magicdragon2 ([info]magicdragon2) wrote,
@ 2004-10-16 12:16:00
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What's Happening Since We Fell into Fall
I've been away from LiveJournal for at least a month, working gruesomely long hours (on top of teaching and research) in writing an Appellate Opening Brief, and filing a late tax return (very complicated when you run several small businesses, have erroneous data from a mortgage company on interest paid, and have a son getting tax credits as tiny rebate for college tuition). But now that I'm back, I'll be catching up.

I've also been very busy submitting and having over 100 accepted and posted on Prime Curios!

In July, we spent a long weekend (along with over 70,000 others) at San Diego Comic-Con.

In late August I started teaching my Fall Semester classes in Intermediate Algebra (2 sections, 55 students) at Woodbury University. My family and I saw, and enjoyed, "Sky Captain and the World of Tomorrow." I coauthored a web page on my silly math discovery:

Eric W. Weisstein et al. "Emirpimes."
From MathWorld--A Wolfram Web Resource.
http://mathworld.wolfram.com/Emirpimes.html


In September, I turned 53 years old (a prime), and my brother Andy turned 51 (an emirpimes, since 51 = 3 x 17, and its reverse 15 = 3 x 5). My wife and I attended CopperCon, in Arizona. I went to a Dodgers-Padres game (before the Dodgers' season sputtered out in early postseason). My 15-year-old son

There's been academic politics galore, but I seem to have won a chunk of a big Federal Grant to rigorously test my innvoative Math teraching methods for 10 weeks in late may 2005-early August 2005, at my consulting rate ($100 to $150 per hours, triple my teaching rate). More on that as it develops.

That's my life in brief: husband, father, brother, teacher, Experimental Mathematician, baseball fan, and giver-of-panels at Science Fiction conventions. It's fun for me, and thank you for letting me share my experiences with you!



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Sorry about my innovative spelling...
[info]magicdragon2
2004-10-16 12:41 pm UTC (link)
Ummmm. "innvoative Math teraching" should read "innovative Math teaching." Sorry about my innovative spelling...

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"Prime Curios" are a matter of Family Values
[info]magicdragon2
2004-10-31 12:21 pm UTC (link)
I'm really enjoying the Prime Curios! web site.

"Prime Curios!" is an exciting collection of curiosities, wonders and trivia related to prime numbers. I have met many folk who could not see the value in stopping to smell a wildflower, collecting a unique coin, or watching the rolling clouds in a spring-time thunderstorm. The old maxim states: "Beauty is in the eye of the beholder." Why not sample a few of our curios and see how our eye compares?

My immediate family has gotten involved in posting to that site. See the listings on the Prime Curios web site:

109 curios about 99 different numbers by Jonathan Vos Post

7 curios about 7 different numbers by Dr. Christine M. Carmichael (mostly about Carmichael Numbers)

2 curios about 2 different numbers by Andrew Carmichael Post

These counts are as of 31 October 2004. The Prime Curios web site had, as of that date, 6403 Prime Curios submitted by 673 submitters.

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Examples of curious facts about Prime numbers
[info]magicdragon2
2004-10-31 01:54 pm UTC (link)
499 is the largest prime whose double is under a thousand. 499^3 = 124251499 which, reversed, is the prime 994152421.

The prime 487 is the sum of three consecutive primes 157 + 163 + 167.

481, is both an octagonal number and a centered square number, the latter because 481 = 15^2+(15+1)^2. Furthermore, 481 = 13 x 37. This latter fact makes 481 a brilliant number, both of whose factors are emirps.

The prime 479 is the sum of 9 (its last digit) consecutive primes (37 + 41 + 43 + 47 + 53 + 59 + 61 + 67 + 71). 479 is also a self number. 479 is a small prime factor of Mersenne(239).

There are 467 (a prime) cyclic numbers < 1000. A cyclic number is an (n-1)-digit integer that, when multiplied by 1, 2, 3, ..., (n-1), produces the same digits in a different order.

The prime 463 is sum of 4 + 6 - 3 = 7 consecutive primes: 53 + 59 + 61 + 67 + 71 + 73 + 79.

The prime 461 is a factor of 20772199, which Carlos Rivera discovered to be the smallest integer where the sum of the prime factors of n and the sum of the prime factors of n+1 both equal 666:

20772199 = 7 x 41 x 157 x 461, and 7+41+157+461 = 666

20772200 = 2x2x2x5x5x283x367, and 2+2+2+5+5+283+367 = 666.

