I picked up a few movies recently including 'Capricorn One' and 'The Conversation'. I really enjoyed Capricorn One. If you haven't seen it or know anything about it, I would definitely watch it. The more you don't know about the movie, the better it will be. It's fairly old, so you don't have the production quality of today's movies, but the story line was great.
The Conversation had Gene Hackman and Harrison Ford. I had read somewhere it was a good movie, and decided to give it a watch. I was really disappointed. It had a lot of elements that were interesting but was really slow paced and hard to follow. And on top of that, I didn't like the ending - left you wanting much more. I don't recommend it at all, go get Enemy of the State instead.
Sunday, January 27, 2008
Monday, January 21, 2008
13^n mod n = 36
No solution to this problem yet. It has turned out to be harder than 2^n mod n = 465. I'm still expecting to find a solution though so still have some processors dedicated to it. I told Max Alekseyev I was optimistic one would be found soon, he said "Will see ;)"
^_^
One fun thing about having a computational search like this, is checking on your computers after a few hours or in the mornings. After I get up and ready for work, I can't wait to see if the fishing nets caught anything. :)
^_^
One fun thing about having a computational search like this, is checking on your computers after a few hours or in the mornings. After I get up and ready for work, I can't wait to see if the fishing nets caught anything. :)
Septoplasty results
Great news!
The surgery went better than expected. I had read a lot of horror stories with bad experiences / results, but none of those things occurred. Re-counting some of this on the blog, so other people considering or going through the surgery can use as a reference (of course each person's situation will be different, but good to have more information around). For those of you not interested in gory details, skip this post :)
My surgery was with Dr. LoveJoy through a Charlotte ENT office and the surgery was done at Carolina's Medical Center, University area.
I took the general aesthesia really fast - seemed like ~5 seconds. I woke up feeling groggy but no pain. They had gauze under my nose (taped horizontally to my cheeks), since it would be bleeding for the next 24-48 hours. Even though it was bleeding and there was swelling, I could already tell a difference in air-flow through the previously blocked nostril.
I had my wife pick me up and they gave me Hydrocodone pills for pain if needed. The nose and my upper lip were pretty sore and sensitive. The nose was expected but not the upper lip, it was kind of like numb from coming back from the dentist and I couldn't smile normally without discomfort. I could tell I would need to take it easy eating. Although there wasn't much in the way of pain/discomfort as long as you didn't touch it, the first day was the worst just from feeling lousy -- constant nose bleed, a bandage taped to your face, and breathing through your mouth.
Breathing through your mouth doesn't sound that bad, but it turned out to be pretty uncomfortable - your mouth gets really dry and especially after sleeping.
The 2nd day was like the first but I felt a lot better and the bleeding gradually stopped. By the end of the 2nd day, I could take off the bandage until I needed to sleep, and manage it here and ther with tissue if needed. I started to over-estimate myself though, and learned if you 'eat normal' it can start to sting a bit (inside the nose). I quickly went back to taking it easy.
By the 3rd day, I could appear normal to anyone and things were pretty settled. At this stage, it had stopped bleeding, and I could tell I had a lot of caked blood in there. I was able to clean out most of it in the immediate area, but was afraid to "dig inside" because it was still sore and healing, and I figured I'd wait until my first follow-up visit (scheduled 1 week after surgery).
At the follow-up visit, he examined me and said it looked good. There was a lot of caked blood so he put two things in my nose, one of which was a kind of suction (similar to at the dentist). It felt pretty weird, but right after he finished, wow could I breathe through that nostril. I was already content with the improvement I observed before hand, and now was even happier with the results.
He mentioned there was a lot of swelling still and that could take ~3-4 weeks to fully calm down, and I should notice even more improvement. Follow-up visit scheduled 6-weeks from now.
I'm happy with the results. Before the surgery, I couldn't breathe at all through one of my nostrils, and now it feels like I can fully breathe through both.
The surgery went better than expected. I had read a lot of horror stories with bad experiences / results, but none of those things occurred. Re-counting some of this on the blog, so other people considering or going through the surgery can use as a reference (of course each person's situation will be different, but good to have more information around). For those of you not interested in gory details, skip this post :)
My surgery was with Dr. LoveJoy through a Charlotte ENT office and the surgery was done at Carolina's Medical Center, University area.
I took the general aesthesia really fast - seemed like ~5 seconds. I woke up feeling groggy but no pain. They had gauze under my nose (taped horizontally to my cheeks), since it would be bleeding for the next 24-48 hours. Even though it was bleeding and there was swelling, I could already tell a difference in air-flow through the previously blocked nostril.
