# 331

Robert Franek wrote a book entitled *The Best 331 Colleges*.

Sound travels just over 331 meters per second in dry (0% humidity) air at zero degrees Celsius. [Necula]

The total population of Rives, Tennessee (the address of one of the authors), as of the 2000 census.

133 331 1333 3331 13333 33331 133333 333331 1333333 3333331 13333333 33333331 composite and prime

The total number of reduced quadratic forms having one class per genus. [Noe]

The United States conducted 331 atmospheric nuclear bomb tests before the test ban treaty of 1962. [McCranie]

331 = 11*13*17-2^2*3*5^2*7, using only the potential prime divisors (with multiplicity) up to the square root; and they use all of them. Can you find an expression for the next prime (337) in such a way? [Wood]

331 is the smallest prime that is good, happy, lucky, and cuban. [Green]

331 = (313) - (3*1*3) + (3^1^3). [Silva]

The only known exponent n such that 83^n-82^n is a (probable) prime. [Hasler]

The first prime to appear in the "commas sequence".

The smallest prime p such that the concatenation of p and p^2 is a Cyclops number (331109561). [Gaydos]

The smallest prime number of lines in a Rhapsody of Homer’s *Odyssey*, i.e. Rhapsody VI. The 331st line of Rhapsody VI of Homer’s Odyssey is: “ἀντιθέῳ Ὀδυσῆι πάρος ἣν γαῖαν ἱκέσθαι”. [Loungrides]

Add the cubes of the digits of p = 331, i.e. 1^3 + 3^3 + 3^3 + 1^3 = 55. Repeat the same steps with 55. It follows that 5^3 + 5^3 = 250, then 2^3 + 5^3 + 0^3 = 133, etc. Is 133 the only reversal of p in the sequence of primes? [Missailidis]

Emmy Noether's doctoral thesis *On Complete Systems
of Invariants for Ternary Biquadratic Forms* contains a
tabulation of a complete system of 331 ternary quartic
covariant forms (degree 4 homogenous polynomials in three
variables). [Beedassy]