Sierp base 6 - team drive #3 - Page 27

Mini-Geek · 2010-12-05, 02:37

I noticed one of these k's is remarkably low weight. k=97131 is so low weight that in my range there are 21 candidates, where the average is ~113. The expected primes per doubling is about 0.0507, or a 4.94% chance.
The chances of finding a prime for this k larger than n=400K and smaller than the current world record prime (which comes to about n=16678234 on this base) is only 24.1%. There aren't even any algebraic factors, it's just low weight naturally. To expect one prime you have to go from n=400K to n=~400G.
Of course, the search would go very quick, relatively for its size, but if you're not lucky it could go on for decades on this one k.

mdettweiler · 2010-12-05, 04:40

Quote:

Originally Posted by Mini-Geek

I noticed one of these k's is remarkably low weight. k=97131 is so low weight that in my range there are 21 candidates, where the average is ~113. The expected primes per doubling is about 0.0507, or a 4.94% chance.
The chances of finding a prime for this k larger than n=400K and smaller than the current world record prime (which comes to about n=16678234 on this base) is only 24.1%. There aren't even any algebraic factors, it's just low weight naturally. To expect one prime you have to go from n=400K to n=~400G.
Of course, the search would go very quick, relatively for its size, but if you're not lucky it could go on for decades on this one k.

Ouch. It's kind of like k=1597 over on the Riesel side in that way, except this one sounds worse.

I suppose it might be an interesting choice for an individual effort for n>400K--maybe take it to 1M or 2M or something on the odd chance of knocking it out early.

Mini-Geek · 2010-12-18, 12:36

390K-400K complete, no primes. Results attached.

mdettweiler · 2010-12-20, 01:32

327K-400K complete, one prime previously reported; results attached.

@Gary: now that everything on this drive is complete up to n=400K, should we start a sieving drive for (say) n=400K-600K?

gd_barnes · 2010-12-20, 09:38

Sieving should rarely be for nmax/nmin < 2. I would suggest n=400K-1M. I'll leave it up to you if you want to start a sieving drive. I'll probably start sieving again on the R6 sieving drive in the next few days and wouldn't work on the S6 drive for a while.

mdettweiler · 2010-12-20, 14:58

Quote:

Originally Posted by gd_barnes

Sieving should rarely be for nmax/nmin < 2. I would suggest n=400K-1M. I'll leave it up to you if you want to start a sieving drive. I'll probably start sieving again on the R6 sieving drive in the next few days and wouldn't work on the S6 drive for a while.

Okay, let's wait until after the R6 sieving drive is done then. (In the meantime, there's plenty of work similar to S6 over in the S/R16 drives.)

gd_barnes · 2011-05-13, 07:05

Sieving for n=400K-1M on this drive has reached P=25T. Optimum depth is P=~115T. It will reach P=65T on June 1st. I anticipate completion by the end of June at which time the drive will resume.

gd_barnes · 2011-05-13, 21:31

Good news here. Lennart is going to do the remainder of the sieving for n=400K-1M to P=115T. I'm sure he'll finish long before I was going to.

gd_barnes · 2011-05-13, 22:10

Quote:

Originally Posted by Mini-Geek

I noticed one of these k's is remarkably low weight. k=97131 is so low weight that in my range there are 21 candidates, where the average is ~113. The expected primes per doubling is about 0.0507, or a 4.94% chance.
The chances of finding a prime for this k larger than n=400K and smaller than the current world record prime (which comes to about n=16678234 on this base) is only 24.1%. There aren't even any algebraic factors, it's just low weight naturally. To expect one prime you have to go from n=400K to n=~400G.
Of course, the search would go very quick, relatively for its size, but if you're not lucky it could go on for decades on this one k.

That is remarkable. I did a little more analysis on this. 97131*6^n+1 has a weight of 250. On the sieve for n=400K-1M to P=25T, there are only 1435 candidates remaining in an n=600K range or 0.24%. Factoring the form to n=100 as shown at http://factorization.ath.cx/index.ph...e=100&format=1 shows that a covering set of [7, 13, 19, 37, 43, 541] leaves only n==(31 mod 36) remaining. If you include the factor of 17, only n==(31, 67, 103 mod 144) remain or 3/144 or 1 out of every 48 k's remaining after eliminating just 7 factors!

An amazingly low weight k!

Lennart · 2011-05-13, 22:49

Quote:

Originally Posted by gd_barnes

Good news here. Lennart is going to do the remainder of the sieving for n=400K-1M to P=115T. I'm sure he'll finish long before I was going to.

ETA May 25.

Lennart

henryzz · 2011-05-14, 09:46

Quote:

Originally Posted by gd_barnes

That is remarkable. I did a little more analysis on this. 97131*6^n+1 has a weight of 250. On the sieve for n=400K-1M to P=25T, there are only 1435 candidates remaining in an n=600K range or 0.24%. Factoring the form to n=100 as shown at http://factorization.ath.cx/index.ph...e=100&format=1 shows that a covering set of [7, 13, 19, 37, 43, 541] leaves only n==(31 mod 36) remaining. If you include the factor of 17, only n==(31, 67, 103 mod 144) remain or 3/144 or 1 out of every 48 k's remaining after eliminating just 7 factors!

An amazingly low weight k!

Add the factor 11 and you are down to 1 out of every 60 k's.

2010-12-05, 02:37	#287
Mini-Geek Account Deleted "Tim Sorbera" Aug 2006 San Antonio, TX USA 17×251 Posts	I noticed one of these k's is remarkably low weight. k=97131 is so low weight that in my range there are 21 candidates, where the average is ~113. The expected primes per doubling is about 0.0507, or a 4.94% chance. The chances of finding a prime for this k larger than n=400K and smaller than the current world record prime (which comes to about n=16678234 on this base) is only 24.1%. There aren't even any algebraic factors, it's just low weight naturally. To expect one prime you have to go from n=400K to n=~400G. Of course, the search would go very quick, relatively for its size, but if you're not lucky it could go on for decades on this one k. Last fiddled with by Mini-Geek on 2010-12-05 at 02:44

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2010-12-20, 09:38	#291
gd_barnes May 2007 Kansas; USA 3³·5·7·11 Posts	Sieving should rarely be for nmax/nmin < 2. I would suggest n=400K-1M. I'll leave it up to you if you want to start a sieving drive. I'll probably start sieving again on the R6 sieving drive in the next few days and wouldn't work on the S6 drive for a while.

2011-05-13, 07:05	#293
gd_barnes May 2007 Kansas; USA 3³·5·7·11 Posts	Sieving for n=400K-1M on this drive has reached P=25T. Optimum depth is P=~115T. It will reach P=65T on June 1st. I anticipate completion by the end of June at which time the drive will resume.

2011-05-13, 21:31	#294
gd_barnes May 2007 Kansas; USA 3³×5×7×11 Posts	Good news here. Lennart is going to do the remainder of the sieving for n=400K-1M to P=115T. I'm sure he'll finish long before I was going to.