k=2003663613 and k=65516468355 primes

Oddball · 2010-07-28, 06:51

This is the k which yielded TPS's first twin. I've tested both the -1 and the +1 sides until n=50K, and the -1 list of primes is below.

Code:

2003663613*2^6-1
2003663613*2^14-1
2003663613*2^19-1
2003663613*2^52-1
2003663613*2^59-1
2003663613*2^108-1
2003663613*2^139-1
2003663613*2^158-1
2003663613*2^396-1
2003663613*2^427-1
2003663613*2^436-1
2003663613*2^484-1
2003663613*2^540-1
2003663613*2^642-1
2003663613*2^806-1
2003663613*2^972-1
2003663613*2^1015-1
2003663613*2^1176-1
2003663613*2^1275-1
2003663613*2^1602-1
2003663613*2^1638-1
2003663613*2^1646-1
2003663613*2^2464-1
2003663613*2^2500-1
2003663613*2^2635-1
2003663613*2^3948-1
2003663613*2^5202-1
2003663613*2^8088-1
2003663613*2^8680-1
2003663613*2^12942-1
2003663613*2^12970-1
2003663613*2^16582-1
2003663613*2^17835-1
2003663613*2^22686-1
2003663613*2^23448-1
2003663613*2^23580-1
2003663613*2^37286-1
2003663613*2^40264-1
2003663613*2^42679-1
2003663613*2^57003-1
2003663613*2^61287-1
2003663613*2^64884-1
2003663613*2^66664-1
2003663613*2^77126-1
2003663613*2^94787-1
2003663613*2^96979-1
2003663613*2^109828-1
2003663613*2^152383-1
2003663613*2^187323-1
2003663613*2^193956-1
2003663613*2^195000-1

And here's the list for the +1 side. As you can see, it too has a high weight and lots of primes.

Code:

2003663613*2^21+1
2003663613*2^29+1
2003663613*2^45+1
2003663613*2^64+1
2003663613*2^80+1
2003663613*2^94+1
2003663613*2^150+1
2003663613*2^184+1
2003663613*2^293+1
2003663613*2^428+1
2003663613*2^478+1
2003663613*2^580+1
2003663613*2^704+1
2003663613*2^1501+1
2003663613*2^1518+1
2003663613*2^1532+1
2003663613*2^1628+1
2003663613*2^1925+1
2003663613*2^2422+1
2003663613*2^3845+1
2003663613*2^4294+1
2003663613*2^5488+1
2003663613*2^12381+1
2003663613*2^13662+1
2003663613*2^16940+1
2003663613*2^32741+1
2003663613*2^36909+1
2003663613*2^38613+1
2003663613*2^46868+1
2003663613*2^49589+1
2003663613*2^69317+1
2003663613*2^87910+1
2003663613*2^97740+1
2003663613*2^129397+1
2003663613*2^132632+1
2003663613*2^145134+1
2003663613*2^154988+1
2003663613*2^183092+1
2003663613*2^195000+1

Reservations:
0-50K: Oddball (complete)
50K-195K: Puzzle-Peter (complete)

This is the k that yielded TPS's second twin. The list of primes for the -1 side is below:

Code:

65516468355*2^15-1
65516468355*2^181-1
65516468355*2^213-1
65516468355*2^315-1
65516468355*2^373-1
65516468355*2^675-1
65516468355*2^1275-1
65516468355*2^2023-1
65516468355*2^4770-1
65516468355*2^7738-1
65516468355*2^13122-1
65516468355*2^17641-1
65516468355*2^24373-1
65516468355*2^58711-1
65516468355*2^206050-1
65516468355*2^333333-1

(completed to 333333)

Here's the +1 side:

Code:

