TAS Note: SIMAP has plenty of work

[petrusbroder]

No. I have the books, opened to critical pages, spread over all the flat surfaces of my work area.

I have discovered a simple, forehead-slapping proof of Legendre's Conjecture by using only Andrica's Conjecture.

The proof works the other direction, too. I have a proof of Andrica's Conjecture using only Legendre's conjecture.

Unfortunately, this doesn't prove either one.

I can also show that if a counter-example to either conjecture is found, a counter-example to the other conjecture occurs at the exact same point on the number line.

I'm trying to find out if this lock-step relationship should be published.

Edit: Of course, now I'm trying to prove that the common, counter-example point cannot occur.

Thus a circular proof? Which thus means that it is not a proof at all??
Is there a known relationship between Legendre's and Andrica's conjectures?

 

[petrusbroder]

Ahhh - a quick check in Wikipedia suggests that there may be a link ...

Legendre's conjecture, proposed by Adrien-Marie Legendre, states that there is a prime number between n2 and (n + 1)2 for every positive integer n. The conjecture is one of Landau's problems (1912) and unproven as of 2010.
The prime number theorem suggests the actual number of primes between n2 and (n + 1)2 (sequence A014085 in OEIS) is about n/log(n), i.e. about as many as the number of primes less than or equal to n.
If Legendre's conjecture is true, the gap between any two successive primes would be

. In fact the conjecture follows from Andrica's conjecture. Harald Cramér conjectured that the gap is always much smaller, O(log2p); if Cramér's conjecture is true, Legendre's conjecture would follow. Cramér also proved that the Riemann hypothesis implies a weaker bound of

on the size of the largest prime gaps. Legendre's conjecture implies that at least one prime can be found in every revolution of the Ulam spiral.

And there Rieman comes in ... that sounds familiar ...

 

[Rudy Toody]

Ahhh - a quick check in Wikipedia suggests that there may be a link ...

And there Rieman comes in ... that sounds familiar ...

Thanks, Peter. I hadn't considered Wikipedia as source. Me bad.

I needed Legendre's Conjecture as part of another proof. And, in that proof is a possible explanation for the Riemann critical line = 1/2. Circular reasoning again?

I can easily demonstrate counter-example points, but they are a bit contrived. I am exploring the possibility of using the contrivance in a proof.

I will check out Wikipedia and chase a few links. I may even have to open all the math books to different critical pages.

 

[petrusbroder]

Well, I do not consider Wiki as a source unless I have checked the references and other scientific work. But I do use Wiki as inspiration though ...

 

[Rudy Toody]

Congratulations to Fardringle for his 900,000 milestone.

Congratulations to Peter Trend for his 50,000 milestone.

 

[zzuupp]

Thanks for the stats, RT. Congrats to the milestone makers!

 

[Rudy Toody]

Congratulations to biodoc for his 600,000 milestone.

Congratulations to zzuupp for his 70,000 milestone.

Congratulations to Zokudu for his 40,000 milestone.

 

[Bradtech519]

21 cores crunching for SIMAP for a couple days..

16 Xeon cores

4 AMD Phenom 2

1 Celeron

 

[petrusbroder]

Very nice, Bradtech519!

 

[Bradtech519]

No Problem.. I am burning in some servers to make sure they are stable before operation.. This won't be a full time thing but any little bit helps.. I'm pretty much straight anandtech SIMAP on CPUs and Milkyway for GPU and the occasional CPU work load. When I add too many projects they seem to take over the SIMAP work.

Very nice, Bradtech519!

 

[Rudy Toody]

When I add too many projects they seem to take over the SIMAP work.

Easy to fix:

Log into your SIMAP account,
Select: Preferences for this project by clicking on the link,
Raise the value of resource share and save. (I have 2500 in my setting.)

As each processor contacts the project, this value is downloaded, and SIMAP will get a larger share of the processor's time.

 

[Bradtech519]

Easy to fix:

Log into your SIMAP account,
Select: Preferences for this project by clicking on the link,
Raise the value of resource share and save. (I have 2500 in my setting.)

As each processor contacts the project, this value is downloaded, and SIMAP will get a larger share of the processor's time.

Awesome!! Thanks

 

[Rudy Toody]

Earlier today I checked Free-DC stats for milestones and found none for yesterday.

However, I am back from a full day of RL, and discovered that Petrusbroder has broken into the top 100 users on SIMAP! WTG, Peter!

 

[petrusbroder]

OK, RudyToody, you sent me some time time ago (I don't exactly remember how long time ago, it could have been in 2008) a CPU. The one condition you set was that it would crunch SIMAP once a month.
Would you regard this condition as been fullfilled?

 

[petrusbroder]

Only 136 680 WUs available ... out of over 3 millions. A very good period of crunching. I will probably pass the milestone "1 000 000 credits crunched in 2 months in SIMAP" ...

 

[Rudy Toody]

OK, RudyToody, you sent me some time time ago (I don't exactly remember how long time ago, it could have been in 2008) a CPU. The one condition you set was that it would crunch SIMAP once a month.
Would you regard this condition as been fullfilled?

Yes. Thank you very much! :biggrin:

It's nice to see that some of its neighbors in the basement decided to help it out!

 

[Rudy Toody]

New workunits approx. until end of August

Since today afternoon we are distributing the last series of workunits containing new environmental sequences from CAMERA metagenomes. Probably these will need until the end of August to be calculated, so we will just continue after them with the regular workunits of September.

Thanks to all of you for crunching this large update!
Best,
Thomas 18 Aug 2010 14:47:16 UTC

Wow! SIMAP is too good to us!

 

[petrusbroder]

Hooray! I may get to 1.6 million credits ...

 

[zzuupp]

Wow! SIMAP is too good to us!

Oh yeah, that makes it easy to get a TeAm score of 12M, and maybe more.

 

[petrusbroder]

Yeah, we will do that today .... only 28K left to reach that goal!

 

[Rudy Toody]

Congratulations to petrusbroder for his 1,400,000 milestone.

Congratulations to zzuupp for his 80,000 milestone.

Congratulations to Ken_g6 for his 9,000 milestone.

 

[zzuupp]

so close:
10 TeAm Anandtech 62 69,309 11,999,924 International None

 

[petrusbroder]

Congratulations to TeAm AnandTech's all contributors in the SIMAP project!
The TeAm has passed the 12 Million credits milestone!

 

[Rudy Toody]

Congratulations to TeAm AnandTech's all contributors in the SIMAP project!
The TeAm ahs passed the 12 Million credits milestone!

Ah, I slept right through it, when I should have been on the edge of my seat!

 

[Rudy Toody]

TeAm Anandtech passed 12,000,000 Yay!

Congratulations to Fardringle for his 950,000 milestone. Will he reach one million? Stay tuned.

Congratulations to rabrittain for his 500,000 milestone.

Congratulations to Peter Trend for his 60,000 milestone.

Congratulations to Bradtech519 for his 150,000 milestone.

Congratulations to Zokudu for his 50,000 milestone.