I had my wife pick me up and they gave me Hydrocodone pills for pain if needed. The nose and my upper lip were pretty sore and sensitive. The nose was expected but not the upper lip, it was kind of like numb from coming back from the dentist and I couldn't smile normally without discomfort. I could tell I would need to take it easy eating. Although there wasn't much in the way of pain/discomfort as long as you didn't touch it, the first day was the worst just from feeling lousy -- constant nose bleed, a bandage taped to your face, and breathing through your mouth.
Breathing through your mouth doesn't sound that bad, but it turned out to be pretty uncomfortable - your mouth gets really dry and especially after sleeping.
The 2nd day was like the first but I felt a lot better and the bleeding gradually stopped. By the end of the 2nd day, I could take off the bandage until I needed to sleep, and manage it here and ther with tissue if needed. I started to over-estimate myself though, and learned if you 'eat normal' it can start to sting a bit (inside the nose). I quickly went back to taking it easy.
By the 3rd day, I could appear normal to anyone and things were pretty settled. At this stage, it had stopped bleeding, and I could tell I had a lot of caked blood in there. I was able to clean out most of it in the immediate area, but was afraid to "dig inside" because it was still sore and healing, and I figured I'd wait until my first follow-up visit (scheduled 1 week after surgery).
At the follow-up visit, he examined me and said it looked good. There was a lot of caked blood so he put two things in my nose, one of which was a kind of suction (similar to at the dentist). It felt pretty weird, but right after he finished, wow could I breathe through that nostril. I was already content with the improvement I observed before hand, and now was even happier with the results.
He mentioned there was a lot of swelling still and that could take ~3-4 weeks to fully calm down, and I should notice even more improvement. Follow-up visit scheduled 6-weeks from now.
I'm happy with the results. Before the surgery, I couldn't breathe at all through one of my nostrils, and now it feels like I can fully breathe through both.
Saturday, January 12, 2008
APA Pool Update
Had a 5-2 race with a 4 in my last APA match. I started out great, but after a break-out shot that hit the 8 in out of turn, everything went to hell in a hurry :) Ended up 4-1 (hill-hill). I had an opportunity to seal the deal, but didn't get out. My opponent made an incredible long bank off the side rail passed the side pockets into the corner to win. Oh well, that's pool. :)
Our team did well though, ending up 3-2 for the night, so we're in great shape.
Our team did well though, ending up 3-2 for the night, so we're in great shape.
GenericPAL program
Here is one of my programs for finding solutions to b^n mod n = c.
http://www.immortaltheory.com/NumberTheory/GenericPAL.zip
http://www.immortaltheory.com/NumberTheory/GenericPAL.zip
Wednesday, January 9, 2008
Upcoming surgery
I have a deviated septum, which makes it hard to breathe through one of my nostrils. I've lived with it all my life, but finally decided to get the surgery done to correct it (septoplasty). I have it scheduled for this coming Monday. Some people say its a very uncomfortable recovery process, but others have had not-so-bad experiences. I'll be asleep for the operation (general anesthesia) while they cut things up inside of my nose (ouch!). I'll probably be 'unpresentable' a few days after, then up to my usual the next week (at least that's my expectation). I'll post some updates here.
First night back at UNCC
I decided to go back to UNCC to finish my computer science degree. I left college early to start work (most programmer jobs don't care about degrees, but about your skillset). The degree will probably be worthless to me from a career perspective since I have a solid background and resume (worked at Microsoft for 7 years, and stay up to date on MS products/technologies). But it's something I want to close out from a past chapter in life.
Tonight was English 1102 "Writing in the Academic Community." Only chosen since it was a requirement for the degree program. Looks like it will be a lot of reading, note taking, and in-class discussion. The instructor is going to center all the material around the U.S. presidential election. We'll see how it goes...
Tonight was English 1102 "Writing in the Academic Community." Only chosen since it was a requirement for the degree program. Looks like it will be a lot of reading, note taking, and in-class discussion. The instructor is going to center all the material around the U.S. presidential election. We'll see how it goes...
Sunday, January 6, 2008
Number Theory Update
I cleaned up my b^n mod n search applications and will be making them available soon (probably this week) in case others wants to use them. I just need to create some Readme.Txt files to go with them, as they may not be intuitive unless you're familiar with the algorithms already.
Home fun
I got a new camera over the week-end, and have been having fun taking pictures of the kids.
