too say how scared and also pleased. You and friends are seeing my work and completing it.
The count of perfect numbers less than a given term by continued 8∆ as fixed by Batalov is conditioned ( may be wrong but cost me a lot of money ).
Please confirm the greatest Mp in a term has to limit date produced its Pn in the next term ( subsequent, it follows in order term?). Example possibilities if pattern holds meaning best made by such as you please.
100% pattern holds~ predict
( If heads in 47 tosses, coin maybe has no tail ) q.v. Bernoulli " Ars Conjectandi " on degree of moral certain in law of great numbers. Use GIMPS data. I have not seen if past 40, please check.
All friends can make more And better tables from given data. Katydid heaven.
Motorola Droid symbols mean your arrows by terms.
Count of Mp minus count of Pn=n (0,1,2,3,4,5,6...

Term(n)Arrow
0___1___^
1___1___>
2___1___>
3___1___>
4___2___^^ Here comes idea based on weak science( Katy not weak in science) metaphor only. We know these numbers are not = to a ball. Throw up the ball. Ball comes down so far away. Faster up, same down, farther away. Escape velocity, ball goes around. Here we see pattern within pattern, cycle within cycle. Except ball may not stay in constant orbit but spiral out further and further if it doesn't come down. Sorry must finish this later. Work in hops field now. Children of family home for Sunday meal. Not all pagans; just work on Sundays a bit.

[danaj]

Originally Posted by CRGreathouse

Hmm. I installed and tested Math::Prime::Util::prime_count and it actually seems to be slower than the Bau's program

Hmm, could be the popcount thing (you have to somehow tell gcc to compile using popcount, e.g. -march=native, or it won't use it -- if I put the asm in, it faults on machines that don't have it). Or it could very well be that Bau's program is just faster!

Kim found that in his testing, the method I'm using for prefix sums is faster at small sizes, but for large ones, the Fenwick trees that Oliveira e Silva recommends are faster. I think without popcount, Bau's method is faster than mine, but I liked how mine was more amenable to parallel use. I should try Fenwick trees.

Re precision: using gp is no fair. :) Good choice.

MPU supports nth prime as well. It computes the values rather than using tables, which is good and bad. There's also approximations and upper/lower bounds for counts and nth primes. Twin primes also have count, nth, and approximations.

[CRGreathouse]

Originally Posted by danaj

Hmm, could be the popcount thing (you have to somehow tell gcc to compile using popcount, e.g. -march=native, or it won't use it -- if I put the asm in, it faults on machines that don't have it). Or it could very well be that Bau's program is just faster!

I have to fess up -- I just told cpan to install it, I didn't even attempt to hack in my architecture. I'd like to do this but I'll have to find out how to get the right parts of the source and a build file. (I'm proficient in Perl, but by no means a master.) Fortunately my CPU does have a 1-cycle popcount instruction.

Bau's comments in his program lead me to believe he thought it wasn't that fast. At least that's what I thought when I read them a few years back.

Originally Posted by danaj

Kim found that in his testing, the method I'm using for prefix sums is faster at small sizes, but for large ones, the Fenwick trees that Oliveira e Silva recommends are faster. I think without popcount, Bau's method is faster than mine, but I liked how mine was more amenable to parallel use. I should try Fenwick trees.

Hmm, not even familiar with the term! I'll have to look into it.

Originally Posted by danaj

MPU supports nth prime as well. It computes the values rather than using tables, which is good and bad. There's also approximations and upper/lower bounds for counts and nth primes. Twin primes also have count, nth, and approximations.

I read through the cpan page. Nice piece of work!

[Kathegetes]

Originally Posted by CRGreathouse

Well, up to 10^17, there's http://primes.utm.edu/nthprime/

In the whole world With so much interest, I guessed there to be an official prime site by China government or such. I heard they have a proud computer. America wants better than EU weather data. Different model for Sandy and Katrina etc. Then people must guess.
Someone says Oliveira person may have a program they think might get me more data. You have not told me how much it cost you. So I guess it was a little interesting.
I'm about to be banished so I want to put a beautiful thing in the soap box corner by the end of this new week. It will be about polygons, fun, and little surprises. People computers can chose great big n= 3,4,5...( I can only do 360*60*60*10) then all these beautiful things happen and you wonder.
It will be a blue line that shows a Zygote game you have to program to play. People won't do it unless someone says, " I loved it."
It has zero words except the name. We know everybody can make them.

[CRGreathouse]

Originally Posted by Kathegetes

You have not told me how much it cost you. So I guess it was a little interesting.

The first four calculations were almost instant on PARI/GP. The fifth one I used that website to get an answer as fast as I could copy/paste it. The sixth one I couldn't compute so I used estimates in a script I had already written, and it took less time than the first four. So overall less than a second of my CPU time for a negligible total electric cost.