malsmath.blogspot.com
Math Research, Tips and Tricks: 04/01/2013 - 05/01/2013
http://malsmath.blogspot.com/2013_04_01_archive.html
Math Research, Tips and Tricks. A224502: Prime numbers (together with one) whose representation in balanced ternary are palindromes. Quite often when I am doing prime number research and/or looking for patterns, I check the various number sequences against OEIS. To see what other algorithms would come up with the same sequence. Usually, every sequence I look for is in there. For example:. And, now that I have published my first sequence to OEIS. For n=5, a(5)=61 and in balanced ternary notation is 1ī1ī1.
malsmath.blogspot.com
Math Research, Tips and Tricks: 10/01/2013 - 11/01/2013
http://malsmath.blogspot.com/2013_10_01_archive.html
Math Research, Tips and Tricks. One of my pet peeves is that we routinely teach kids that things are impossible, unknowable, too complicated, et cetera. Another is when our equations are dirtied with exceptions to rules. One example of this was my implementation of pi. That in turn was based on a modification of the continued fraction library. To be a bit cleaner in the implementation. It bugged me that my implementation of pi. Started with an exception. My numerator at index=0 was 2. What does this mean?
malsmath.blogspot.com
Math Research, Tips and Tricks: Division by Zero
http://malsmath.blogspot.com/2009/04/division-by-zero.html
Math Research, Tips and Tricks. I've been on this kick lately where I have started question some of the basic assumptions I learned in math. things like "you can't easily define pi" or the concept of an "irrational number". Today's philosophical debate is on the idea of division by zero. Now, if there are 5 people, everyone gets 2 pennies. Simple. If there are 3 people, everyone gets 3 pennies and 1 is left on the table. If there are no people, then there is still 10 pennies on the table. So, in essence:.
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Math Research, Tips and Tricks: Primality of 1
http://malsmath.blogspot.com/2009/05/primality-of-1.html
Math Research, Tips and Tricks. When I was in school, I remember them teaching that a prime number was any number divisible by only 1 and itself. Thus, in school, they taught that 1 was prime. Since then, I have noticed that everyone insists that 1 is not prime. Since many of the patterns I find work better with 1 being prime, I decided to try to figure out why the discrepancy. And Zeisel. Derrick Norman Lehmer. S list of primes up to 10,006,721, reprinted as late as 1956,. As stated, is valid, i.e.
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Math Research, Tips and Tricks: Shor's Algorithm
http://malsmath.blogspot.com/2006/12/shors-algorithm.html
Math Research, Tips and Tricks. Pick a random number a. This may be done using the Euclidean algorithm. 8800; 1, then there is a nontrivial factor of N. So we are done. Otherwise, use the period-finding subroutine (below) to find r. Of the following function:. Ie the smallest integer r. Is odd, go back to step 1. 8801; -1 (mod N. Go back to step 1. The factors of N. Subscribe to: Post Comments (Atom). Entities for Symbols and Greek Letters. Table of Mathematical Symbols. The first 15 million primes.
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Math Research, Tips and Tricks: 11/01/2011 - 12/01/2011
http://malsmath.blogspot.com/2011_11_01_archive.html
Math Research, Tips and Tricks. Shor, I’ll do it. I ran into this article. By Scott Aaronson today and thought I would share it. To wet your taste, here's the first sentence of the second paragraph:. Alright, so let’s say you want to break the RSA cryptosystem, in order to rob some banks, read your ex’s email, whatever. Overall, I found it to be a pretty good writeup for the layman. It's a little esoteric when it comes to explaining the QFT, but still - he did a good job. Links to this post.
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Math Research, Tips and Tricks: Slashdot: 47th Mersenne Prime Confirmed
http://malsmath.blogspot.com/2009/06/slashdot-47th-mersenne-prime-confirmed.html
Math Research, Tips and Tricks. Slashdot: 47th Mersenne Prime Confirmed. The new prime, 2 42,643,801 - 1, is actually smaller than the one discovered previously. Subscribe to: Post Comments (Atom). Entities for Symbols and Greek Letters. Table of Mathematical Symbols. The first 15 million primes. The On-Line Encyclopedia of Integer Sequences. Slashdot: 47th Mersenne Prime Confirmed. Why 1 ≠ 2 (and how divide by zero can work). Awesome Inc. template. Powered by Blogger.
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Math Research, Tips and Tricks: Prime digits
http://malsmath.blogspot.com/2009/05/prime-digits.html
Math Research, Tips and Tricks. A coworker made a comment to me Friday about the distribution of digits in prime numbers. He was referring to a recent Slashdot article talking about the first digit in the prime number. But I have never liked thinking of the 1st digit as the far left. I'd prefer to think of the far right digit as digit 0. Can't help it - it's the whole positional notation thing (10 3 10 2 10 1 10 0 . 10 -1 10 -2 etc). So I started looking at the distribution of the primes on the right side.
malsmath.blogspot.com
Math Research, Tips and Tricks: Demystifying pi
http://malsmath.blogspot.com/2013/10/demystifying-pi.html
Math Research, Tips and Tricks. One of my pet peeves is that we routinely teach kids that things are impossible, unknowable, too complicated, et cetera. Another is when our equations are dirtied with exceptions to rules. One example of this was my implementation of pi. That in turn was based on a modification of the continued fraction library. To be a bit cleaner in the implementation. It bugged me that my implementation of pi. Started with an exception. My numerator at index=0 was 2. What does this mean?
malsmath.blogspot.com
Math Research, Tips and Tricks: 08/01/2012 - 09/01/2012
http://malsmath.blogspot.com/2012_08_01_archive.html
Math Research, Tips and Tricks. Solid State Quantum Computer? The Shor quantum factoring algorithm. Has been run for the first time on a solid state device and it successfully factored a composite number. So a few thoughts. Solid state quantum computer? First time on solid state device? No, I don't think so. First time on a quantum computer? According to Wikipedia, many have done that in the last 11 years. 48% of the time isn't of practical use? To our mathematical models ;). Links to this post.