R6

masser · 2017-06-13, 03:42

If I were to begin sieving a new range for R6, what limits should I use for the sieve?

VBCurtis · 2017-06-13, 04:53

I'd pick a range with 1.5 expected primes, or more. We want it to be the last sieve done for this base!

I suppose a less sieve-happy person might pick a range with just 1 expected prime; an optimist would expect to find it. (hah, geddit?)

On R27, I'm doing 2-20M.

gd_barnes · 2017-06-13, 10:17

In my opinion sieving something that would take > ~3 years to have its primality testing completed is a potential waste of resources due to future increases in computing capacity/speed and improvements in software -and- of course the possibility of finding a prime early in testing.

For R6 I would suggest n=5-10M or maybe n=5-15M since it is very light weight.

mdettweiler · 2017-06-14, 08:26

BTW: if some sieving gets done for R6 in the relatively near term, I would be happy to throw everything I've got at the LLR effort if others would be willing to share the range in a PRPnet server (I'm thinking port 1300, which we've generally kept focused on bases <=32 with few k's remaining).

Unfortunately I don't have time these days to help out with sieving (too much manual effort, unless someone feels like writing a SieveNet system one of these days), but I am very interested in seeing this base get knocked out. It's been a long time since we proved any bases in the project's original scope (bases <=32), yet we have so many temptingly "easy" (or so they seem) targets with 1 or 2 k's remaining...

(Disclaimer: since the bulk of my crunching resources are work machines, I can't guarantee that I won't lose access to them for a period of time for some reason or other, as happened for most of last year due to an unfortunate SSH key snafu that made bulk management of the machines difficult...but I have them back now and the key issue is fixed, so I am optimistic for the future.

)

VBCurtis · 2017-06-15, 19:06

Wow, Gary wasn't kidding about low-weight! I ran n=5-30M to 1G, with 212k candidates remaining. Extrapolating from the candidates removed going from 1e8 to 1e9, a sieve to 1e13 should leave less than 150k candidates.

I admit that I can't imagine testing candidates at n=20M, so 30M seems a bit of folly for big-N.

I'm willing to donate 2-3 core-months this summer to help sieve, perhaps more if Max isn't the only interested LLR party (and Masser wants to share).
Edit: Some really rough estimating suggests a sieve depth of something like 1e16 for 5-30M. {gulp} That's something like 5000 core-days? I don't feel so generous anymore, offering 100 core-days...

masser · 2017-06-16, 04:41

I haven't found a sieve range yet with the expected number of primes greater than 1.0. I will continue experimenting with ranges.

The search for the prime that will finish off this conjecture is quixotic. However, there might be some side benefits to pursuing the sieving and testing of these ranges.

I will follow-up in a couple days (when I'm less busy) with some ideas I've been kicking around.

masser · 2017-06-21, 06:16

For the numbers below, I used srsieve on the R6 sequence up to Ps = 1.0e9 over the range 5M < n < 3200M. I then studied subsets of the resulting newpgen file.

Expected number of primes for various exponent ranges:
5M < n < 10M: E=0.1186
5M < n < 20M: E=0.2374
5M < n < 25M: E=0.2756
5M < n < 50M: E=0.3943
5M < n < 100M: E=0.5129
5M < n < 130M: E=0.5578 (100M digit candidates!)
5M < n < 200M: E=0.6316
5M < n < 400M: E=0.7502
5M < n < 800M: E=0.8689
5M < n < 1600M: E=0.9875
5M < n < 3200M: E=1.106 (Expectation > 1!)

Number of candidates for various exponent ranges:
5M < n < 10M: N=42476
5M < n < 20M: N=127615
5M < n < 25M: N=170169
5M < n < 50M: N=382870

I am thinking about further sieving the 20M range. I will look at testing times before I proceed much further. Any suggestions welcome.

gd_barnes · 2017-06-21, 07:55

That is painful.

Another interesting 1-k base that is not being worked on is Sierp base 9. It is nearly double the weight and only searched to n=2M and so might be worth looking at instead at this point.

2017-06-13, 03:42	#1
masser Jul 2003 Behind BB 11101011101₂ Posts	R6 If I were to begin sieving a new range for R6, what limits should I use for the sieve?

