Bases 501-1030 reservations/statuses/primes

[MyDogBuster]

More closet cleaning

R523 CK=132 Primes=40 Remain=2
R597 CK=116 Primes=54 Remain=1 1 algebraic factor
R730 CK=171 Primes=112 Remain=1
R747 CK=120 Primes=54 Remain=4 1 algebraic factor
R753 CK=144 Primes=64 Remain=4 1 algebraic factor

[MyDogBuster]

Reserving S596 and R798 as new to n=25K

[unconnected]

Sierp base 666, CK=231.

Base proven.

Edit: Gary, I have S369, S444 and S666 pages complete MDB

[vmod]

2*869^49149+1 is prime!

Sierpinski base 869 conjecture proven.

[paleseptember]

Originally Posted by rogue

I'll see what we can do, but I'm not too concerned about it.

Cheers Rogue.

Okay, next strange thing (sorry sorry!) Having ran the new-bases-4.3 script to 2500, I have taken the pl_remain file to be the input for srsieve for the next step. First thing srsieve says is:

WARNING: 1600*603^n-1 has algebraic factors.
WARNING: 1600*603^n-1 has algebraic factors.
WARNING: 5476*603^n-1 has algebraic factors.
WARNING: 5476*603^n-1 has algebraic factors.

Do I need to do anything about these two k-values?

[rogue]

Originally Posted by paleseptember

Cheers Rogue.

Okay, next strange thing (sorry sorry!) Having ran the new-bases-4.3 script to 2500, I have taken the pl_remain file to be the input for srsieve for the next step. First thing srsieve says is:

WARNING: 1600*603^n-1 has algebraic factors.
WARNING: 1600*603^n-1 has algebraic factors.
WARNING: 5476*603^n-1 has algebraic factors.
WARNING: 5476*603^n-1 has algebraic factors.

Do I need to do anything about these two k-values?

I'll leave this for someone else to answer. I think the answer is no, but others most likely have better informed opinions

[gd_barnes]

Originally Posted by vmod

2*869^49149+1 is prime!

Sierpinski base 869 conjecture proven.

Nice. Good work vmod. This was one of the bases where only k=2 remained. It will now be removed from the 1k and recommended bases threads.

[gd_barnes]

Originally Posted by paleseptember

Cheers Rogue.

Okay, next strange thing (sorry sorry!) Having ran the new-bases-4.3 script to 2500, I have taken the pl_remain file to be the input for srsieve for the next step. First thing srsieve says is:

WARNING: 1600*603^n-1 has algebraic factors.
WARNING: 1600*603^n-1 has algebraic factors.
WARNING: 5476*603^n-1 has algebraic factors.
WARNING: 5476*603^n-1 has algebraic factors.

Do I need to do anything about these two k-values?

No, nothing NEEDS to be done. One optional thing that you could do is remove all of the even n-values for those k's from the sieve file to save a little bit of testing time. There won't be very many of them but they will be there.

As an explanation: Because those 2 k's are perfect squares, the even n-values will always be composite due to algebraic factors but sr(x)sieve does not know to automatically remove them. It is because x^2-1 factors as (x-1)*(x+1). As a specific example here, when n is even as in 1600*603^(2n)-1, it factors to (40*603^n-1)*(40*603^n+1).


Gary

[MyDogBuster]

Reserving S529 and R696 and S696 as new to n=25K

[gd_barnes]

Per an Email from Mathew, he is at n=18.5K on R703. 24 k's are remaining. Continuing to n=25K.

[MyDogBuster]

Riesel Base 696
Conjectured k = 288
Covering Set = 17, 41
Trivial Factors k == 1 mod 5(5) and k == 1 mod 39(139)

Found Primes: 224k's - File emailed

Remaining: 2k's - Tested to n=25K
152*696^n-1
225*696^n-1

k=169 proven composite by partial algebraic factors2

Trivial Factor Eliminations: 59k's

Base Released