[XPM] [ANN] Primecoin High Performance | HP14 released!

[Trillium]

it would be nice if somebody create a calculator how much could i mine XPM per day on diffrent CPU

http://anty.info/primecoin-calculator

This has come up in previous pages. The answer is: its complicated, and difficult to achieve.

The calculations to estimate your XPM per day have been discussed quite a bit by mikaelh and in my own posts, suggest you look through our comment histories for examples.

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[Trillium]

After reading some comments, i understand that me not finding a block in 2 days is ok
Because i thought something is broken, and couldn't figure out what. But it's pure luck. LOL.
Since 22.10 i have solo mined 43 blocks which were sold for 1.3 BTC and now nothing for 2 days.
OK i'll wait

Yes. the fractional difficulty is currently very high (.96 or more) This means only 4% or less of the chains suggested by the chainsperday value would be accepted by the network.

If my understanding is correct, when we hit 10.000 diff, then the chainsperday value will change to a much lower number since its related directly to the whole integer value of the difficulty.

If you only have one (or a small few) machines then you probably wont see a block each day anymore.

[mhps]

If my understanding is correct, when we hit 10.000 diff, then the chainsperday value will change to a much lower number since its related directly to the whole integer value of the difficulty.

If you only have one (or a small few) machines then you probably wont see a block each day anymore.

I think it is mistake, because  longer (>9) length chains are ignored when the block-found probability  is calculated. See http://www.peercointalk.org/index.php?topic=695.msg6311#msg6311
If the longer chains are included, there is no jump in block-found difficulty when the network difficulty goes over an integer limit.

[Subw]

Yes. the fractional difficulty is currently very high (.96 or more) This means only 4% or less of the chains suggested by the chainsperday value would be accepted by the network.

If my understanding is correct, when we hit 10.000 diff, then the chainsperday value will change to a much lower number since its related directly to the whole integer value of the difficulty.

If you only have one (or a small few) machines then you probably wont see a block each day anymore.

Thank you for the explanation!
After my post until now two blocks were found, so i'm calm

How much CPU power do you use?

[mikaelh]

If my understanding is correct, when we hit 10.000 diff, then the chainsperday value will change to a much lower number since its related directly to the whole integer value of the difficulty.

If you only have one (or a small few) machines then you probably wont see a block each day anymore.

I think it is mistake, because  longer (>9) length chains are ignored when the block-found probability  is calculated. See http://www.peercointalk.org/index.php?topic=695.msg6311#msg6311
If the longer chains are included, there is no jump in block-found difficulty when the network difficulty goes over an integer limit.

Yes, my original formula here actually wasn't accurate for high fractional difficulties. The issue boils down to the probability of the 10th number being prime. I thought that the probability would be negligible but actually it is about 3.5% according to my estimates (this number depends on the primorial used during mining). That means that about 3.5% of 9+-chains turn out to be 10-chains (9+-chains refers to chains at least of length 9). As the fractional difficulty increases, the number of accepted 9-chains diminishes while the 10-chains remain unaffected. Eventually there will be more 10-chains qualifying for blocks than 9-chains.

So my latest estimate for the amount of blocks found is:
blocks/day = chains/day * (1 - fracDiff + 0.035)

There will be a jump in the difficulty when difficulty goes to 10.0. That's because none of the 9-chains will qualify for blocks and we have to start looking for 10+-chains. I've actually been working on a paper related to this. Right now it looks like 10.0 will be more difficult than 9.996 will be which means we could get stuck between 9.996 and 10.0 for a while.

You can actually see that happening before in my charts:
http://xpm.muuttuja.org/charts/

If you look closely enough, the network block rate seems to have dropped when we went from 8.996 to 9.0. Of course we were using an older version of the mining algorithm back then which probably behaved slightly different.

[cabin]

If my understanding is correct, when we hit 10.000 diff, then the chainsperday value will change to a much lower number since its related directly to the whole integer value of the difficulty.

If you only have one (or a small few) machines then you probably wont see a block each day anymore.

I think it is mistake, because  longer (>9) length chains are ignored when the block-found probability  is calculated. See http://www.peercointalk.org/index.php?topic=695.msg6311#msg6311
If the longer chains are included, there is no jump in block-found difficulty when the network difficulty goes over an integer limit.