2017-06-15, 19:06	#5
VBCurtis "Curtis" Feb 2005 Riverside, CA 5,279 Posts	Wow, Gary wasn't kidding about low-weight! I ran n=5-30M to 1G, with 212k candidates remaining. Extrapolating from the candidates removed going from 1e8 to 1e9, a sieve to 1e13 should leave less than 150k candidates. I admit that I can't imagine testing candidates at n=20M, so 30M seems a bit of folly for big-N. I'm willing to donate 2-3 core-months this summer to help sieve, perhaps more if Max isn't the only interested LLR party (and Masser wants to share). Edit: Some really rough estimating suggests a sieve depth of something like 1e16 for 5-30M. {gulp} That's something like 5000 core-days? I don't feel so generous anymore, offering 100 core-days... Last fiddled with by VBCurtis on 2017-06-15 at 19:16

2017-06-16, 04:41	#6
masser Jul 2003 Behind BB 5·13·29 Posts	Extremely low probabilities I haven't found a sieve range yet with the expected number of primes greater than 1.0. I will continue experimenting with ranges. The search for the prime that will finish off this conjecture is quixotic. However, there might be some side benefits to pursuing the sieving and testing of these ranges. I will follow-up in a couple days (when I'm less busy) with some ideas I've been kicking around.

2017-06-21, 06:16	#7
masser Jul 2003 Behind BB 5×13×29 Posts	Some Numbers For the numbers below, I used srsieve on the R6 sequence up to Ps = 1.0e9 over the range 5M < n < 3200M. I then studied subsets of the resulting newpgen file. Expected number of primes for various exponent ranges: 5M < n < 10M: E=0.1186 5M < n < 20M: E=0.2374 5M < n < 25M: E=0.2756 5M < n < 50M: E=0.3943 5M < n < 100M: E=0.5129 5M < n < 130M: E=0.5578 (100M digit candidates!) 5M < n < 200M: E=0.6316 5M < n < 400M: E=0.7502 5M < n < 800M: E=0.8689 5M < n < 1600M: E=0.9875 5M < n < 3200M: E=1.106 (Expectation > 1!) Number of candidates for various exponent ranges: 5M < n < 10M: N=42476 5M < n < 20M: N=127615 5M < n < 25M: N=170169 5M < n < 50M: N=382870 I am thinking about further sieving the 20M range. I will look at testing times before I proceed much further. Any suggestions welcome.

2017-06-21, 07:55	#8
gd_barnes May 2007 Kansas; USA 24736₈ Posts	That is painful. Another interesting 1-k base that is not being worked on is Sierp base 9. It is nearly double the weight and only searched to n=2M and so might be worth looking at instead at this point. Last fiddled with by gd_barnes on 2017-06-21 at 07:56

2017-06-13, 04:53	#2
VBCurtis "Curtis" Feb 2005 Riverside, CA 5,279 Posts	I'd pick a range with 1.5 expected primes, or more. We want it to be the last sieve done for this base! I suppose a less sieve-happy person might pick a range with just 1 expected prime; an optimist would expect to find it. (hah, geddit?) On R27, I'm doing 2-20M.

2017-06-13, 10:17	#3
gd_barnes May 2007 Kansas; USA 2·23·233 Posts	In my opinion sieving something that would take > ~3 years to have its primality testing completed is a potential waste of resources due to future increases in computing capacity/speed and improvements in software -and- of course the possibility of finding a prime early in testing. For R6 I would suggest n=5-10M or maybe n=5-15M since it is very light weight.

2017-06-14, 08:26	#4
mdettweiler A Sunny Moo Aug 2007 USA (GMT-5) 3·2,083 Posts	BTW: if some sieving gets done for R6 in the relatively near term, I would be happy to throw everything I've got at the LLR effort if others would be willing to share the range in a PRPnet server (I'm thinking port 1300, which we've generally kept focused on bases <=32 with few k's remaining). Unfortunately I don't have time these days to help out with sieving (too much manual effort, unless someone feels like writing a SieveNet system one of these days), but I am very interested in seeing this base get knocked out. It's been a long time since we proved any bases in the project's original scope (bases <=32), yet we have so many temptingly "easy" (or so they seem) targets with 1 or 2 k's remaining... (Disclaimer: since the bulk of my crunching resources are work machines, I can't guarantee that I won't lose access to them for a period of time for some reason or other, as happened for most of last year due to an unfortunate SSH key snafu that made bulk management of the machines difficult...but I have them back now and the key issue is fixed, so I am optimistic for the future. )