Here's the camera I got. It was about $200 at Best Buy. We're really happy with it
http://reviews.cnet.com/digital-cameras/canon-powershot-sd1000-digital/4505-6501_7-32314638.html
My kids have been re-enacting this parody of Harry Potter we saw on the web. It's called "The Mysterious Ticking Noise" If you search on "potter pals" on Google Videos you'll find it and others in the same theme. I got a good video of them singing that one.
Other than that, we've been playing Rock Band off and on (XBox 360 game). My 4 year old's favorite song now is "Mississippi Queen". He'll be the microphone, and my daughter on drums. My wife and I usually take the guitar parts. If you haven't seen or played Rock Band or Guitar Hero series, I highly recommend them!
Here's the camera I got. It was about $200 at Best Buy. We're really happy with it
http://reviews.cnet.com/digital-cameras/canon-powershot-sd1000-digital/4505-6501_7-32314638.html
My kids have been re-enacting this parody of Harry Potter we saw on the web. It's called "The Mysterious Ticking Noise" If you search on "potter pals" on Google Videos you'll find it and others in the same theme. I got a good video of them singing that one.
Other than that, we've been playing Rock Band off and on (XBox 360 game). My 4 year old's favorite song now is "Mississippi Queen". He'll be the microphone, and my daughter on drums. My wife and I usually take the guitar parts. If you haven't seen or played Rock Band or Guitar Hero series, I highly recommend them!
8-ball Express and tourney result
Tonight was the first night of our 8-ball express league. We play out of Rack'em in Matthews NC. They run a small Sunday tournament starting a 5pm. I got there a little early to play in it.
They have me down as an "8" in the tournament, so when I played a 2 it was an 8-2 race (ouch!). She got a game on me after 4 racks, she needed only one more and I still needed 4 more. I stayed focused to eventually capture that match and continue on.
I ended up making it to the end on the winner's bracket. I got some breaks here and there - I wouldn't say I got lucky rolls, but didn't get unlucky is how I would describe it. It was late so I offered to split the pot on the final match with a $10 cut in my favor ($95 / $75). He agreed and we paid our tabs and headed home.
While waiting for the loser's bracket to finish, I played another 5 for my league match, a 5-3 race. I was "dialed in" from playing in the tournament and took another 5-0 victory.
They have me down as an "8" in the tournament, so when I played a 2 it was an 8-2 race (ouch!). She got a game on me after 4 racks, she needed only one more and I still needed 4 more. I stayed focused to eventually capture that match and continue on.
I ended up making it to the end on the winner's bracket. I got some breaks here and there - I wouldn't say I got lucky rolls, but didn't get unlucky is how I would describe it. It was late so I offered to split the pot on the final match with a $10 cut in my favor ($95 / $75). He agreed and we paid our tabs and headed home.
While waiting for the loser's bracket to finish, I played another 5 for my league match, a 5-3 race. I was "dialed in" from playing in the tournament and took another 5-0 victory.
Thursday, January 3, 2008
Number Theory Update
I haven't found a solution to 13^n (mod n) = 36 yet, but not without a good bit of searching. I've run the factorization method using ECM, and variants of the prime and line algorithm, including a two-prime version, all without success.
Sometimes that's the case with these equations though, like with 2^n (mod n) = 465. I think that took me about a week with focus on it to find n=164196324252985941533.
It's another open problem whether solutions exist to it. I'm pretty sure they do, but the reason I think some are much harder than others is because of the primes that cannot divide n for specific equations.
In 2^n (mod n) = 465, you can show that if p divides n, then p cannot be 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43. Only when you get to 47 is that a possible prime factor. Because of all these small primes being impossible, you have a huge range of n eliminated, and cause other primes to get eliminated -- when GCD(order2p, log2 of 465 mod p) contains a bad factor.
For 13^n (mod n) = 36, only the primes 23, 53, 79 below 107 are possible divisors of n. So it's not surprising a small solution does not exist (Max Alekseyev reported n must be > 10^17).
Sometimes that's the case with these equations though, like with 2^n (mod n) = 465. I think that took me about a week with focus on it to find n=164196324252985941533.
It's another open problem whether solutions exist to it. I'm pretty sure they do, but the reason I think some are much harder than others is because of the primes that cannot divide n for specific equations.
In 2^n (mod n) = 465, you can show that if p divides n, then p cannot be 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43. Only when you get to 47 is that a possible prime factor. Because of all these small primes being impossible, you have a huge range of n eliminated, and cause other primes to get eliminated -- when GCD(order2p, log2 of 465 mod p) contains a bad factor.