Yes, my original formula here actually wasn't accurate for high fractional difficulties. The issue boils down to the probability of the 10th number being prime. I thought that the probability would be negligible but actually it is about 3.5% according to my estimates (this number depends on the primorial used during mining). That means that about 3.5% of 9+-chains turn out to be 10-chains (9+-chains refers to chains at least of length 9). As the fractional difficulty increases, the number of accepted 9-chains diminishes while the 10-chains remain unaffected. Eventually there will be more 10-chains qualifying for blocks than 9-chains.

So my latest estimate for the amount of blocks found is:
blocks/day = chains/day * (1 - fracDiff + 0.035)

There will be a jump in the difficulty when difficulty goes to 10.0. That's because none of the 9-chains will qualify for blocks and we have to start looking for 10+-chains. I've actually been working on a paper related to this. Right now it looks like 10.0 will be more difficult than 9.996 will be which means we could get stuck between 9.996 and 10.0 for a while.

You can actually see that happening before in my charts:
http://xpm.muuttuja.org/charts/

If you look closely enough, the network block rate seems to have dropped when we went from 8.996 to 9.0. Of course we were using an older version of the mining algorithm back then which probably behaved slightly different.

I actually think 10.0 will be a bit 'easier' than 9.99. The reason is the stock miner will have finally switched to searching for 10-chains in the sieve and it will find a few more 10 chains than when it was searching for 9-chains. Once the diff passes .96 I think it is better to search for 1-higher chains. The biggest factor is just the nature of division though.. going from 9.0 to 9.5 cuts in half the number of 9-chain-blocks you will find (from 100% to 50%). But so does going from 9.98 to 9.99 (from 2% to 1%)

[rdebourbon]

I actually think 10.0 will be a bit 'easier' than 9.99. The reason is the stock miner will have finally switched to searching for 10-chains in the sieve and it will find a few more 10 chains than when it was searching for 9-chains. Once the diff passes .96 I think it is better to search for 1-higher chains. The biggest factor is just the nature of division though.. going from 9.0 to 9.5 cuts in half the number of 9-chain-blocks you will find (from 100% to 50%). But so does going from 9.98 to 9.99 (from 2% to 1%)

I agree. My pool miner has already auto re-targeted to 10 (unless manually overridden), and I'm finding that the block rate is marginally better than if targeting the current network difficulty.. As I'm sure you're aware the difficulty calculation is not perfectly linear, so while the fractional part appears to indicate only 4% of 9ch's are valid now, it is actually less than 4% that is valid at the moment..

On the positive side, the step up to a target of 10.0 comes with a decent reduction in primes needed for sieving, as well each sieve returns fewer candidates for primality testing - so the raw number of candidates sieved/tested per second increases quite nicely.. This increased speed and the fact that *any* 10.0+ is currently a block solver makes it worth the switch IMO.. The way the pool miners work is that if a chain less than target but greater than submission difficulty is found the "share" is submitted.. In this instance, when solo mining with the pool miners the target can be set to 10, and while that sieves away a good percentage of the 9ch's.. it leaves enough for you to still encounter some block solving chains in the 9ch range..

Also, if you look at the difficulty charts from a historical perspective, once a target length is breeched the network difficulty quickly increases to the x.3-x.4 range - and I expect this to be the case with 10 as well..

[cabin]

I actually think 10.0 will be a bit 'easier' than 9.99. The reason is the stock miner will have finally switched to searching for 10-chains in the sieve and it will find a few more 10 chains than when it was searching for 9-chains. Once the diff passes .96 I think it is better to search for 1-higher chains. The biggest factor is just the nature of division though.. going from 9.0 to 9.5 cuts in half the number of 9-chain-blocks you will find (from 100% to 50%). But so does going from 9.98 to 9.99 (from 2% to 1%)

I agree. My pool miner has already auto re-targeted to 10 (unless manually overridden), and I'm finding that the block rate is marginally better than if targeting the current network difficulty.. As I'm sure you're aware the difficulty calculation is not perfectly linear, so while the fractional part appears to indicate only 4% of 9ch's are valid now, it is actually less than 4% that is valid at the moment..

