Primes for k=115029915 to n=120K; continuing
 

I have tested k=115029915 from n=0 to 120K to confirm prior testing and fill 2 gaps. Below are the additional primes that were found. For ease of reference, I am listing an already found prime at the beginning and end of each gap.

[quote]
gap 1:
9975, 10085, 10118, 11651, 14714, 15710, 16732, 19616, 20835, 24709

gap 2:
46463, 58718, 61202, 62091, 63950, 68769, 68800, 68969, 71114, 77402, 85247, 87561, 88270, 93761, 97410, 102118, 102727, 103766, 105197, 106805, 115255
[/quote]

All primes already posted up to n=120K were confirmed correct.

This is an outstanding performing k for its size. The 100th prime was found at n=85247 and this makes a total of 121 primes up to n=385K! k=8331405 is the only lower k on our summary site that has more total primes. More remarkable is that k=115029915 has 115 primes up to only n=156921, which is more than the 110 primes that k=8331405 had at that point.

One note on this one...I suspect that there is at least a partial gap between n=156921 and 269264. According to the top-5000 site, there was over 2 years between the time that these two primes were found and it was a different person who found them. I did find a thread on this forum that shows that it may have been tested from n=210K to 269264 but I wasn't completely convinced.

Regardless, I plan to test this one up to n=200K and then include it in my large sieve of multiple heavy-weights. In those efforts, all ranges will be verified and/or unknown gaps filled.


Gary

k=102765 tested 200K-250K; no more primes
 

I have now tested k=102765 up to n=250K. No more primes were found.

I am a definite dry spell on these high-weight k's in testing over n=200K. Previously posted testing of k=2145 from n=215K to 240K, k=19437 from n=215K to 250K, and now this one from n=200K to 250K all yielded no primes. :mad:


Gary

k=1000065
 

More primes for n<=200k:

100487, 106483, 107980, 110543, 114270, 125023, 130134, 158970

Please note that 1000065*2^146+/-1 is a twin prime :smile:

Primes for k=120023475 to n=125K; continuing
 

I have tested k=120023475 from n=0 to 125K to fill the gap below previously found primes and to confirm the first one already found. Below are the primes that were found.

[quote]
3, 4, 7, 16, 18, 20, 22, 23, 34, 40, 43, 46, 58, 74, 77, 89, 92, 101, 107, 119, 123, 160, 164, 199, 241, 243, 269, 270, 342, 388, 452, 453, 489, 506, 572, 638, 663, 699, 768, 795, 840, 847, 992, 1020, 1074, 1130, 1159, 1474, 1555, 1699, 1894, 2567, 2587, 2762, 3002, 3827, 4064, 4298, 4508, 4598, 5278, 5592, 5596, 5885, 6195, 7100, 7190, 7984, 8441, 9209, 10878, 11359, 11830, 12295, 12910, 14720, 16490, 20420, 22350, 23327, 23825, 26221, 27437, 29109, 29143, 29884, 30510, 30594, 33626, 34955, 36079, 38550, 39157, 40441, 40651, 42142, 42580, 45155, 47188, 47743, 50383, 51246, 56208, 60721, 73008, 73367, 75470, 106329, 115597
[/quote]

This k is even better for its size then k=1150229915 that I recently posted primes for. The 100th prime was found at only n=47743! This is the fastest of any k that I have tested, most of them heavy-weights far greater than this k. Despite dieing off a little between n=75K and 106K, this makes a total of 109 primes in my testing and 112 primes up to previous testing of n=161.5K.

I plan to test this one up to n=200K and include it in my large sieve of multiple heavy-weights.


Gary

Primes for 2055,2085,2115,2145,2175
 

Here are the primes I have discovered for these k's. This list begins at 1e4, since Gary has already posted the smaller primes.
2055: 10655, 11438, 26301, 26858, 35649, 38130, 44826, 61481, 77237, 81938, 90848

2085: 11190, 12065, 13556, 13775, 17963, 21559, 27536, 36460, 43238, 46654, 54318, 92568, 93450, 106978, 124759

2115: 11837, 12008, 14168, 17420, 17696, 21857, 21997, 46019, 48923, 57130, 77696

2145: 10238, 12404, 15075, 15926, 20148, 23550, 24879, 25527, 35062, 35387, 73217, 83553, 94980, 115899, 138411, 139373, 140432

2175: 11142, 13409, 14096, 14243, 24201, 31873, 36265, 38550, 38942, 57231, 64065, 74009, 76293, 83741, 84233, 93078, 106442, 107318, 128058, 136985, 159486, 162240

These lists are complete to 166k for all 5 k's. Gary has taken over testing of 2145, while the rest are reserved by me.
-Curtis

progress on k=11069
 

I just got the following message from Templus. It has some additional primes to post for k=11069.

