# 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]

(There are 7 curios for this number that have not yet been approved by an editor.)