Bases 251-500 reservations/statuses/primes

[gd_barnes]

Max,

I have now posted all bases <= 360 from my prior k=2 search on the web pages with 3 exceptions that are shown in the details below. Here are the newly posted bases > 250 with some footnotes:

Riesel:
278 (a)
298

Sierp:
257
305 (c)
353 (b)

Footnotes:
(a) Only k=2 is remaining at n=25K.

(b) Two k<>2 remaining at n=10K.

(c) Proven.

More details:

1. All k=2 have been tested to n=25K for bases <= 360 and to n=10K for bases 361-1024.

2. All k<>2 have been tested to n=10K for bases <= 500 and to n=2500 for bases 501-1024. Some straggling bases > 500 with few k's remaining had their k<>2 k's also searched to n=10K.

3. As stated above, there were 3 bases <= 360 not posted. This is because the base conjecture was not done due to a high conjecture. They are: Riesel bases 276 (k=2 prime at n=2484) and 303 (no k=2 prime at n=25K) and Sierp base 287 (k=2 prime at n=5467).

4. There are 19 Riesel bases and 28 Sierp bases with k=2 remaining. To give an idea of how much more difficult it is to find a prime for the higher bases, at n=10K, there were 20 Riesel and 30 Sierp bases remaining. Of those, in the lower half of the bases, i.e. bases <= 512, only 5 Riesel and 10 Sierp bases remained or only 30% of all of bases. At this time, there are only 4 Riesel bases <= 512 remaining. They are: 170, 278, 303, & 383. Only base 383 k=2 is at n=10K. The other k=2 are at n=25K.

5. I ran the base conjectures only where k=2 still remained at n=1500 and the conjecture was reasonable sized. So all of the above will have k=2 remaining or a prime for k=2 at n>1500.

6. Many more bases > 360 still need to be posted. They are extremely low priority and so will be posted when I get in the mood.


Now you have 1 more base with only 1 k remaining at n=25K (or n=10K if k<>2). Another one that you might consider after Sierp bases 101 and 206 that had already been posted is Riesel base 170. It only has 2 k's remaining (also k=8 at n=10K) and is currently the lowest Riesel base that has k=2 remaining at n=25K.

A warning to anyone interested in taking on such high bases: With some possible exceptions, most of these high bases are extremely difficult to find primes for. The size grows far more rapidly than bases <= 32. Even bases in the 20's grow in size much faster than bases <= 10. The good news is that if you search base 300, a prime at n=100K comes in at ~247,000 digits (base 200 at ~230,000). It doesn't take long to get into top-5000 territory.


Gary

[appeldorff]

Reserving Sierp Base 257 (all k's) from n=10K-25K

[appeldorff]

Awesome... starting out with a double post -.- anyway

Sierp base 257 n=10k to n=25k is complete (no primes)

Results attached

[gd_barnes]

Originally Posted by appeldorff

Awesome... starting out with a double post -.- anyway

Sierp base 257 n=10k to n=25k is complete (no primes)

Results attached

Hi Appeldorff. Welcome to Conjectures R Us! If you have any questions, be sure and ask. People are quite helpful and responsive here. The co-admin is out of town right now but I'm usually on a few times each day.

I'll delete your duplicate post.

That was nice and quick work of Sierp base 257! Thanks for posting the results.


Gary

[appeldorff]

I'd like to reserve Sierp base 255 from 5.1k - 25k (all k's)

I already started work on this range but it's still going to take some time

[gd_barnes]

Originally Posted by appeldorff

I'd like to reserve Sierp base 255 from 5.1k - 25k (all k's)

I already started work on this range but it's still going to take some time

Good luck! Since it is a high base, that will be a lot of work. You'll probably want at least a full quad on it, otherwise it will likely take many months.

If you'd like to stop before n=25K, feel free to unreserve it and post the remainder of your sieve file. Eventually someone always tests the bases with available files.


Gary

[mdettweiler]

2*278^43908-1 is prime! (5764.2308s+0.0959s)

Another k=2 conjecture bites the dust.

One thing of note is that the proof of this prime by N+1 took an extremely long time. Even as the only thing running on its core, it still took upwards of 20 seconds just to get to the next 2500-iteration progress mark. As such, I left it running overnight alongside my usual two-core load, which means that in reality it didn't quite take the 5764 seconds shown above (my guess would be about 2/3 of that). Nonetheless, this still is an extremely long time considering that the original PRP test took only 247 seconds. Also, when I went to prove the prime I first accidentally ran an N-1 test instead of N+1, and didn't notice until it went through two runs and was starting on its third; interestingly enough, the N-1 test took only 717 seconds to do two runs.

Anyone know why the N+1 test took so long? Is it something peculiar to do with the high base?

[gd_barnes]

Nice! Now you'll have to take a crack at the lowest Riesel base where k=2 remains and see if you can knock out both k=2 and k=8...base 170. Note: k=8 is at n=10K.

It can vary widely on how long it takes to prove similarly-sized numbers prime. It depends on how many PRP bases it has to go through. If you watch it, you can see how many. It usually takes the same amount of time per base but varies on the number of them. I don't know why this is but I'm pretty sure it has to do with the factorization of P+1 (or P-1 for Sierp).

Congrats on yet another proof! This is becoming old hat.


Gary

[mdettweiler]

Originally Posted by gd_barnes

It can vary widely on how long it takes to prove similarly-sized numbers prime. It depends on how many PRP bases it has to go through. If you watch it, you can see how many. It usually takes the same amount of time per base but varies on the number of them. I don't know why this is but I'm pretty sure it has to do with the factorization of P+1 (or P-1 for Sierp).

I recall that it only did one PRP base, which is why I was confused by this. It seems that only one base with N+1 took many times the amount it took to do TWO bases with N-1.

[Batalov]

Will take Sierp. base 353 to 50K: 1 k down, 1 last k to go.
12*353^20261+1 is prime

[appeldorff]

An update on my Sierp255 reservation:

I am currently at the halfway mark (n=15000). 208 primes found and proven so far. I've attached them to this post.

Also, it appears there is a small typo regarding Sierp base 255. It says there are 547 k's remaining yet there are 548 k's listed.

208 down, 340 to go