Integers n and n+1 having the same sum of prime factors are the famous Ruth-Aaron pairs. Mike Keith says (20772199, 20772200) is the smallest beastly Ruth-Aaron pair.

The prime 457, sum of three consecutive primes (149 + 151 + 157), is a self number, truncates to 57 in more than one base (it is 557 base 9), and is palindromatic in more than one base as 292 (base 13) = 151 (base 19).

The brilliant number 451 = 11 * 41 appears in the title of Ray Bradbury's classic dystopian novel "Fahrenheit 451."
451 is the 11th decagonal number (11 being a prime factor of 451) and the 12th (11+1) Wedderburn-Etherington number. The reciprocal 1/451 has period 4 + 5 + 1 = 10, and it is the smallest number with this period.

The prime 449 is sum of 5 consecutive primes (79 + 83 + 89 + 97 + 101). Note that 449 concatenates 3 square digits, and the product of those digits 4*4*9 = 144 also concatenates 3 square digits.

441 is a square, a product of squares, and the sum of the cubes of the first six positive integers:
441 = 21^2 = 3^2 x 7^2 = 1^3 + 2^3 + 3^3 + 4^3 + 5^3 + 6^3.

440 Hertz is the standard frequency to which most orchestras tune their A above middle C.

439 is a prime number, the sum of 3 consecutive primes (139 + 149 + 151), and the sum of 9 consecutive primes (31 + 37 + 41 + 43 + 47 + 53 + 59 + 61 + 67). Note that 3^2 = 9, and 439 truncates to the concatenation of a square and 3 and 9.

436 is one of the integers figuring in the smallest number expressible as the sum of two cubes in 3 different ways, namely 87539319, discovered in 1957 by John Leech (1926–1992):

87539319 = 167^3 + 436^3 = 228^3 + 423^3 = 255^3 + 414^3

436 = 2^2 x 109 is the smallest number to be palindromatic in both base 14 and base 15: 436 (base 10) = 232 (base 14) = 1E1 (base 15).

The prime 433 is the 9th star number, which is both a centered 12-gonal number and a centered hexagram (the shape of a Chinese checkers board), satisfying the formula 6N * (N - 1) + 1, in this case for N = 9.

The prime 421, the sum of 4+2-1 consecutive primes (73 + 79 + 83 + 89 + 97), is a centered square number because 421 = 14^2+(14+1)^2. Note that 14^2 uses the same digits as 421.

409 is a prime concatenated from three square digits, as well as the 17th (a prime) centered triangular number. 409^8 = 783044537099820227521 which, upon reversal, is the prime 125722028990735440387.

404 = 2^2 x 101 and thus the product of 3 palindromic primes.
404 is both a nontotient and a noncototient.
404 is well-known to Web users as the HTTP status code for "file not found."

403 is the smallest number to be product of two 2-digit emirpimes:
403 = 13 × 31.
403^2 = 162409 which, upon reversal, becomes the prime 904261.

The prime 401 is a tetranacci number, the sum of seven consecutive primes (43 + 47 + 53 + 59 + 61 + 67 + 71), sum of nine consecutive primes (29 + 31 + 37 + 41 + 43 + 47 + 53 + 59 + 61), and a two-base palindrome as 401 (base 10) = 191 (base 16) = 101 (base 20).
401^2 = 160801 which, upon reversal, becomes the prime 108061.

(Reply to this)


(Anonymous)
2005-06-08 07:39 am UTC (link)
Please, please, please could you shut up occasionally. Moderate yourself. You make me want to avoid my favorite sites because I don't want to read yet more of your postings.

You have some really cool things to say, and I've really apprciate some of them. But it gets absolutely lost in the static. Stop and think "is this neccessary before you post, OK?

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Self-screening
[info]magicdragon2
2005-06-08 08:34 am UTC (link)
I never used to screen myself, but now I have a wife and a son, who outnumber me, and can kick me under the table if I blather on too long at a dinner party.

And I never got that grant anyway. Instead, I got fired for correctly asserting that the Department Chairman was an illiterate unpublishable idiot, who obviously didn't write his own Doctoral Dissertation, which was an Ed.D. anyway, so he was not a Scientist. What was that you said about screening? Hmmmmm....

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