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Message boards : Proth Prime Search : The SoB multipliers k=4847 and k=5359 in PPSE

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Message 117552 - Posted: 27 Apr 2018 | 14:24:40 UTC

What is the status of the two multipliers k=4847 and k=5359 within the Proth Prime Search Extended (LLR) project?

It looks like the old Seventeen or Bust project searched these two, many years ago, until they eventually left them after they had eliminated them (proved them non-Sierpiński by finding primes 4847*2^3321063 + 1 and 5359*2^5054502 + 1).

When I look at subproject status, PPSE (LLR) stats, I do see rows for 4847 and 5359.

/JeppeSN

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Message 117553 - Posted: 27 Apr 2018 | 15:20:05 UTC
Last modified: 27 Apr 2018 | 15:23:11 UTC

I don't think they have any special status in PPSE. There are tasks for them, just like for all other k's. You can use available tools to search if they had more primes found (they didn't)

They have less tasks than neighboring k's up to the currently loaded n, but that's expected.

edit: ah, I didn't notice that the first primes for them were way above what PPSE is testing right now. Well, oops

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Message 117554 - Posted: 27 Apr 2018 | 15:20:43 UTC - in response to Message 117552.

What is the status of the two multipliers k=4847 and k=5359 within the Proth Prime Search Extended (LLR) project?

It looks like the old Seventeen or Bust project searched these two, many years ago, until they eventually left them after they had eliminated them (proved them non-Sierpiński by finding primes 4847*2^3321063 + 1 and 5359*2^5054502 + 1).

When I look at subproject status, PPSE (LLR) stats, I do see rows for 4847 and 5359.

/JeppeSN


Ah, so you're asking whether we're testing those two k's, and the reasoning behind that.

Assuming that nobody here had ever thought of this before, which would you advise doing:

A) Not test those two k's. That's 2 k's out of 4400 k's in PPSE, or about half of one tenth of one percent of all the k's. Both k's appear to be very low weight, so in terms of total processing time, we'd probably save less than that.

B) Test the k's anyway, even though we probably won't find any primes there until we've past beyond where SoB primes were found. That won't happen for many, many years. Unless, of course, they missed a prime. Current SoB double check results seem to indicate that about 1 in 30 SoB tests were incorrect, and they did find two primes while double checking older work.

Although that might seem like a rhetorical question, it's not. It's a serious question.

(For the record, I have never considered this before, but I don't know if anyone else has.)
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Message 117562 - Posted: 27 Apr 2018 | 19:48:35 UTC
Last modified: 27 Apr 2018 | 19:49:09 UTC

I'd certainly never thought about this before. We're DCing other SOB project work now, why not run these two k's? As Mike said, they're pretty lightweight. While you're the only one who ever thought about this, if we remove those other two k's we'll be answering questions about why they're missing on a regular basis forever.

And in case you were wondering, the server pulls down the Top 5000 list once or twice an hour. All the work generators will skip any candidate that shows up in that list. Getting a bit off-topic, another job checks that Top 5000 list and will alert us to any prime matching an open conjecture. I forget about this most times when I report a conjecture prime and then wake up the next day to an inbox full of emails about it.

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Message 117563 - Posted: 27 Apr 2018 | 20:05:14 UTC - in response to Message 117554.

Ah, so you're asking whether we're testing those two k's, and the reasoning behind that.

Assuming that nobody here had ever thought of this before, which would you advise doing:

A) Not test those two k's. That's 2 k's out of 4400 k's in PPSE, or about half of one tenth of one percent of all the k's. Both k's appear to be very low weight, so in terms of total processing time, we'd probably save less than that.

B) Test the k's anyway, even though we probably won't find any primes there until we've past beyond where SoB primes were found. That won't happen for many, many years. Unless, of course, they missed a prime. Current SoB double check results seem to indicate that about 1 in 30 SoB tests were incorrect, and they did find two primes while double checking older work.

