3611911875*2^n-1
 

Inspired by gap busting activities by Gary I closed the gap of k=3611911875 between 101 and 134k and, what a surprise, found 7 new primes :shock: for following n's:

108192, 112822, 120412, 132051, 132188, 133748, 133992

Four of them in the narrow 132-134k range! A new Sophie Germain was very close :w00t: k=3611911875 now has 119 primes in the n=1-400,000 range ([I]no gaps[/I]).

BTW, this k was the first one I sieved and tested by myself. I began at the end of 2003 and started tests at n=134k. Very soon I found the first prime at n=134124 which at the time was just a few hundred bits shy of Top-5000. n=157455 and 171662 were first reprotable primes followed by n=175306 found during the New Year's night of the New 2004! :cool:

[quote=Kosmaj;109598]Inspired by gap busting activities by Gary I closed the gap of k=3611911875 between 101 and 134k and, what a surprise, found 7 new primes :shock: for following n's:

108192, 112822, 120412, 132051, 132188, 133748, 133992

Four of them in the narrow 132-134k range! A new Sophie Germain was very close :w00t: k=3611911875 now has 119 primes in the n=1-400,000 range ([I]no gaps[/I]). [/quote]


Wow, that's awesome and rather amazing too. I don't think I've seen one with 4 primes within 133992 / 132051 - 1 = 1.47% of each other at any level of n. That would be an interesting research project.

Cheers to the gap fillers! :smile:


Gary

Primes for k=775784295 for n=175K-200K; continuing
 

I've now tested the amazing k=775784295 from n=175K to 200K and it continued its outstanding performance and then some! I found 4 more primes for a total of 109 primes so far. They are shown below.

This now makes an astounding 50 primes for the range of n=10K and 200K, which is far more than any other k listed on the entire summary site for that range; even for k's much larger than it.

775784295*2^176818-1
775784295*2^181075-1
775784295*2^188983-1
775784295*2^189983-1 <-- that is correct, they are exactly 1000 apart


Status:
1. k=686701125, tested so far from n=173K to 195K. Will stop and post primes at n=200K.
2. k=1019370495, just now started testing entire range from n=150K to 200K.
(above will complete all of my reserved k's except for one up to n=200K)
3. k=289, one core complete from n=260K to 370K, other complete from n=400K to 470K. I have stopped it several times to work on other activities so its a little behind the estimate on my last status. It should be done in about 4 days allowing time for additional stoppages.
4. Upcoming...k=19437 and k=102765 from n=200K to 250K, more gap-busting activities, and extending comprehensive twin-prime search efforts.


Gary

Primes for k=686701125 for n=173K-200K; continuing
 

I've now tested k=686701125 from n=173K to 200K. This is the one that I took over from Cedric from where he left off after he released it so there are no gaps. I found 3 more primes for a total of 119 primes so far. They are:

686701125*2^178589-1
686701125*2^187188-1
686701125*2^193005-1


Reference my last status, I'm going to test the newly reserved k=2145 before continuing on k=19437 and 102765.


Gary

Gaps busted on 5 k's
 

I've tested k=11069, 12379, 18885, 22971, and 23005 from ground zero (i.e. n=1) up through n=25K. The attached busts the entire gaps on all except k=11069, which probably shouldn't be a gap (see below). I show an asterisk (*) by primes that are already posted.

I compared the primes in the attached list to primes on the summary site where n<25K for the 5 k's and found two problems:

1. k=11069 shows tested up to n=450K. This is incorrect. In addition to primes at n=16 and n=40 shown on the summary site, I found 5 additional primes up to only n=25K. I saw the note from Templus where he says that he tested it up to n=450K but he doesn't say where he started nor does he list any primes. I see two possibilities to make it correct: (1) Change it to show tested to n=25K, which is what I have done here. (2) Contact Templus (I don't think he's very active anymore) and ask where he started testing and what primes he found. Simply saying that one has 'tested to 450K' does nothing for us here.

2. k=18885; the prime for n=1 should be n=2. (It's odd that this is the second one I've found with the exact same error.) 18885*2^1-1 is 179*211. 18885*2^2-1 is prime.

I used srsieve since I did multiple k's across the same range here so there is no issue with low n's being erroneously removed.

Because this is a little messy, I'm attaching both the primes and the results files. Since it's two files and the results are rather large, it's in zipped format.


Gary

Primes for k=2145 to n=120K to fill gap
 

I have tested k=2145 from n=1 to n=120K to confirm prior primes and fill the gap between n=50K and n=115899. All primes below n=50K and at n=115899 are correct. I found 3 additional primes to fill the gap that now makes a total of 69 primes up to previous testing of n=214994:

2145*2^73217-1
2145*2^83553-1
2145*2^94980-1


I am now testing from n=120K to 166569 to confirm prior primes up to that point. Above that, Curtis has already sent me sieve files from n=166570 to n=240K. I will start with his files after finishing my testing up to n=166569.


Gary

Gaps busted on 4 more large k's
 

Attached are the primes for testing the following k's and n-ranges to completely fill 4 more gaps on large k's. Due to the different ranges of n, these were tested one at a time so there is one file per k. I did some overlap with existing testing to confirm its starting point, of which I found all to be correct. I show an asterisk (*) by the primes already posted.

1. k=8311875 up to n=40K.
2. k=360949875 up to n=15K.
3. k=387376275 up to n=28K.
4. k=1222853775 up to n=16K.

I'm currently testing 31 different low-weight k's shown on the summary page up to n=100K, mainly ones with 2 or less primes for n<100K. I'm most interested in the ones that show no primes, which can't be correct in some cases. Most don't have gaps but I've found two so far that are missing some low n's. The testing should be done in a couple of days and I'll forward any problems found at that time.


Gary

primes for k=1425 to n=100K to fill gap
 

I have tested k=1425 from n=0 to 100K to fill the gap in testing below n=50852. I confirmed that the 4 primes that are currently posted are correct for a total of 59 primes, which are attached. I show the ones already posted with an asterisk (*).


Gary

Primes for k=1019370495 n=150K-175K; continuing
 

I've now tested k=1019370495 from n=150K to 175K. After a slow start, this one has started to come on strong. I found 3 more primes for a total of exactly 100 primes. This makes 6 primes from n=135236 to 172433. The primes that I found were:

1019370495*2^165050-1
1019370495*2^166521-1
1019370495*2^172433-1

I've got this one running consecutively up to n=200K.


Gary

Gary, I moved your posts about k=289 to the [URL="http://www.mersenneforum.org/showthread.php?t=8621"]k<300 thread[/URL], and about 31 low weight k's to the [URL="http://www.mersenneforum.org/showthread.php?t=2934"]low weight thread[/URL]. Please post further follow-ups there. Thanks!

I'll delete this message in a day or two.

[quote=Kosmaj;110406]Gary, I moved your posts about k=289 to the [URL="http://www.mersenneforum.org/showthread.php?t=8621"]k<300 thread[/URL], and about 31 low weight k's to the [URL="http://www.mersenneforum.org/showthread.php?t=2934"]low weight thread[/URL]. Please post further follow-ups there. Thanks!

I'll delete this message in a day or two.[/quote]


OK, good idea. I'm still learning the ropes here a little. I figured all small primes went here, regardless of the size or nature of k.

Obviously you can delete your message and this message now too after you read it, if you wish.


Gary