k=2145 status and upcoming work
 

I've now tested k=2145 from n=180K to n=200K as confirmation of prior work. No additional primes were found. I am now stopping that one and getting all of my reserved k's tested up to n=200K that aren't already there.

Current and upcoming work:
k=1019370495 from n=175K to 200K. Currently working on.
k=3428677395 from n=175K to 200K. To be started after I'm done with either the above or my other computer is done with k=289.
Verification of primes on low-weight k's from k=200K to 1M. Currently working on.
k=19437 from n=200K to 250K. Just started on.
k=102765 from n=200K to 250K. Later on.
k=2145 from n=200K to 240K using the sieve file given to me by Curtis. Later on.

I delayed k=19437 and 102765 in order to get all of my k's to the same point in testing so that I can use srsieve to begin sieving all my k's across the same range at once.

I'll probably release 2 or more k's at n=250K. The heavy-weight k's take a lot of time!


Gary

k=19437 tested to n=212K; gap filled
 

On my k=19437, I've now completed testing it up to n=212K. This completely fills the gap below the only previously known prime before my testing at n=211357, which I confirmed. There were no additional primes to report. We're still standing at 73 primes.

I'm temporarily stopping on this one to finish my last k that has not been tested to n=200K, that is k=3428677395. The only other one that I have not reported up to n=200K, k=1019370495, is nearly complete LLRing to that level. I'll have primes to report on it tomorrow.


Gary

Primes for k=1019370495 n=175K-200K; continuing
 

I've now completed tested k=1019370495 from n=175K to 200K. This one continues to roll on...I found 3 more primes for a total of 103 primes. This now makes 9 primes from n=135K to 200K. The primes that I found were:

1019370495*2^185973-1
1019370495*2^188238-1
1019370495*2^192246-1


Gary

k=531131527270075522241760982081252274580435
 

Karsten,

See a complete lists of primes for k=531131527270075522241760982081252274580435 from n=1 to 173K that were posted by Robert at the end of the "a new very prime k" thread. I had asked him to post them all and he did about a month ago. I mention it here because I saw that they didn't get in the latest summary page update and it's COOL :cool: to have so many primes for a k! It's the highest k on the site.

My perception is that he decided to stop testing it at n=173K because it quit performing as well as it was for n>100K. We might need to ask him if he wishes to keep it reserved. I don't want to reserve it for further testing but someone else might want to.


Gary

Primes for k=3428677395 n=175K-200K; continuing
 

I've now tested k=3428677395 from n=175K-200K. There was 1 more prime found for a total of 85 primes so far:

3428677395*2^175112-1


All of my heavy-weight k's are now up to n=200K.


Gary

k=2145 & 19437 tested 200K-225K; no more primes
 

I have now tested k=2145 and k=19437 from my last stop off point of 200K up to 225K. No additional primes were found other than those already posted on the 300<k<3010 site.

For k=2145, n=213621, 214257, and 214994 were confirmed prime.
For k=19437, n=211357 was confirmed prime.

All testing gaps are now eliminated on both k's.

Upcoming LLR testing:
k=2145 to n=225K to 240K to complete Curtis's sieve file that he sent me.
k=19437 from n=225K to 250K
k=102765 from n=200K to 250K
More gap filling on k's with Woodall primes and a couple of misc. ones.
More low-weight k verification.

The above LLR testing will complete all files where I singularly sieved individual k's across small ranges. I am now in the process of using srsieve to sieve all 11 of my k's from n=200K to 400K (from n=250K on the above two). The sieve is up to about P=120G now and there's still around 300,000 candidates! :surprised Once that is done, I will be testing all of my k's at once. This will be a slow effort as all 11 of my k's are heavy-weight and 7-8 of them are very heavy weight, i.e. weight > 5000. In order to speed the LLR process up, I'll be using 3 different cores on 2 very fast machines -and- I'll probably drop 2-3 k's or more by n=250K to 275K. I'm hoping to finish it all in under 6 months.


Gary

Gap filling on k=1103, 1211, & 1455; n=0 to 50K
 

I have tested k=1103, k=1211, and k=1455 from n=0 to 50K to confirm prior primes and both fully and partially fill some gaps. Here are the results:

k=1103:
5 primes for n < 50K previously posted were confirmed. No additional primes found. This partially fills the gap. There is now a remaining gap from n=50K to 162884.

k=1211:
2 primes for n < 50K previously posted were confirmed. No additional primes found. Gap fully filled.

k=1455:
50 primes for n < 50K previously posted were confirmed. 10 additional primes were found as shown below. There is now a remaining gap from n=50K to 288478.

1455*2^11069-1
1455*2^12180-1
1455*2^12599-1
1455*2^12837-1
1455*2^15103-1
1455*2^18554-1
1455*2^20460-1
1455*2^35159-1
1455*2^38686-1
1455*2^43857-1

A prime at n=24866 is already posted and confirmed. This now makes a total of 64 primes for this k.


Gary

k=1000065
 

More primes for n<=100k:

1000065*2^69122-1
1000065*2^76111-1
1000065*2^80702-1

To all contributors:

Please, try to post long list of small primes in-line.

Instead of appending a part of "primes.txt" as it is, please delete the leading k, and replace each <new-line> with <comma, space>. It can be easily done using emacs or another text editor. With many long list of primes, it's hard to follow and read the thread.

Thanks!

k=2145, 19437, & 102765 update; no more primes
 

I have now completed testing on k=2145, 19437, and 102765 as shown below. No more primes were found since the last status report.

k=2145 to n=240K completes the sieve file given to me by Curtis
k=19437 to n=250K
k=102765 to n=220K

I will take k=102765 up to n=250K and that will be all on testing my heavy-weight k's with the exception of k=2145 until my huge sieve of all of them up to n=400K is complete. On k=2145, I'll start on it when Curtis is done sieving it a little further.

With the completion of the above, I just now started two cores working on my huge sieve. It has been working just over a week on a single core and is just past P=200G. I expect that it will need to go to a little over P=1T (just a rough guess at the moment), which should take 2-3 weeks on 2 cores before I can start primality testing again.


Gary

More gap filling for Woodall k's and one other k
 

I've done some more gap filling on k's with Woodall primes and one misc. k. I've tested k=11111, 49363, 71509, and 151023 from n=0 to 160K to fully fill the gap on the 3 Woodall's and partially fill the gap on k=11111. The primes are shown below.

[QUOTE]

11111: 18, 34, 1458, 1798, 2754, 6598, 13926, 147406

49363: 75, 99, 123, 547, 859, 14439, 22075, 98727

71509: 5, 9, 15, 23, 35, 47, 63, 83, 405, 455, 731, 899, 1037, 1379, 2141, 3065, 3087, 3527, 3627, 3839, 3899, 6461, 11927, 12969, 18159, 18443, 30437, 57599, 143019

151023: 7, 10, 14, 19, 36, 56, 74, 80, 112, 122, 127, 376, 430, 644, 734, 814, 835, 850, 854, 1063, 1966, 2106, 3256, 3867, 5040, 6366, 6382, 10166, 13863, 17539, 21276, 23596, 37016, 37899, 41799, 50106, 57392, 77086, 77976, 80906, 90026, 114730, 115606, 122832, 151023


[/QUOTE]

This was sieved with srsieve so there is no issue with incorrect removal of small primes.

Let me know if this format is what you're looking for. It took me a while to set up the 'concatenate' command in Excel correctly to get it to come out right. It should go quickly in the future.


Gary