Tuesday, June 03, 2003

123 days to go
Part III: Just go to bed, Dave!


I re-fixed the timestamp. This is mostly a test to see if it worked.

Here's some info on the prime number 313:

One of Donald Duck's auto license plate numbers in the comics. [Haga]
313 (base 10) = 100111001 (base 2). The only 3-digit palindromic prime with this property. Note that 100111001 (base 10) is a prime as well! [Larsen]

The largest known prime that divides a Unitary Perfect number.



The Russian cosmonaut Sergei Krikalev spent exactly 313 days in space aboard the Mir Space Station.

The smallest multi-digit palindromic prime of the form n x phi(n) + 1, where phi(n) is the Euler function. [Russo]

Islam's first battle (The Battle of Badr) against the pagans of Mecca was fought by 313 Muslims, and won. [Daniyal]

Frenicle challenged Wallis to solve x2 - 313y2 = 1. [Beiler]

Elizabeth Haich's book Initiation analyzes the significance of 313 in ancient Egyptology.

313 = 122 + 132. [De Geest]

If 313 people (or ducks for that matter) are chosen at random, then the probability that at least 5 of them will share the same birthday is greater than 50%.

Wood's History of Alameda County, California, published in the decade around the first U.S. centennial, includes 313 men and not one woman! [Haga]

The smallest Weakly prime in base 5. [Duisenberg & Dionne]

313 x 285672 + 1 is prime. [Melo & Gallot]

In Shi'ism, it is believed that "Imam Mehdi" (the ultimate savior of the believers) will appear when there are 313 true and sincere Shia followers in the world. [Daniyal]

313 is the smallest number to appear exactly 3 times in itself factorial (313!). [ten Voorde]

10313 + 313 is prime. [Broadhurst & Titanix]

The Mayan ruin Coba near Tulum in the Yucatan peninsula contains a pyramid that is surrounded by 313 large stones with hieroglyphs. [Haid]

In the movie Somewhere In Time, Christopher Reeve checks into Room 313 of the Grand Hotel. [Haga]

The only 3-digit palindromic prime which is not the sum of consecutive composite numbers. [Russo]

(2^3+1)/3, (2^31+1)/3, (2^13+1)/3, and (2^313+1)/3 are prime. [Aggarwal]

The smallest Happy number which is a multi-digit palindromic prime. [Gupta]

1/313 produces a string of decimals that repeat it self after 312 (one less than itself) decimals. Only 5 of the 3-digit palidromic primes have this ability. [Vatshelle]

313, 313 - 2, 313 - 2*3, 313 - 2*3*5 & 313 - 2*3*5*7 are all prime numbers. [Rivera]

Hope all this works.

dave

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