Post small primes and tell us about your progress here

[gd_barnes]

I have completed testing k=26565 and k=49335 up to n=150K. On k=26565, there were 69 instead of 66 primes below n=10K as shown on the summary site. On k=49335, there were 72 instead of 68 primes below n=10K as shown. I have found these counts to frequently be incorrect by as many as 5 primes. I often wonder how people arrived at them since they didn't actually post the primes for them.

For these two k's plus k=16995, I will be testing all of them straight through to n=400K and verifying all previously found primes along the way.

Here are the primes:

26565: 1, 4, 8, 9, 12, 16, 17, 22, 24, 26, 29, 35, 36, 37, 50, 61, 64, 70, 75, 96, 101, 108, 136, 143, 178, 182, 190, 193, 194, 195, 215, 220, 314, 317, 385, 424, 429, 490, 526, 529, 554, 634, 636, 701, 726, 748, 782, 949, 994, 1362, 1415, 1700, 1874, 2017, 2676, 2680, 2998, 3057, 3061, 3203, 3337, 4022, 4400, 4460, 6058, 7734, 8894, 8950, 9741, 10954, 11315, 12613, 13928, 17120, 19271, 20789, 23115, 23305, 25728, 32734, 37649, 42817, 48973, 56385, 58607, 59665, 72445, 74104, 84434, 86554, 109141, 112017, 124714, 141212, 145695

49335: 1, 2, 5, 9, 10, 13, 14, 15, 17, 21, 27, 28, 29, 35, 36, 37, 51, 54, 61, 84, 92, 121, 122, 155, 163, 169, 205, 253, 268, 350, 367, 522, 523, 553, 627, 645, 730, 899, 1025, 1039, 1066, 1095, 1274, 1445, 1486, 2124, 2188, 2372, 2655, 2691, 2781, 3188, 3313, 3573, 3735, 3788, 4113, 4239, 4423, 4438, 4628, 4785, 5045, 6091, 6143, 6548, 6998, 7111, 7181, 7559, 9273, 9559, 11309, 11547, 12745, 15649, 19957, 22007, 24726, 26383, 26618, 27314, 37177, 48473, 49206, 61270, 64285, 67402, 71082, 96933, 103926, 109681, 118471, 127033, 134655, 142876

On k=26565, this makes a total of 103 primes up to the highest found prime around n=306K with the 100th prime found at n=264851. It is not clear how far this has been tested.

On k=49335, this makes a total of 99 primes up to n=250K; the limit of testing shown on the site.

On both k's, there don't appear to be any testing gaps past n=109K but I don't think we'll know for sure until I get them tested all the way through.


Gary

[kar_bon]

info: the terms like "(60 primes 10k)" in the summary page i got from this thread from post #9 (March 11, 2005) by lsoule. he gave only the number of primes till n=10k without any other information. perhaps his count of primes was incorrect because low n were deleted by newpgen.
another example is k=2330445.
Karsten

[gd_barnes]

I am concurrently searching all 12 of my original high-weight k's that include k=19437, 102765, 3545685, 111546435, 115029915, 120023475, 290499495, 686701125, 775784295, 968911515, 1019370495, and 3428677395 from n=200K to 400K. I am using 3 cores on the range of n=333335 to 400K and 2 cores on the range of n=200K to n=333334.

Status:

1. The 3 cores on the higher range have completed n=333335 to 336K. 3 primes were found and one previously found prime was confirmed as previously shown in the 'post lots of primes' thread.

2. The 2 cores on the lower range have completed n=200K to 206.5K. 2 new primes were found as follows:

3428677395*2^203702-1
775784295*2^206406-1


Note that my k's = 19437, 102765, and 686701125 have already been searched to n=250K so are not included in the lower search range until it gets up to that point.

In the future for the statuses on this effort, I will just refer to "my original high-weight k's" when referring to all 12 of these k's.


Gary

[gd_barnes]

Here is status update #2 on my original high-weight k effort. See the original status update in the last post for the k's involved.

