Monday, September 25, 2006

The 1st week of Sunmart training

My Sunmart training started on the Wednesday, unlike the previous Saturday for most people in the group. I promptly missed the Thursday 5-mile run, of course missed the Friday cross-training and landed up at HOL on saturday morning looking forward to a fun run on the trail again.

Anurag was in town, that and a dentist appointment kept Ani away. Sanjeev and Gaurav were going to do 7mi. Ganesh was planning to do a 7 and 7. Santhosh and myself planned to do the 10 and 7. We started off nicely, quickly got down the HOL, crossed the dam, and made our way up the hill towards the Powerline. Soon there was a fork, and the larger wider road along the right fork was apparently to be avoided. Santhosh promptly went along the wider road, and soon we lost sight of all flags, and came to another fork. Here we again randomly took the right fork, and after some time, voila, there were the flags again. Turned out, although we did not immediately realise, we had done a loop (2 miles) and come back to the start of the hill, right at the dam. Eventually, we meandered and muddled our way through forks, came upon Jim, our saviour for the day, and got to the top of the Powerline after 6miles of running instead of 4. Around then my allergies started acting up. We continued down Hill of Death, across Sculpture Falls, and almost up to 360 and back we came up the Hill of Life. By then I was sneezing incessantly.

I've always breathed through my mouth during running. But today I discovered that breathing only through the mouth, with a fully blocked nose, and continuous sneezing, is not a breezy proposition. As we started our second loop of 7mi, I was fairly out of breath, and had to start walking. That was when I first noticed that Santhosh with his colorful Motive socks, looked like he was wearing Clif Bars on the back of his legs. After a long time, I finally made it to the top of the Powerline. Having by then discovered a pace which kept my breathing steady, although heavy, I decided to run the remaining 3 miles back. At one point Santhosh heard my breathing and likened it to an asthmatic bull dog. All good things of course come to an end, so did the run. The rest of the weekend was spent in bed fighting the damned allergies.

Wednesday, September 20, 2006

And we are off...

The first day of SunMart 50M training. Fairly unsure about running on trails, and sufficiently scared by the laughs of Joe and Steve at the info-session, we joined forces at the head of Hill of Life. Santhosh could not make it since he was with the Half marathon folks, and Ganesh I think had an exam the next day. Gaurav, Ani, Sanjeev and myself started with the rest of the runners and of course Joe. Joe turned out crazier than we had expected, and most of the other runners had run ultras before or at the very least seemed very comfortable with trail running and the Greenbelt trails.

Steve's post had said the workout would involve 20 repeats of 30s-hard-30s-easy intervals. Without a watch, Gaurav and myself started counting (mississippi-ly) and we went past 10 repeats, then 20, then 30, when we decided we had to be lost. At that point we figured the smart thing to do was to conserve energy and water, and we walked some distance. Finally we saw Joe's flags again and made it back to the base of Hill of Life, only to find a smiling Joe who said we ran 6miles, and that Steve sets the workouts, while he, Joe, charts the route!!

All in all, a great start to the training. Trail running is incredible fun. Having run on the roads continuously for more than three years now, I discovered trail running is a whole different ball game. I am sure there are aspects of it which will make it much harder than road running. However, today, trail running was a far far better fun run than most road runs.

Wednesday, September 06, 2006

a new Mersenne prime

A new Mersenne prime was discovered a few weeks ago, the largest prime number discovered to date --- "2 raised to the 30,402,457th power minus 1".

Mersenne primes are a special category of primes expressed as 2 to the "p" power minus 1, in which "p" also is a prime number. The theorems around mersenne primes turn out to be so aesthetic, that they had to have "come straight from the book". :)

Mersenne primes have a very interesting history:
[a] pre 1532
Mathematicians conjectured that all (2^n - 1) were primes for every prime n.

[b] 1532
Regius proved that (2^11 - 1) was not a prime.

[c] 1600
Cataldi proved (2^17 - 1) and (2^19 - 1) were both primes and conjectured that the theorem was true for primes 23, 29, 31, and 37.

[d] 1640
Fermat proved Cataldi was wrong about 23 and 37.

[e] 1644
Mersenne conjectured the theorem was true for primes 2, 3, 5, 7, 13, 17, 19, 31, 61, 127 and 257 and false for any other prime less than 258.

[f] 1947
It took excess of 3 centuries for folks to come to a mathematical conclusion about Mersenne's conjecture. Turned out, his conjecture was pretty close. He was right about all this primes, and had missed out 89 and 107. Took a lot of mathematicians, from Euler to our very own Ramanujam to verify Mersenne's theorem.

Subsequently, various folks have come up with tests for checking primality based on Mersenne primes (including the non-exponential primality test from IIT Kanpur) and with all the computing power available for brute force testing, what was discovered recently was the 43rd Mersenne prime.

Back in 1965 or so, math dept of Urbana cracked the Mersenne prime for n=11213. They were so kicked, they made a stamp out of it and would imprint it on all postal letters going out of the Urbana math dept (see below). This of course lasted until 1976 when Urbana math dept cracked the four-color theorem and proved it correct. After that for a while, the four-color theorem was on the envelopes.

More details about Mersenne Primes here

fun stuff.