R423
 

R423 complete to n=100k

Only 2 primes found from n=50k-100k
1106*423^50490-1
1052*423^58212-1

11 k values remain. Residues emailed. Base released

R406
 

Releasing R406 - No work done

[QUOTE=Mathew;354200]I would like to reserve

R:483,487
S:367,387,396,471

to n=50K[/QUOTE]

Complete

Primes:
[CODE]1528*483^43858-1

396*487^25167-1
1148*487^29427-1
1710*487^32973-1
1892*487^33189-1

552*367^27584+1
2742*367^29246+1
3216*367^33961+1

1466*387^26076+1
766*387^27587+1
1596*387^27933+1
264*387^29733+1

3785*396^39141+1
1930*396^43845+1
5080*396^44367+1

2740*471^43077+1[/CODE]This should complete all bases ≤500 with k's remaining ≤25 to n=50K.

I would like to reserve R430 to n=25K

S316 status update: at n=20k, 362 k values remain. Still plugging away...

R298, R315, R320 are completed to n=200K.
There is one prime: 53*320^115706-1
Results attached.

Morning all,

I'm looking for some advice on possibly starting R270. I've not yet reserved it but if I can understand how everything works then I intend to.

I ran the new bases code to n=2500 and it generated all of the expected files, which I've attached. I ran srsieve on the remaining k values but something happened that I don't understand.
There was a number of entries removing algebraic factors such as for 4*270^n-1 when n%2=0 as k=2^2, but at the very bottom it has "removed candidate sequence 3600*270^n-1 from the sieve"


So before I reserve R270 I have 2 questions:
1) Why does srsieve remove k=3600?
2) Have I missed anything such as other k's that can be removed or more k's I should test?

Cheers,
Rob

[QUOTE=rob147147;358458]1) Why does srsieve remove k=3600?[/QUOTE]

All values of n in the range you are sieving have factors.

[QUOTE=rob147147;358458]Morning all,

I'm looking for some advice on possibly starting R270. I've not yet reserved it but if I can understand how everything works then I intend to.

I ran the new bases code to n=2500 and it generated all of the expected files, which I've attached. I ran srsieve on the remaining k values but something happened that I don't understand.
There was a number of entries removing algebraic factors such as for 4*270^n-1 when n%2=0 as k=2^2, but at the very bottom it has "removed candidate sequence 3600*270^n-1 from the sieve"


So before I reserve R270 I have 2 questions:
1) Why does srsieve remove k=3600?
2) Have I missed anything such as other k's that can be removed or more k's I should test?

Cheers,
Rob[/QUOTE]

As far as I can tell, you have missed nothing. To add a little more detail to what rogue said; you have encountered an unusual situation. Most commonly, a k can be removed from testing where all odd n have a small factor such as 5 and all even n are of the form k^2*b^(2n)-1 and so have algebraic factors of (k*b^n-1)*(k*b^n+1). There are no such k's for R270.

BUT...in this case, k=3600*270^n-1 can be removed because:
1. All odd n have a covering set of factors [7, 13, 37]. That is, all odd n have either a factor of 7, 13, or 37.
2. Since k is a perfect square, all even n have algebraic factors as shown above.

Therefore the k will always be composite but is not considered the conjecture of the base because it does not have a full covering set of "numeric" (as opposed to algebraic) factors.

You said in your PM that you are a math major so I'm guessing that after a little looking, this will be clear to you. But if not, don't worry. It doesn't come up often and this knowledge is not needed to run the conjectures since srsieve is now "smart" enough to remove such k's.

One more thing: My PM response to you was wrong when I said that the base has no k's that can be removed as a result of algebraic factors. I had not considered unusual cases such as this. At this point, all you need to do is not attempt to test k=3600. It is not considered as a remaining k.


Gary

As I now understand all of this, I'll reserve R270 to 50k

R366
 

tested n=400k to 500k, nothing. Continuing...

c10ck3r has completed R306 with conjecture k=39295 to n=5K and has released the base. There are 233 k's remaining. I have added it to the recommended list to n=25K.