Bases 251-500 reservations/statuses/primes

[Batalov]

One deleted:
64*266^26843-1 is prime.

[henryzz]

S298, CK=183, Two ks remaining.
Primes attached.
Base tested to 25k and released.

[MyDogBuster]

Reserving R273 and R287 as new to n=25K

[gd_barnes]

Originally Posted by Batalov

One deleted:
64*266^26843-1 is prime.

With the proof of R266, this is just the 2nd time that this has happened at CRUS and it is by far the largest base that it has occurred on:

4 consecutive bases in numeric progression have been proven! Riesel bases 263 thru 266 have no k's remaining.

The only other bases to do this are R11 thru R14.

A related 7 consecutive base area is interesting: R8 thru R14. 6 bases are proven (R8, R9, & the 4 bases above) and R10 only has 2 k's remaining. Good but not quite as good is S8 thru S14. 4 are proven, S8, S11, S13, & S14, and the remainder, S9, S10, & S12 all only have one k remaining at various search depths n>=460K.

Also, a related 6 consecutive base area is interesting: R181 thru R186. 3 consecutive are proven, R183 thru R185, and the remainder, R181, R182, and R186 all only have one k remaining at n=100K.

If anyone else spots any unusual base proof oddities, feel free to post them. To be considered interesting, they must be consecutive bases with at least half of them proven and none with more than 3 k's remaining.

[gd_barnes]

Originally Posted by gd_barnes

With the proof of R266, this is just the 2nd time that this has happened at CRUS and it is by far the largest base that it has occurred on:

4 consecutive bases in numeric progression have been proven! Riesel bases 263 thru 266 have no k's remaining.

The only other bases to do this are R11 thru R14.

Well...wouldn't you know it...not more than 2 hours after posting this, I finished up posting and uploading the final few of Mark's multitude of base proofs from a week or so ago and here comes another 4-peat:

Riesel bases 472 thru 475 are proven!

Even better: Riesel base 476 only has one k remaining at n=25K. Prove that one and we're looking at our first 5 in a row! It is far easier to prove than anything else that could make a 5-peat.

Based on that, I think I'll add 49*476^n-1 to the recommended thread.

[gd_barnes]

Added 49*476^n-1 to the recommended bases list for n=25K-100K. The proof of R476 would give us 5 consecutive proven bases in numeric succession for the first time. R472 thru R475 are already proven.

[Batalov]

Based on that, I druther ...reserve R471.

[gd_barnes]

Reserving S428 to n=25K as the final base to complete the Sierp CK=10 and 12 bases.

[unconnected]

Sierp base 500, CK=166.
Primes attached.

Remaining k's:
22*500^n+1
24*500^n+1
29*500^n+1
52*500^n+1
64*500^n+1
65*500^n+1
83*500^n+1
92*500^n+1
116*500^n+1
151*500^n+1
160*500^n+1
164*500^n+1

Base completed to 25K and released.

[10metreh]

S341, CK=20: Complete to 25K and released.
1 k remaining: 10*341^n+1

Primes:

2*341^1+1
6*341^2+1
8*341^1+1
12*341^1+1
18*341^5+1

The rest have trivial factors.

Sorry this took so long.

[Batalov]

R471 didn't give up easily.
3 k remain at n=25K: 144, 302, 408. (lists are attached)

Continuing to n=75K.