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]

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

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