Post small primes and tell us about your progress here

[gd_barnes]

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.

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

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

[gd_barnes]

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.


Gary

[arminius]

More primes for n<=200k:

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

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

[gd_barnes]

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.

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

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

[VBCurtis]

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

[gd_barnes]

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

Gary

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)

[gd_barnes]

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 (..) 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

[Flatlander]

Originally Posted by Flatlander

Not sure where this should be posted but, here is the complete list of primes for k = 3045, up to n = 371469

...
also 3045*2^388363-1 is prime.

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

About 85 candidates per 1000 after sieving to 1.2T.

[gd_barnes]

Originally Posted by Flatlander

...
also 3045*2^388363-1 is prime.

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

About 85 candidates per 1000 after sieving to 1.2T.

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) unless they hit another drive like low-weight or n<300.

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


G

[gd_barnes]

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. Total still 69 primes.

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


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

[arminius]

More primes for n<=250k:

220897, 241662