Bases 501-1030 reservations/statuses/primes

[gd_barnes]

Reserving R737 to n=300K for Ian and me.

[rebirther]

R624 tested to n=2.5k + sieved to 1G (2.5-10k)

19002 remain

Results emailed - Base released

[rebirther]

Reserving R652 as new base using the new-base script up to 2.5k and sieving to 10k (1G) with srsieve2

[MyDogBuster]

Reserving S763 to n=10K

[gd_barnes]

Originally Posted by rebirther

R624 tested to n=2.5k + sieved to 1G (2.5-10k)

19002 remain

Results emailed - Base released

It turns out there were two different types of algebraic factors on this one. The first type, which would have been caught by srsieve2, has 212 k's. The second type, which would not be caught by srsieve2, has 34 k's.

This leaves 18977 k's remaining for R624 at n=2500.

Files are attached for each type of algebraic factors. See the main Riesel page for their breakdown.

I removed the applicable k's from the sieve file.

[rogue]

Originally Posted by gd_barnes

It turns out there were two different types of algebraic factors on this one. The first type, which would have been caught by srsieve2, has 212 k's. The second type, which would not be caught by srsieve2, has 34 k's.

This leaves 18977 k's remaining for R624 at n=2500.

Files are attached for each type of algebraic factors. See the main Riesel page for their breakdown.

I removed the applicable k's from the sieve file.

What is the form of the algebraic factor that srsieve2 doesn't catch?

[NHoodMath]

624=16*39
624=4^2*39
Any k that is a square times the leftover non-square part of the base (39) has algebraic factors for odd n. These sometimes combine with a trivial factor (in this case 5) to eliminate the k.
For example, Riesel base 96 has algebraic factors for k=6*n^2 because 96=4^2*6, or R288 has algebraic factors for 2*n^2 because of 288=12^2*2. There are even cases where the base itself can be used as the non-square part, ex R79 where 79*n^2 has algebraic factors on odd n.

This can also happen for cubes, 5th powers, etc. but is much less likely to yield a full k elimination. Ex. R432 has algebraic factors for n=1 (mod 3) on k's where k=4*n^3, but it doesn't yield any eliminated k because 432=2*6^3, and to complete the cube in the base 2^2=4 is still needed.

[gd_barnes]

That type 2 algebraic factors that NHood described...I don't recommend that srsieve2 try to catch them...unless you want to go to a long dark place to try to code for and extensively test them. It becomes complex to attempt to nail them down correctly for all bases. The complexity of the different variations of them that NHood describes is mainly why I don't recommend it.

It's unusual for any base to have more than about 5 full k's that can be eliminated that fit that type. Obviously R624 was an exception.

[rogue]

Originally Posted by gd_barnes

That type 2 algebraic factors that NHood described...I don't recommend that srsieve2 try to catch them...unless you want to go to a long dark place to try to code for and extensively test them. It becomes complex to attempt to nail them down correctly for all bases. The complexity of the different variations of them that NHood describes is mainly why I don't recommend it.

It's unusual for any base to have more than about 5 full k's that can be eliminated that fit that type. Obviously R624 was an exception.

srsieve2 does have code to try to detect these. I'll take a look to see why it doesn't find them.

[gd_barnes]

Originally Posted by rogue

srsieve2 does have code to try to detect these. I'll take a look to see why it doesn't find them.

It does not appear to. I've found many of these types of k's even recently that I had to manually remove where people have used srsieve2.

For testing purposes, use base R624. If you can make it find 35 of these "type2" algebraic factors where the k's are completely removed then the code should be correct. The k's are documented in the "type2" named file attached to that last post.

[rebirther]

Reserving R1008 as new base using the new-base script up to 2.5k and sieving to 10k (1G) with srsieve2