Old ranges list - Page 4

Xyzzy · 2004-01-19, 01:39

Just for fun, I'm burning through this range, split between two boxes... It is going *very* fast...

cheesehead · 2004-01-19, 20:42

Of course it's going very fast -- there are only a very small number of candidate factors below 2^32 for each exponent in that range, almost all of which will be eliminated by the small-prime sieve before any need for division into the Mnumber.

2^32 = 4,294,967,296.

For p = ~250M, 2p = ~500M. The only 2kp+1 candidate factors below 2^32 are for k = 1,2,3,4,5,6,7,8 and it's unlikely that even one of those will survive the small-prime sieve (e.g., at least two of them must be divisible by 3, at least one by 5, and at least one by 7).

For p = ~500M, 2p = ~1G. The only candidate factors below 2^32 are for k = 1,2,3,4, and the chance that any of them will actually need to be divided into the Mnumber is quite small.

Let us know how many factors you find, and what percentage that is of the total.

Xyzzy · 2004-01-20, 02:26

One box has done from 250M to 290M and has found 175,190 factors so far...

nfortino · 2004-01-20, 02:40

Quote:

Originally posted by Xyzzy
One box has done from 250M to 290M and has found 175,190 factors so far...

That is an impressive 8.5% of the exponents in that range. (Found using http://primes.utm.edu/nthprime/index.php).

bayanne · 2004-01-21, 11:04

Completed and took about 12 days to do on P166.
140199 factors found from 292104 exponents.

michael · 2004-01-29, 18:38

Anyone bothered if i explore this region a little deeper? Say i take the exponents that didn't have a factor up to 50 bits depth and search to 55 orso...

-michael

bayanne · 2004-01-29, 19:41

Quote:

Originally Posted by michael

Anyone bothered if i explore this region a little deeper? Say i take the exponents that didn't have a factor up to 50 bits depth and search to 55 orso...

-michael

How are you going to remove the factors found, and set the parameters for this next search?

I'm interested as would like to do the same on the range I worked through....

michael · 2004-01-29, 22:17

I just use the grep utility Xyzzy talked about in the other thread. Then i edited the text a bit and made the lines in worktodo.ini look like
AdvancedFactor=exponent,exponent,50,56
When i tried Factor=exponent it wouldn't work, perhaps cause the exponent is too big for that command, i wouldn't know.

I already did 185 to 186M and found 2450 new factors (50-56bit depth)

-michael

hbock · 2004-01-29, 23:00

If you just want to remove exponents, ie. to find a first factor, then that's ok. But if you would like to find more (new) factors then it's better to check all (prime) exponents in the higher bit range or even better : start at 33 bit !
In the latter case you will find lots of already known factors (from the first run 28-50) but also a lot of new factors for exponents where the first factor found was pretty small, ie. <=32 bit.

ThomRuley · 2004-02-05, 18:10

I was about to build a new computer, so I can take this range.

ThomRuley

ThomRuley · 2004-02-23, 21:56

Here's an update. I just finished building this computer, and I have already assigned the range 240-250M to my old machine.

2004-01-19, 01:39	#34
Xyzzy Aug 2002 3×43×67 Posts	250M - 500M to 2^32 Just for fun, I'm burning through this range, split between two boxes... It is going very fast...

2004-01-19, 20:42	#35
cheesehead "Richard B. Woods" Aug 2002 Wisconsin USA 17014₈ Posts	Re: 250M - 500M to 2^32 Of course it's going very fast -- there are only a very small number of candidate factors below 2^32 for each exponent in that range, almost all of which will be eliminated by the small-prime sieve before any need for division into the Mnumber. 2^32 = 4,294,967,296. For p = ~250M, 2p = ~500M. The only 2kp+1 candidate factors below 2^32 are for k = 1,2,3,4,5,6,7,8 and it's unlikely that even one of those will survive the small-prime sieve (e.g., at least two of them must be divisible by 3, at least one by 5, and at least one by 7). For p = ~500M, 2p = ~1G. The only candidate factors below 2^32 are for k = 1,2,3,4, and the chance that any of them will actually need to be divided into the Mnumber is quite small. Let us know how many factors you find, and what percentage that is of the total.

2004-02-05, 18:10	#43
ThomRuley May 2003 126₁₆ Posts	240-250M to 2^50 I was about to build a new computer, so I can take this range. ThomRuley

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2004-01-20, 02:26	#36
Xyzzy Aug 2002 21C3₁₆ Posts	One box has done from 250M to 290M and has found 175,190 factors so far...

2004-01-21, 11:04	#38
bayanne "Tony Gott" Aug 2002 Yell, Shetland, UK 2·5·37 Posts	Completed and took about 12 days to do on P166. 140199 factors found from 292104 exponents.

2004-01-29, 18:38	#39
michael Dec 2003 Belgium 5×13 Posts	Anyone bothered if i explore this region a little deeper? Say i take the exponents that didn't have a factor up to 50 bits depth and search to 55 orso... -michael

2004-01-29, 22:17	#41
michael Dec 2003 Belgium 5·13 Posts	I just use the grep utility Xyzzy talked about in the other thread. Then i edited the text a bit and made the lines in worktodo.ini look like AdvancedFactor=exponent,exponent,50,56 When i tried Factor=exponent it wouldn't work, perhaps cause the exponent is too big for that command, i wouldn't know. I already did 185 to 186M and found 2450 new factors (50-56bit depth) -michael

2004-01-29, 23:00	#42
hbock Feb 2003 163 Posts	If you just want to remove exponents, ie. to find a first factor, then that's ok. But if you would like to find more (new) factors then it's better to check all (prime) exponents in the higher bit range or even better : start at 33 bit ! In the latter case you will find lots of already known factors (from the first run 28-50) but also a lot of new factors for exponents where the first factor found was pretty small, ie. <=32 bit.

2004-02-23, 21:56	#44
ThomRuley May 2003 2×3×7² Posts	Here's an update. I just finished building this computer, and I have already assigned the range 240-250M to my old machine.