65516468355*2^23+1
65516468355*2^59+1
65516468355*2^81+1
65516468355*2^91+1
65516468355*2^94+1
65516468355*2^113+1
65516468355*2^144+1
65516468355*2^155+1
65516468355*2^173+1
65516468355*2^176+1
65516468355*2^188+1
65516468355*2^219+1
65516468355*2^253+1
65516468355*2^275+1
65516468355*2^289+1
65516468355*2^296+1
65516468355*2^365+1
65516468355*2^443+1
65516468355*2^505+1
65516468355*2^523+1
65516468355*2^600+1
65516468355*2^745+1
65516468355*2^759+1
65516468355*2^949+1
65516468355*2^1000+1
65516468355*2^1033+1
65516468355*2^1268+1
65516468355*2^1435+1
65516468355*2^3216+1
65516468355*2^3721+1
65516468355*2^3728+1
65516468355*2^5089+1
65516468355*2^5583+1
65516468355*2^5588+1
65516468355*2^6115+1
65516468355*2^6480+1
65516468355*2^6505+1
65516468355*2^8436+1
65516468355*2^10896+1
65516468355*2^13907+1
65516468355*2^16635+1
65516468355*2^20264+1
65516468355*2^20709+1
65516468355*2^21105+1
65516468355*2^21263+1
65516468355*2^28323+1
65516468355*2^30845+1
65516468355*2^45420+1
65516468355*2^67296+1
65516468355*2^70983+1
65516468355*2^79625+1
65516468355*2^80756+1
65516468355*2^97171+1
65516468355*2^103856+1
65516468355*2^159247+1
65516468355*2^236464+1
65516468355*2^276270+1
65516468355*2^305518+1
65516468355*2^318484+1
65516468355*2^333333+1

(completed to 333333)

Reservations:
0-333333: Merfighters (in progress)

kar_bon · 2010-07-28, 07:01

Quote:

Originally Posted by Oddball

This is the k which yielded TPS's first twin. I've tested both the -1 and the +1 sides until n=50K, and the -1 list of primes is below.

Code:

2003663613*2^52-1
...
2003663613*2^195000-1

And here's the list for the +1 side. As you can see, it too has a high weight and lots of primes.

Code:

2003663613*2^45+1
...
2003663613*2^195000+1

I don't intend to test either side further than the current limit of n=50K, but if anyone wants to carry on, it'll be nice if you post here to keep us informed about your progress.

And you missed again small primes here!

On the -1 side the series is prim for n=6, 14 and 19 and on the +1 side prime for n=21 and 29!

So be sure you know what you're doing and please use srsieve NOT NewPGen for small primes!

Oddball · 2010-07-28, 07:10

Quote:

Originally Posted by kar_bon

And you missed again small primes here!

On the -1 side the series is prim for n=6, 14 and 19 and on the +1 side prime for n=21 and 29!

OK, I'll add those primes to the list.

Quote:

So be sure you know what you're doing and please use srsieve NOT NewPGen for small primes!

I didn't use NewPGen for n<5000, I used Proth.exe

NewPGen was only used for sieving 5000<=n<=50000.

Merfighters · 2010-08-18, 05:03

Quote:

Originally Posted by Oddball

I didn't use NewPGen for n<5000, I used Proth.exe

NewPGen was only used for sieving 5000<=n<=50000.

Proth.exe also misses small primes!

Anyway, can I try k=65516468355? (Twin record k)

Edit: Can you edit the name of this thread?

Oddball · 2010-08-18, 05:11

Quote:

Originally Posted by Merfighters

Anyway, can I try k=65516468355? (Twin record k)

Sure! When you're done, just tell us the primes you found and the search limits, and I'll add them to the first post.

Oddball · 2010-08-18, 18:05

Quote:

Originally Posted by Merfighters

Edit: Can you edit the name of this thread?

Give us some k=65516468355 primes for the plus and minus sides, and it'll be done.

Puzzle-Peter · 2010-08-19, 13:18

OK, I'll fill the gaps 50001 - 195000 for k=2003663613.

One question: when I run WinPFGW with -t switch and I get entries in a file called pfgw-prime.log, are they primes or just PRPs to be proven later?

Thanks, Peter

10metreh · 2010-08-19, 13:26

Quote:

Originally Posted by Puzzle-Peter

One question: when I run WinPFGW with -t switch and I get entries in a file called pfgw-prime.log, are they primes or just PRPs to be proven later?

Firstly, pfgw-prime.log contains proven primes.
Secondly, only use the -t switch for the +1 side. Use the -tp switch for the -1 side.
Thirdly, it's faster to run PRP tests (i.e. no -t or -tp) instead of deterministic tests, then prove the PRPs with -t or -tp as necessary.

