# 331

This number is a prime.

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]

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]

Alexandria, Egypt (birthplace of Euclid) was founded in 331 BC by Alexander the Great. [Hurdman]

331 is the smallest integer n that has the same sums of digits as the nth prime number (2221) and the nth composite number (412). [Gaydos]

331 is a prime formed from the first three digits in the decimal expansion of the square root of eleven. [Akash]

When Alexander the Great prepared to invade deeper into the Persian Empire in 331 BC, a lunar eclipse was observed during the summer and taken as a good omen of success. [Rodgers]

The smallest lucky Honaker number. [Gaydos]

(There is one curio for this number that has not yet been approved by an editor.)