For 13^n (mod n) = 36, only the primes 23, 53, 79 below 107 are possible divisors of n. So it's not surprising a small solution does not exist (Max Alekseyev reported n must be > 10^17).
APA Pool League
Tonight (Thursday) was the first match of our APA 8-ball league team. We play out of the Green Room in Charlotte NC. I'm also in another league (8-ball Express) playing on Sunday nights.
I'm a skill level 7 and went up against a 5 named Mike. This meant I had to win 5 games to his 3. I ended up winning 5-0. Since I won the lag that means I also get a 'rackless patch' for that night. Although I won strong, I had at least two games where it was close (he got down to the 8 but missed).
I'm a skill level 7 and went up against a 5 named Mike. This meant I had to win 5 games to his 3. I ended up winning 5-0. Since I won the lag that means I also get a 'rackless patch' for that night. Although I won strong, I had at least two games where it was close (he got down to the 8 but missed).
Wednesday, January 2, 2008
Problem from Feb 2007
I was looking around for another computational challenge and remembered there was still one left from Feb 2007 in some email correspondence I had with Robert G. Wilson (Bob).
Find a solution to 13^k (mod k) = 36
Background:
Bob was collecting solutions b^k (mod k) and updating the OEIS (Online Encyclopedia of Integer Sequences). He sent an email to me, Alexander Adamchuk, David Wilson, Don Reble, Max Alekseyev, Ryan Propper, and Neil Sloane asking about finding some missing values.
Max and I quickly found values to all the equations except the above one. Max and Ryan followed up with searches to verify least solutions on some of them.
Reference:
http://www.research.att.com/~njas/sequences/A127821
I'm continuing a search for this with one of my machines. I'll make a version of the program I wrote for this (VC++/GMP) available for download soon as well.
Find a solution to 13^k (mod k) = 36
Background:
Bob was collecting solutions b^k (mod k) and updating the OEIS (Online Encyclopedia of Integer Sequences). He sent an email to me, Alexander Adamchuk, David Wilson, Don Reble, Max Alekseyev, Ryan Propper, and Neil Sloane asking about finding some missing values.
Max and I quickly found values to all the equations except the above one. Max and Ryan followed up with searches to verify least solutions on some of them.
Reference:
http://www.research.att.com/~njas/sequences/A127821
I'm continuing a search for this with one of my machines. I'll make a version of the program I wrote for this (VC++/GMP) available for download soon as well.
Recent Number Theory Work
Late December 2007, I came across the following open problem
http://garden.irmacs.sfu.ca/?q=op/does_every_odd_number_coprime_to_its_euler_totient_divides_some_carmichael_number
I had done some earlier work on a related problem and adapted those methods to quickly find solutions to the computational challenge (finding Carmichael numbers that are multiples of 885, 2391, 2517, 2571, 2589, 2595, 2685, 2949).
This was to complete a list that Dr. Gerard P. Michon worked on. After sending those solutions in and corresponding with Gerard and Max Alekseyev through email, we extended the list from 3000-10000 in a short time.
http://home.att.net/~numericana/data/crump.htm
Gerard did the first pass through the list eliminating all the entries where no solution was found with 17 digits or less. I then followed up to fill in the gaps.
I used Visual C++ and the GMP arithmetic library for the programming. You can get one of the programs I wrote for this here:
http://immortaltheory.com/NumberTheory/gmp_michon.zip
It was used primarily for all the 3000-10000 multiples, with the exception of 8805 (it was found with a later program using a different method)
http://garden.irmacs.sfu.ca/?q=op/does_every_odd_number_coprime_to_its_euler_totient_divides_some_carmichael_number
I had done some earlier work on a related problem and adapted those methods to quickly find solutions to the computational challenge (finding Carmichael numbers that are multiples of 885, 2391, 2517, 2571, 2589, 2595, 2685, 2949).
This was to complete a list that Dr. Gerard P. Michon worked on. After sending those solutions in and corresponding with Gerard and Max Alekseyev through email, we extended the list from 3000-10000 in a short time.
http://home.att.net/~numericana/data/crump.htm
Gerard did the first pass through the list eliminating all the entries where no solution was found with 17 digits or less. I then followed up to fill in the gaps.
I used Visual C++ and the GMP arithmetic library for the programming. You can get one of the programs I wrote for this here:
http://immortaltheory.com/NumberTheory/gmp_michon.zip
It was used primarily for all the 3000-10000 multiples, with the exception of 8805 (it was found with a later program using a different method)
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