Reserving R112 to n=500k (400-500k) for BOINC
Reserving S228 to n=500k (403-500k) for BOINC

S228 tested to n=500k (403-500k)

nothing found, 2 remain

Results emailed - Base released

R112 tested to n=500k (400-500k)

nothing found, 2 remain

Results emailed - Base released

Reserving R162 to n=500k (300-500k) for BOINC

Progress update
 

K4 S174 at 1M -res file attached.
Base released

S102 300-330k
 

complete to 350k, but that batch is going up to 360k so no results yet.

Carpetpool has completed S157 to n=450K; one prime was found for n=300K-450K previously reported; 2 k’s remain; he is releasing the base.

I will reserve S157 to n=500K.

S102 330-360k
 

I apologize for the ambiguity of the naming of these residue files...

R111 passed n=408K, continuing to 500K as planned. No further primes found other than the 1 reported.

S157 is complete to n=500K; no primes were found for n=450K-500K; 2 k's still remain; base released.

R162 tested to n=500k (300-500k)

nothing found, 2 remain

Results emailed - Base released

S102 380K-400K Residues
 

360K-380K should be available in a few hours.

S102 360K-380K Residues
 

Base released.

Reserving S217 to n=600k (500-600k) for BOINC

K4 S155 at 1.55 M

Reserving S214 to n=500k (300-500k) for BOINC
Reserving R217 to n=500k (300-500k) for BOINC

Reserving R161 up to n=150K.

S217 tested to n=600k (500-600k)

nothing found, 1 remain

Results emailed - Base released

S214 tested to n=500k (300-500k)

nothing found, 2 remain

Results emailed - Base released

R217 tested to n=500k (300-500k)

nothing found, 2 remain

Results emailed - Base released

K4 S155 at 1.575 M

Reserving R103 to n=800k (600-800k) for BOINC

Reserving R157 to n=500k (400-500k) for BOINC

Reserving R241 to n=500k (400-500k) for BOINC

R103 tested to n=800k (600-800k)

nothing found, 1 remain

Results emailed - Base released

I'm currently for testing purpose, investigating how long a n=2.5K-10K range takes to test.

So for now, since a fifth of the work has been done, I would like to reserve S180 to n=10K using the available sievefile.

There is almost 5,000 primes found already.

Testing is being done using PFGW64 Version 4.0.3 (GWNum 29.8)

No residues are collected. Primes will be verified and send to Gary on completion. This conjecture seems very prime.

R157 tested to n=500k (400-500k)

nothing found, 4 remain

Results emailed - Base released

[QUOTE=KEP;615639]So for now, since a fifth of the work has been done, I would like to reserve S180 to n=10K using the available sievefile.[/QUOTE]

S180 is complete to n=10K, a total of 11141 primes found.

Reserving R103 to n=1M (800k-1M) for BOINC
Reserving S118 to n=1M (740k-1M) for BOINC

R241 tested to n=500k (400-500k)

1 prime found, 16 remain

Results emailed - Base released

Progress update
 

K4 S155 at 1.6 M

S118 tested to n=1M (740k-1M)

nothing found, 1 remain

Results emailed - Base released

Reserving S218 to n=1M (600k-1M) for BOINC

R103 tested to n=1M (800k-1M)

nothing found, 1 remain

Results emailed - Base released

Reserving S157 to n=1M (500k-1M) for BOINC

R111 is now at n=459K, the server crashed 2 months ago but I havent lost any progress just the time. No further primes where found, will continue to up n=500K.

R161 reached n=155K, no primes found in this range. Releasing this base.

Reserving R161 to n=300k (155-300k) for BOINC

Progress update
 

K4 S155 at 1.63 M

S218 tested to n=1M (600k-1M)

nothing found, 1 remain

Results emailed - Base released

R161 tested to n=300k (155-300k)

3 primes found, 14 remain

Results emailed - Base released

Reserving S117.

[QUOTE=MisterBitcoin;620135]R111 is now at n=459K, the server crashed 2 months ago but I havent lost any progress just the time. No further primes where found, will continue to up n=500K.

R161 reached n=155K, no primes found in this range. Releasing this base.[/QUOTE]

R111
I had an other crash and lost about a week, right now I am on n=479K. About 2 months or so, if nothing fails again.
No prime found.

Reserving S141 as new base using the new-base script up to 2.5k

S157 tested to n=1M (500k-1M)

nothing found, 2 remain

Results emailed - Base released

S141 tested to n=2.5k

283945 remain

Results emailed - Base released

splitted in 2 pieces:
0-60M = 127754 remain
60-130M = 156191 remain

S117 completed to n=1e6. No primes found. Base released. Residues attached.

