Bases 501-1030 reservations/statuses/primes

[gd_barnes]

Originally Posted by rogue

Reserving

Mark,

I just finished S878 to n=25K. See my recent post. If you've started on it, feel free to doublecheck it though.


Gary

[rogue]

Originally Posted by gd_barnes

Mark,

I just finished S878 to n=25K. See my recent post. If you've started on it, feel free to doublecheck it though.

I haven't started it yet, so I'll get rid of it.

In case people are curious, I am dumping all of these into a PRPNet server trying to keep two computers "fed" through the next week as I will be on vacation. Right now I have about six days of work queued up, but if k fall, then that six days gets reduced. I'm only reserving whenever I have the time to sieve. I've been taking conjectures on the Sierspinski side because it hasn't had as much "love" as the Riesel side. There will be (unfortunately) an number of new single k conjectures when I'm done.

And speaking of such, I'll reserve S702, conjectured k of 75.

[rogue]

Base 548

2*548^1+1
3*548^6+1
4*548^2+1
5*548^1+1
6*548^115+1
7*548^4+1
8*548^5311+1
9*548^1+1
10*548^12+1
11*548^1+1
12*548^1+1
13*548^22+1
14*548^1+1
15*548^1+1

Conjecture proven.

Base 679

6*679^4+1
10*679^1+1
12*679^10+1

k=4 remains at n=25000. Releasing.

Base 740

2*740^1+1
3*740^1+1
5*740^1+1
6*740^1+1
7*740^2+1
8*740^83+1
9*740^1+1
10*740^12+1
12*740^5+1

k=4, 11, and 13 remain at n=25000. Releasing.

Base 812

2*812^1003+1
3*812^1+1
4*812^26+1
5*812^5+1
6*812^19+1
7*812^2+1
8*812^3461+1
9*812^1+1
10*812^18+1
11*812^1+1
12*812^6+1
13*812^2+1
14*812^1+1
15*812^31+1

Conjecture proven.

Base 866

2*866^1+1
3*866^7+1
5*866^5+1
6*866^1+1
7*866^2+1
10*866^2+1
11*866^35+1
12*866^531+1
13*866^1492+1
15*866^8+1

k=8 remains at n=25000. Releasing.

[rogue]

Base 934

3*934^1+1
6*934^4+1
7*934^6+1
9*934^429+1
10*934^1+1
12*934^44+1
13*934^1+1
15*934^1+1

k=4 remains at n=25000. Releasing.

Base 935

2*935^1+1
4*935^2+1
6*935^8+1
8*935^1+1
12*935^3+1

k=10 remains at n=25000. Releasing.

Base 968

2*968^917+1
3*968^2+1
4*968^90+1
5*968^3+1
6*968^40+1
7*968^8+1
8*968^7+1
9*968^1+1
10*968^162+1
12*968^1+1
13*968^2+1
14*968^1+1
15*968^20+1

k=11 remains at n=25000. Releasing.

Base 1013

2*1013^1+1
4*1013^2+1
6*1013^1+1
12*1013^1+1

k=8 remains at n=25000. Releasing.

Note that any other k that appear to be "missing" have trivial factors.

[rogue]

Reserving

[rogue]

Reserving

[Mathew]

R788 is proven
CK=14

Largest prime

7*788^1663-1

k=9 is removed by algebraic factors

attached are the results

[MyDogBuster]

k=9 is removed by algebraic factors

Factor 3 can never eliminate k's due to algebraic factors. Gary will have to explain the math. k=9 will have to be tested. Ian

[gd_barnes]

Originally Posted by Mathew Steine

R788 is proven
CK=14

Largest prime

7*788^1663-1

k=9 is removed by algebraic factors

attached are the results

Algebraic factors only remove the even n. There is no common factor for the odd n. As Ian said, you'll need to test k=9. If there was a common factor for the odd n, then you could make the statement: k=9 is removed by partial algebraic factors. You could never make the statement that k=9 is removed by algebraic factors unless the base was also a perfect square. In that case, k's that are perfect squares are removed by (full) algebraic factors because the algebraic factors occur on all n; not just the even n.

To determine which common factor(s) for the odd n that there could be for a k that is a perfect square on a base, prime factor the base + 1 and only consider factors (f) that are f==(1 mod 4). Here:

789 = 3 * 263

Since 3 and 263 are both f==(3 mod 4), there can be no common factor for any odd n on squared k's for base 788. Therefore all squared k's must be tested unless they are eliminated by trivial factors, which the script would do automatically.

We'll wait to show this on the pages until you let us know that you've tested k=9.


Gary

[Mathew]

R788 is proven

9*788^11325-1 is 3-PRP! (44.1679s+0.0027s)
Primality testing 9*788^11325-1 [N+1, Brillhart-Lehmer-Selfridge]
Running N+1 test using discriminant 7, base 1+sqrt(7)
Calling Brillhart-Lehmer-Selfridge with factored part 79.21%
9*788^11325-1 is prime! (458.7986s+0.0052s)

Edit: Thanks Mathew

[MyDogBuster]

Riesel 908 the last k (8*908-n-1) tested n=25K-50K. Nothing found

Results attached - Base released