This number is a prime.
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.
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]
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]