Reserving R123.

If a sieve file is available, that means the range has been sieved to the appropriate depth?

Not necessarily. You should check whether removal rate and PRP'ing are comparable in time. If it is drastically different, it needs more sieving.

Can I find the removal rate somewhere or should I test-sieve?

I was wondering about the depth, because R123 has about 20000/400000 = 5% of candidates left. For a low-weight Proth I went to about 1.5%. I have no idea though how sieving and PRP testing scales with the base.

[QUOTE=bur;625839]Reserving R123.

If a sieve file is available, that means the range has been sieved to the appropriate depth?[/QUOTE]

Unlike a few years ago, all sieve files on our reservations pages have now been fully sieved unless it shows "additional sieving needed" or something like that. You can see the sieve depth in the header line of the sieve file. At P=1e15, R123 is definitely fully sieved. You will most definitely be able to run a primality test faster with PFGW or LLR than you could find a factor by sieving. Like most of the files on our reservations pages, it was sieved by the big BOINC effort at Yoyo.

Anything sieved to P>=5e14 was done by Yoyo.

With a weight of 2758, R123 is our heaviest weight 1k Riesel base remaining, which is why so many candidates are remaining even after a deep sieve. On the entire project, it is our 2nd heaviest weight 1k base. Only S781 with a weight of 2853 is greater.

See a list of our 1k bases and their weights here:
[url]https://mersenneforum.org/showpost.php?p=201642&postcount=1[/url]

Are you comfortable taking on a base with this many tests?

R123 is on our goals list for 2023 as shown in our recommended bases thread here:
[url]https://mersenneforum.org/showpost.php?p=209366&postcount=1[/url]

I just thought I'd make you aware of the goal to have it at n=1M by year-end 2023.

Thanks, yes, I saw that goal.

I should be able to do 150 tests per day on average over that range, so the 20 000 remaining candidates would take about 6 months.

I can't promise that I'll keep at it for that long, but I'll either go at it full force or unreserve.

If you feel like I should rather take a different base, that's not problem of course.

[QUOTE=bur;625879]Thanks, yes, I saw that goal.

I should be able to do 150 tests per day on average over that range, so the 20 000 remaining candidates would take about 6 months.

I can't promise that I'll keep at it for that long, but I'll either go at it full force or unreserve.

If you feel like I should rather take a different base, that's not problem of course.[/QUOTE]

That sounds great! It would be an excellent accomplishment for such large tests on a very high-weight base. Fire away!

Alright, would be nice if a prime turned up. For a random odd number of that size about 1 in 1.9 million would be expected to be prime.

Number of the form 24*123^n-1 additionally aren't divisible by 3. So can we thus say it's closer to 1.9E6 * 2/3 = 1.3E6?

Doesn't sound too bad of a chance for 400 000 candidates.

[QUOTE=bur;625953]Alright, would be nice if a prime turned up. For a random odd number of that size about 1 in 1.9 million would be expected to be prime.

Number of the form 24*123^n-1 additionally aren't divisible by 3. So can we thus say it's closer to 1.9E6 * 2/3 = 1.3E6?

Doesn't sound too bad of a chance for 400 000 candidates.[/QUOTE]

How many cores are you running this on? Are you using something this PRPNet to manage the work so that if a prime is found then you can stop testing across all cores?

I honestly never got to set PRPnet up. I've been running a Proth number with fixed k for almost 3 years now and what I do is have one folder per sllr2 instance each running in a separate tmux window. I manually load a 10 000 wide n-range every 7-8 days for each of them. Tmux seems perfect for SSH access.

It's surely more work than using PRPnet, but tools like sed make it fast and reliable and I like the manual control I have over it. If something is wrong, I soon notice. Also it divides the long work into small milestones. With a range done every week it is nice from a psychological point of view.

So far I have the same system in place for R123.

[QUOTE]How many cores are you running this on?[/QUOTE]Currently 6, but will switch to 12 soon. FFT is 337k, which makes 12 tests slightly too large for the 32 GB L3 cache. I'll see what the Prime95 throughput benchmark will yield.

If you are running on multiple machines, I think that you will like having PRPNet as you won't need to interact with all of the clients on a regular basis. PRPNet stats can be accessed from a browser so you can see current status at any time from any computer that can access the server. I cannot make you use it. I'm just recommending it because I think it will make participating in CRUS much easier, especially if you work on bases with multiple remaining k. It is the best way to not waste cycles.

[QUOTE=bur;625953]Alright, would be nice if a prime turned up. For a random odd number of that size about 1 in 1.9 million would be expected to be prime.

Number of the form 24*123^n-1 additionally aren't divisible by 3. So can we thus say it's closer to 1.9E6 * 2/3 = 1.3E6?