This one is an open question for me.. but I think it might be working against us. I see an abnormal number of 9.99999 chains and never see the corresponding 9.000001 chains. But the possible reasons behind that are over my head, other than it is non-linear.

On the positive side, the step up to a target of 10.0 comes with a decent reduction in primes needed for sieving, as well each sieve returns fewer candidates for primality testing - so the raw number of candidates sieved/tested per second increases quite nicely.. This increased speed and the fact that *any* 10.0+ is currently a block solver makes it worth the switch IMO.. The way the pool miners work is that if a chain less than target but greater than submission difficulty is found the "share" is submitted.. In this instance, when solo mining with the pool miners the target can be set to 10, and while that sieves away a good percentage of the 9ch's.. it leaves enough for you to still encounter some block solving chains in the 9ch range..

Also, if you look at the difficulty charts from a historical perspective, once a target length is breeched the network difficulty quickly increases to the x.3-x.4 range - and I expect this to be the case with 10 as well..

Yup, as long as the network grows going from 10.0 to 10.4 (not even double the difficulty) will be a piece of cake and really quick, compared to going from say 9.80 to 9.95 (almost 4 times the difficulty).

[mikaelh]

That's definitely interesting if you are seeing increased block production when targeting length 10 instead of 9.

I'm aware that the distribution of the fractional remainder isn't really uniform. That's one major issue which may be screwing up my calculations. I'll need to check how big the impact is at some point. I'll also need to double check my earlier calculations too. I have already accounted for the fact that lots of 9-chains are found when targeting length 10. In fact, I assumed that ten times more 9-chains are found than 10-chains when targeting length 10.

Also, if you look at the difficulty charts from a historical perspective, once a target length is breeched the network difficulty quickly increases to the x.3-x.4 range - and I expect this to be the case with 10 as well..

I would argue that the difficulty increase to the 9.3 range was caused by the momentum left after the transition to 9.0. The block rate was about 1.5 blocks/minute on July 22 after the transition to 9.0. Cutting that rate by 1/3 brings it to the target rate of 1 block/min. The difficulty rising to about 9.3 does just that. The chart also shows that the block rate was about 3.0 blocks/minute before the transition. That means that going from 8.996 to 9.0 somehow seems to have cut the block rate in half.

This one is an open question for me.. but I think it might be working against us. I see an abnormal number of 9.99999 chains and never see the corresponding 9.000001 chains. But the possible reasons behind that are over my head, other than it is non-linear.

I looked at the fractional remainder a while back. I remember seeing a large number of 0xFFFFFF (this is the 24-bit version of the fractional difficulty) values which should statistically be nearly impossible (if you wanted to assume that it would be uniformly distributed).

[cabin]

Here are the stats and calculations I get when hard coding the sieve size:

Diff: 9.96
Probability of finding a 10th chain link when you have a 9 chain and are sieving on 9-chains: 1 / ln(2^256) = 0.005635

Sieve Size 9:
9-chains per day: 0.54 (reported by miner)
10-chains per day: 0.54 * 0.005635 = 0.00304
block per day = 0.54*0.04 + 0.00304 = 0.025

Sieve Size 10
9-chains per day: 0.22 (reported by miner)
10-chains per day: 0.02 (reported by miner and inline with 0.22*0.095)
block per day: 0.22*0.04 + 0.02 = 0.029

Size 10 wins! But I welcome critique of these calcs..

[mikaelh]

Probability of finding a 10th chain link when you have a 9 chain and are sieving on 9-chains: 1 / ln(2^256) = 0.005635

That's not quite right. The primorial that is embedded in the chain origin actually changes the probability a lot. If you filter out the prime p_i, the probability increases by

1 / (1 - 1/p_i)

If you take a product of those up to p_17 which is 59, you get 7.47493. So that's how many times bigger the probability will be if the number is a multiple of 59#. Also, I usually assume that the numbers are about 300 bits in size. So then the probability for the 10th number being prime becomes:

7.47493 * 1/ln(2^300) = 0.0359468

And if I plug that number into your calculations, I get:

Sieve Size 9:
9-chains per day: 0.54 (reported by miner)
10-chains per day: 0.54 * 0.0359468 = 0.0194113
block per day = 0.54*0.04 + 0.0194113 = 0.0410113

And now size 9 wins by a significant margin.