Puzzle-Peter · 2010-08-19, 17:49

Quote:

Originally Posted by 10metreh

Firstly, pfgw-prime.log contains proven primes.
Secondly, only use the -t switch for the +1 side. Use the -tp switch for the -1 side.
Thirdly, it's faster to run PRP tests (i.e. no -t or -tp) instead of deterministic tests, then prove the PRPs with -t or -tp as necessary.

Thanks! Even with -t it seems to be just as fast. Looks like doing a PRP test first anyway and switching to a 'real' primality test when PRP is positive?

mdettweiler · 2010-08-19, 19:40

Quote:

Originally Posted by Puzzle-Peter

Thanks! Even with -t it seems to be just as fast. Looks like doing a PRP test first anyway and switching to a 'real' primality test when PRP is positive?

It may seem just as fast early on when you're doing tiny tests, but the difference piles up rather quickly--by the time you get to n=195K it will be quite significant.

In response to your second question, I'm not sure what you mean; if you're asking whether it switches to a "real" primality test automatically, the answer is no. What you do is first run PFGW to do PRP tests, like this:
pfgw -l input.txt
(or however you're inputting your candidates--if you're using -fx to factor the candidates one at a time before testing, you'll want to include that as well)
Then, when the range is done, results will be output to pfgw.out, and your PRPs will be output to pfgw.log. Now prove them with:
pfgw -t pfgw.log (for the +1 side)
pfgw -tp pfgw.log (for the -1 side)
The proven primes will be output to pfgw-prime.log.

Actually, since you're doing a straight-up prime search (as opposed to something fancier like a conjecture search), I would recommend using LLR instead of PFGW for testing. Of course, you'll need to sieve the range first instead of having the numbers factored one at a time prior to PRP testing; but it shouldn't take long to sieve to a reasonably optimal depth for numbers this small. The nice thing about using LLR is that it does a "real" primality test right from the get-go, but since it's doing an LLR or Proth test instead of an N-1/N+1, there's no speed penalty to using the full primality test.

(Note that some of what I've said above is incorrect for bases other than 2, but your search here is strictly base 2 so I didn't bother expounding in that direction.)

Puzzle-Peter · 2010-08-19, 20:09

That's exactly what I was wondering about, thank you!

This is unknown territory for me. I did and do a lot of manual sieving and LLRing for Prime Grid, but I never had to create the candidate files. First I thought about using NewPGen for sieving, but this is a fixed-k search. Using the "increase n by 1" option would have given me 145,000 files with one or zero candidates each, right? That's why I preferred PFGW. After reading the documentation I realized the input file was only two lines and created within a few seconds ;)

Right, so I switched to PRPing and will do the conclusive primality tests only for the PRPs.

Something related: I tried using LLR on candidates of the form k*b^n-1 with b =/= 2 and the output was giving me "not prime" or "PRP". Can I use PFGW for the final primality test on these PRPs?

Sorry for stretching your patience...

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2010-08-19, 13:18	#7
Puzzle-Peter Jun 2009 683 Posts	OK, I'll fill the gaps 50001 - 195000 for k=2003663613. One question: when I run WinPFGW with -t switch and I get entries in a file called pfgw-prime.log, are they primes or just PRPs to be proven later? Thanks, Peter

2010-08-19, 20:09	#11
Puzzle-Peter Jun 2009 683 Posts	That's exactly what I was wondering about, thank you! This is unknown territory for me. I did and do a lot of manual sieving and LLRing for Prime Grid, but I never had to create the candidate files. First I thought about using NewPGen for sieving, but this is a fixed-k search. Using the "increase n by 1" option would have given me 145,000 files with one or zero candidates each, right? That's why I preferred PFGW. After reading the documentation I realized the input file was only two lines and created within a few seconds ;) Right, so I switched to PRPing and will do the conclusive primality tests only for the PRPs. Something related: I tried using LLR on candidates of the form k*b^n-1 with b =/= 2 and the output was giving me "not prime" or "PRP". Can I use PFGW for the final primality test on these PRPs? Sorry for stretching your patience...