Higher range has completed n=333335 to 340K (going to n=400K). No new primes were found since the last status. One prime that had already been found was confirmed:

Confirmed prime:
115029915*2^337129-1


Lower range has completed n=200K to 215K (going to n=333334). New primes were found and previously found primes were confirmed since the last status as follows:

New primes:
968911515*2^207877-1
1019370495*2^210362-1
968911515*2^213176-1
968911515*2^214518-1

Confirmed primes:
111546435*2^209565-1
111546435*2^210761-1


k=968911515 is finally getting untracked but still trails most of the others with 91 primes up to n=215K.


Gary

[gd_barnes]

On k=16995, 26565, and 49335, I have done the following:
1. Sieving completed for all 3 from n=150K to 400K to P=2T.
2. LLR completed for all 3 from n=150K to 200K. All of them had already been tested in this range so it effectively was a double-check effort. No missing or incorrect primes were found.

On k=2145, I have received a sieve file from Curtis for n=280K to 600K. Testing has already been completed for n < 280K.

On all 4 k's I am doing a combined 'small high-weight k' test from n=200K to 400K in a manner similar to my large 'original high-weight k' test. For this test, I am running 3 cores as follows:
1. One core will LLR the range of n=200K to 333334. Of course for k=2145, candidates will not start until n=280K.
2. Two cores will LLR the range of n=333335 to 400K.
3. After #2 is complete, 2 cores will LLR k=2145 from n=400K to 600K.

#1 and #2 started earlier today.


Gary

[gd_barnes]

Kosmaj and Karsten,

I have created a web page where I will be showing status updates on the progress of my various k's every 1-2 days. It is at http://gbarnes017.googlepages.com/.

For a permanent record here at RPS, I will still update statuses about once per month. But with the web page, I will not inundate you with statuses every 1-2 weeks and you will still be able to get my most recent status on everything that I'm working on right before you update the www.15k.org pages.


Gary

[arminius]

More primes for n from 250k to 350k:
1000065*2^309643-1

[VBCurtis]

It pains me to see a 300k+ prime listed in "small primes" thread.
Sign of the times, I suppose.

[gd_barnes]

Here's an end-of-the month status off my web page for permanent record here:

For k=2145, 16995, 26565, and 49335; ranges and primes:

n=200K to 237.9K complete; confirmed previously found prime:

k / n
26565 217001

n=333335 to 354K complete; one prime found shown in 'lots of primes' thread

k=19437, 102765, 3545685, 111546435, 115029915, 120023475, 290499495, 686701125, 775784295, 96891151, 1019370495, and 3428677395; ranges and primes:

n=200K to 231K complete; primes found and confirmed:
k / n
111546435: 209565, 210761 <-- confirmed primes previously found
290499495: 224928
775784295: 206406, 222937, 227488
968911515: 207877, 213176, 214518, 226971
1019370495: 210362, 225325
3428677395: 203702

n=333335 to 347K complete; 5 primes found shown in 'lots of primes' thread. Confirmed 2 previously found primes:
k / n
115029915: 334568, 337129

Gary

[gd_barnes]

To fill in the gap below my large twin find, here are the primes and twins for k=1046619117 up to n=100K:

primes: 4, 14, 18, 34, 37, 69, 74, 120, 122, 140, 145, 260, 345, 742, 1020, 1188, 1344, 1900, 2304, 2750, 3204, 3500, 3602, 3912, 4038, 4669, 4894, 6614, 7874, 10077, 10520, 10641, 14234, 14437, 28317, 41248, 42154, 74329, 77937, 100000

twins: 18, 100000

Total of 40 primes. The Nash weight is 2883.


Gary

[gd_barnes]

To fill in the gap below my large quad find, here are the primes and twins for k=477707955423 up to n=25K:

primes: 36, 46, 58, 78, 119, 143, 178, 226, 444, 630, 663, 1060, 1164, 1686, 1924, 2539, 2932, 3163, 3586, 3659, 3802, 4524, 5382, 6247, 7319, 7892, 20783

twin, triplet, & quad: 3802

There was no prime for n<36. The only twin, triplet, and quad was n=3802.

Total of 27 primes. The Nash weight is 2838.


Gary