[satriani]

can anybody tell me what happen when we cross difficult 10 at PrimeCoin?
and how much supply will be at PrimeCoin (5-10mln or 20-30mln or 50-100mln -> which one is the most probability?)

[cabin]

Probability of finding a 10th chain link when you have a 9 chain and are sieving on 9-chains: 1 / ln(2^256) = 0.005635

That's not quite right. The primorial that is embedded in the chain origin actually changes the probability a lot. If you filter out the prime p_i, the probability increases by

1 / (1 - 1/p_i)

If you take a product of those up to p_17 which is 59, you get 7.47493. So that's how many times bigger the probability will be if the number is a multiple of 59#. Also, I usually assume that the numbers are about 300 bits in size. So then the probability for the 10th number being prime becomes:

7.47493 * 1/ln(2^300) = 0.0359468

And if I plug that number into your calculations, I get:

Sieve Size 9:
9-chains per day: 0.54 (reported by miner)
10-chains per day: 0.54 * 0.0359468 = 0.0194113
block per day = 0.54*0.04 + 0.0194113 = 0.0410113

And now size 9 wins by a significant margin.

Interesting..that does change things! So all that sieving really just bumps you from 3.5% chance of a prime to ~9.5%.. not as big a help as I thought.

[mhps]

There will be a jump in the difficulty when difficulty goes to 10.0. That's because none of the 9-chains will qualify for blocks and we have to start looking for 10+-chains. I've actually been working on a paper related to this. Right now it looks like 10.0 will be more difficult than 9.996 will be which means we could get stuck between 9.996 and 10.0 for a while.

So now we know before reaching 10.0 ony 1/256 (0.4%) 9-chains found qualify. At the same time there are ~3% number of 9-chains of 10-chains qualify. So it looks like going over the 10-chain boundary would cause an 0.004/(0.03+0.004) = 10% decrease of chance to find a block.

Of course as mikaelh pointed out this assumes a flat distribution of Ferma-test remainder that is used to calculate the fractional part of the difficulty.

You can actually see that happening before in my charts:
http://xpm.muuttuja.org/charts/

If you look closely enough, the network block rate seems to have dropped when we went from 8.996 to 9.0. Of course we were using an older version of the mining algorithm back then which probably behaved slightly different.

From the chart the difficulty reached 8.996 at c.a. 15:10 on July 21, and reached 9 less than 1.5 hours later. I guess 10.0 will be reached before December.

[Sunny King]

The difficulty adjustment works like an oscillator at the stepup/stepdown boundary, so the block spacing target is still maintained. For example it could stabilize at probability(difficulty <=9+255/256) = a, probability(difficulty >= 10) = 1-a. This should allow block spacing target to be maintained at 1 minute. Thus the difficulty jump (up/down) at the boundary has no negative effect on the network.

[satriani]

sunny: so the diff will drop when block/min fall (and power of network doesnt change) ?

[mikaelh]

The difficulty adjustment works like an oscillator at the stepup/stepdown boundary, so the block spacing target is still maintained. For example it could stabilize at probability(difficulty <=9+255/256) = a, probability(difficulty >= 10) = 1-a. This should allow block spacing target to be maintained at 1 minute. Thus the difficulty jump (up/down) at the boundary has no negative effect on the network.

Thanks Sunny. That's what I suspected would happen.

[Trillium]

Great discussion it will be interesting to see how this plays out over the next week or two.

blocks/day = chains/day * (1 - fracDiff + 0.035)

This would be good to have in the FAQ on the OP since a lot of newbies seem to be in denial about how hard it is to mine these days.

I have 192 E3-series xeon vCPU going offline today, maybe it will make the diff 0.001 lower for you guys 

[belltown]

I have 192 E3-series xeon vCPU going offline today, maybe it will make the diff 0.001 lower for you guys 

192!!!! Wow. This does not look like botnet at all

[ivanlabrie]

I have 192 E3-series xeon vCPU going offline today, maybe it will make the diff 0.001 lower for you guys 

192!!!! Wow. This does not look like botnet at all

Not botnet, probably work pc's.