Doesn't sound too bad of a chance for 400 000 candidates.[/QUOTE]

The expected number of primes for the 20,395 tests in that file for a sieve depth of 1e15 is 0.332. That gives you about a 28.3% chance of finding a prime for n=600K-1M.

It is very challenging now to prove a base here. If you are able to complete that range, that's a very good chance. Having many tests makes it tough to complete but gives a much better chance than most bases for finding a prime.

[QUOTE=rogue;625965]If you are running on multiple machines, I think that you will like having PRPNet[/QUOTE]You're absolutely right in general. It's just one machine though and just one k. I know that PRPnet is still more efficient, but I enjoy the 100% control and regular little milestones.

[QUOTE=gd_barnes;625978]The expected number of primes for the 20,395 tests in that file for a sieve depth of 1e15 is 0.332. That gives you about a 28.3% chance of finding a prime for n=600K-1M.[/QUOTE]Ah, that agrees well with 0.4E6/1.3E6 I estimated. How was the 0.332 obtained? Same way but multiplying with (p-1)/p for all p < 1e15?

[QUOTE]It is very challenging now to prove a base here. If you are able to complete that range, that's a very good chance. Having many tests makes it tough to complete but gives a much better chance than most bases for finding a prime.[/QUOTE]Let's see, even if they are all composite there's at least the advancement of n to 1M.

[QUOTE=bur;625981]
Ah, that agrees well with 0.4E6/1.3E6 I estimated. How was the 0.332 obtained? Same way but multiplying with (p-1)/p for all p < 1e15?
Let's see, even if they are all composite there's at least the advancement of n to 1M.[/QUOTE]

I have an "odds of prime" spreadsheet set up with formulas obtained from a mathematician on this forum named AXN about 15 years ago. I don't know if he's still around but he had all kinds of good insights.

The formulas allow me to plug in a base, n-value, sieve depth, and # of tests and it will spit out the expected number of primes and chance of finding at least one. It was set up for a fixed n-value so generally for a file with a wide n-range, I usually use something a little below the 50% point of the n-range for the n-value.

That was up through 2021. Last year I created a spreadsheet using the similar formulas that allows me to plug in an entire sieve file and it gives a very exact estimated number of primes for each test (like .0000015). It then adds them all up to give the expected prime count for the whole file. It's not very slick because I have to copy the formulas down as far as the file goes. It works well enough for my needs because it should be highly accurate for this and that's all that I'm looking for.

I was somewhat amazed that your quick calculation came in so close to what I came up with.

AXN is still around, I occasionally see posts by him. What I did was simply using the prime number theorem and then saying the number is neither divisible by 2 nor by 3, which should decrease the expected number of candidate to try before finding a prime by 1/2 * 2/3. I'm not 100% sure this is correct, which is why I was glad your number agreed with mine.

When sieving up to q, then it would be the product [TEX]\Pi_{2}^q(1-1/p)[/TEX] of all primes up to q. The value of that product can be quickly estimated by some function involving the Euler-Mascheroni constant, but I always forget its name. Maybe that's what is done in that Excel sheet.

Maybe one of the actual mathematicians can confirm whether or not what I wrote makes any sense...

[QUOTE=bur;626138]The value of that product can be quickly estimated by some function involving the Euler-Mascheroni constant, but I always forget its name[/QUOTE]
[url]https://en.wikipedia.org/wiki/Mertens%27_theorems#Theorems[/url]

Ah thanks, that's it. I kept thinking about Chebyshev.

I know it's getting off-topic, but is it correct to use that function to estimate the probability to pick a prime from numbers asserted to not be divisible by primes < p?

Some months ago I was looking for primes around highly composite numbers and the empirical results seemed to agree well with what I estimated by using that method.

Quick status update for R123:

3600/20396 done (18%)


Some trivia:

For n > 695K the FFT size increased from 384K to 400K and a test takes about 6950 s. At n > 805000 the FFT size reaches 640K which will be too large for single-threading. Due to the architecture of the Ryzen 9 chip that means switching to 4x3 threads for the rest of tests.

Reserving R247 to n=25K.

R247 is complete to n=25K; 653 primes were found for n=10K-25K; 1913 k's remain; base released.

Reserving S171 to n=500k (300-500k) for SRBase

Progress update
 

K4 S155 at 1.7 M

R123 between 816K and 855K.

Bitwise I'm at slightly more than 50% now after 3 months, so I assume it will be 4-5 months left. I'll post status updates more frequently. Then you can decide if expected completion is getting too close to the end of the year, and not risk missing the 2023 goal for it.

I underestimated how much the increasing FFT size impacts iteration times.