Although that might seem like a rhetorical question, it's not. It's a serious question.

(For the record, I have never considered this before, but I don't know if anyone else has.)


In my opinion it depends on the amount of information we have about what SoB did back then.

For example, if we know they tested and double checked this region, there is no point in doing work there again.

If we know they tested only once, and if we have access to their residues, and if their residues can be compared to ours, of course it would make sense to import their results and only do the double checking.

If we do not really know what SoB did for those two k, for n values near 1.5 million, it is hard to say what is rational. We might as well run them just to be sure.

As you say, the two k are probably "low weight", or "thin". Since they were among the seventeen last k related to the Sierpiński conjecture, maybe it is natural that they are low-weight? Right now I see "Tasks in progress" 0 out of 14435, and "Tasks waiting" 62 out of 1242605 (that is 0.005%).

/JeppeSN

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Message 117564 - Posted: 27 Apr 2018 | 20:08:28 UTC - in response to Message 117563.

If we do not really know what SoB did for those two k, for n values near 1.5 million, it is hard to say what is rational. We might as well run them just to be sure.


We have no information and no residues.
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Message 117567 - Posted: 27 Apr 2018 | 20:28:45 UTC

A related question: Did we start PPSE at n=1, or at some higher exponent?

I ask because there are still some k values in the stats_ppse_llr page with no primes found. Since these k are not among the ones ever considered for Seventeen or Bust, someone must have found at least one (possibly very tiny) prime in each of those k.

The same question can be asked for (non-extended) PPS (stats_pps_llr, stats_mega_llr). Now I took k=167 as an example, and I find some tiny primes (k=167: n in {7, 103, 151, 247, 10183, ...}).

/JeppeSN

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Message 117569 - Posted: 27 Apr 2018 | 20:55:19 UTC - in response to Message 117564.

If we do not really know what SoB did for those two k, for n values near 1.5 million, it is hard to say what is rational. We might as well run them just to be sure.

We have no information and no residues.

I have 4847 completely verified (single pass) and 5359 up to 3M (yes, I also missed this PPSE thing). With residues. If you'll load them to SoB DC pool, they'll be crunched in few days. I also have all remaining SoB (10223, 19249, 27653, 28433, 33661) up to 3M if you ever wish to DC them and confirm that there are no missing primes. For remaining 10, 5 are currently DC'ed by PG, 5 are too small (around 1M) and could be easily validated by anybody.

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Message 117573 - Posted: 27 Apr 2018 | 21:52:32 UTC - in response to Message 117567.

A related question: Did we start PPSE at n=1, or at some higher exponent?

I ask because there are still some k values in the stats_ppse_llr page with no primes found. Since these k are not among the ones ever considered for Seventeen or Bust, someone must have found at least one (possibly very tiny) prime in each of those k.

The same question can be asked for (non-extended) PPS (stats_pps_llr, stats_mega_llr). Now I took k=167 as an example, and I find some tiny primes (k=167: n in {7, 103, 151, 247, 10183, ...}).

/JeppeSN


PPSE has had several incarnations before the current BOINC project.

It used to run on several PRPNet ports. And before that, people were running it manually.

You don't have to look far in that table for a k without a prime: the very first k, 1201, has no prime. That table, however, only looks at the BOINC results.

If, instead, you look at the primes page for 1201, you'll see there's 6 PPSE primes with a k of 1201.

If you look at the bottom of the PPSE primes list it appears that the earliest PPSE searching we did started at n=20K.

Likewise, looking at the last page of PPS primes it appears that we started searching PPS at n=100K.

It should be noted that for PPS, even though we started testing at n=100K, that doesn't mean that PrimeGrid tested everything above 100K. The PPS search started on the Mersenne forums and some ranges were done on PrimeGrid and some by others over at the Mersenne forums.
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Message boards : Proth Prime Search : The SoB multipliers k=4847 and k=5359 in PPSE

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