k's for last search
 

I just realized that I didn't include all of the k's that I searched in the last post. They are all of the ones marked in light blue for 8M < k < 12M on the summary page. But for future historical reference, I'll list them all here. To get the prior list of primes, I searched all of the following low-weight k's up to n=100K:

[quote]
8288233
8376239
8922449
9096613
9705763
9770317
10013593
10108837
10247561
10284899
10296007
10346561
10453199
10463923
10544249
10598947
10639619
10671431
10805593
10813783
10906603
10932097
10943321
11223059
11311003
11319193
11468609
11553221
11639819
11658187
11716993
11741347
11846279
11847299
11932211
11955659
[/quote]

Gary

k=24186941
 

tested above k upto n=1M. one prime found at n=3802.
no further reservation of this k.

k=371944871 tested to n=255k
filled gap: 26, 38, 98, 326, 1658, 2222, 58706, 217502*, 253358*
(*=confirmed)
no further reservation

k=50227
 

tested upto n=1M, no more primes, no further reservation

I'm wondering...what is the difference between high weight and low weight k's? I was reading some of the earlier posts in this thread and I was kind of confused. Do low weight k's LLR faster or slower than high weight ones? Does sieving tend to remove more candidates earlier on for low weight, or high weight? Which ones generally have a higher concentration of primes?

Low weight k's have lots of values of n with small factors and therefore after sieving to a given depth there are fewer candidates remaining to LLR. Conversely high weight k's do not have the small factors and therefore there are lots of candidates remaining to LLR at the same sieve depth. Thus high weight k's would be expected to have more primes in a given range of n.

The weight does not make any difference to the time to LLR a given candidate as LLR time depends on the value of n and the size of the FFT that has to be used to perform the LLR. The size of the FFT is dependent on the value of k - larger values of k require larger FFT's. Thus k<300 are faster to LLR at a given value of n than larger k's.

[quote=amphoria;118208]Low weight k's have lots of values of n with small factors and therefore after sieving to a given depth there are fewer candidates remaining to LLR. Conversely high weight k's do not have the small factors and therefore there are lots of candidates remaining to LLR at the same sieve depth. Thus high weight k's would be expected to have more primes in a given range of n.

The weight does not make any difference to the time to LLR a given candidate as LLR time depends on the value of n and the size of the FFT that has to be used to perform the LLR. The size of the FFT is dependent on the value of k - larger values of k require larger FFT's. Thus k<300 are faster to LLR at a given value of n than larger k's.[/quote]
Thanks! :smile:

Milestone report for k=3343
 

k=3343 tested till n=2M, I'm still working on it :flex:

k=3343 tested till n=2.1M, I'm still working on it.

k=3343 tested till n=2.2M, I'm still working on it.

k=161464717
 

tested till n=1M
2 primes: 181 and 182845 (reported by Thomas)
no further testing