Gary

[quote]
Hello,

I read on the forums that you were unaware of my progress for k=11069. I have 1 computer here working on it, it is now at n=575k, and the k is prime for the following numbers:

11069 16
11069 40
11069 580
11069 1996
11069 3600
11069 6456
11069 12880
11069 35140
11069 76828
11069 158860

I hope I have informed you well now, and I apologize for this late message.

Kind Regards,

Templus (Ingmar Goudt)
[/quote]

Progress on various k's
 

Karsten,

I figured I should give you a status update before you go on vacation. While doing my large sieve of all my k's from n=200K to 400K, there are some side efforts going to make the sieve a less intense effort. I'm getting well-sieved files from Curtis on k=2145 and had already gotten an almost completed sieved file from Cedric on k=686701125 so I have been testing them separately, although am including the latter in my sieve for n > 250K. And on k=115029915 and 120023475, those were recent reservations so I'm working to get them up to n=200K before finishing the sieve. Here is the status and some more primes that were found:

1. k=2145; I just started back up on this one after getting another file from Curtis. From n=240K to 242K, no additional primes found. Total still 69 primes.

2. k=115029915; from n=120K to 177K; previous primes found and confirmed at n=122047, 122269, 122892, 141059, and 156921. Two additional primes found at n=161898 and 167323. Total 123 primes up to n=385K!

IMPORTANT NOTE: This confirms what I said in a prior posting. There is definitely a testing gap between n=156921 and 269264 even though one is not shown. The next time you do an update, I would suggest showing your patented (..) :smile: gap notation between n=177K and 269264. (I will probably be up to n=200K by then but the same would still apply at that point.) With this huge gap in testing, it makes the prime count even more remarkable.

3. k=120023475 from n=125K to 173K; previous primes found and confirmed at n=142158, 148159, and 150913. Two additional primes found at n=170384 and 172591. Total 114 primes up to my testing point; almost an even race with #2. What's even better is that previous testing took this one up to n=161.5K. So I found 2 more primes in just another 11.5K.

4. k=686701125 from n=200K to 248K; two new primes found at n=225149 and 238938. Total 121 primes; another outstanding k.


Have a great vacation!


Gary

[quote=Flatlander;106976]Not sure where this should be posted but, here is the complete list of primes for k = 3045, up to n = 371469[/quote]
...
also [B]3045*2^388363-1 is prime.[/B]

I think k=3045 has been the 'best' reasonably small k I have found.
6 primes between 100,000 and 200,000.
5 primes between 200,000 and 300,000.
4 primes between 300,000 and 400,000. (So far.)
3 between 400,000 and 500,000 would be nice :smile:

About 85 candidates per 1000 after sieving to 1.2T.

[quote=Flatlander;112698]...
also [B]3045*2^388363-1 is prime.[/B]

I think k=3045 has been the 'best' reasonably small k I have found.
6 primes between 100,000 and 200,000.
5 primes between 200,000 and 300,000.
4 primes between 300,000 and 400,000. (So far.)
3 between 400,000 and 500,000 would be nice :smile:

About 85 candidates per 1000 after sieving to 1.2T.[/quote]


I would probably post them in the 'post lots of primes here' thread. My thinking on that thread is that it's intended for any misc. top-5000 primes. I use this thread for non-reportable primes (which have been ALL of mine so far) :grin: unless they hit another drive like low-weight or n<300.

Speaking of that, here comes a few more non-reportable primes...:smile:


G

Status update; large-LLR coming up
 

Karsten,

Here is my final status update on my 13 heavy-weights before testing my large sieve of them all at once, which will be ready to start LLRing on Wednesday 8/22.

1. k=2145; LLR complete thru n=280K. No more primes found. :mad: Total still 69 primes.

Note: I think Curtis is removing all the primes before sending me his sieve files on this one! :lol: That's no more primes found (above what had been previously found) since n=180K. :ermm:


2. k=115029915; LLR complete thru n=200K; one more prime at n=183984 since last status report on Aug. 9th. Total 124 primes to n=385K.

Note: This further confirms the gap in prior testing. It now still has a gap from n=200K to 269264.

3. k=120023475; LLR complete thru n=200K; two more primes at n=181527 and 182241 since last status report on Aug. 9th. Total 116 primes to n=200K.

4. k=686701125; LLR complete thru n=250K; no more primes since last status report on Aug. 9th. Total 121 primes to n=250K.


Note that I recently reserved k=16995, 26565, and 49335. Those will be a separate effort that will produce top-5000 primes more quickly then the above. I'm currently in the process of filling gaps in them right now.


Gary

k=1000065
 

More primes for n<=250k:

220897, 241662