307

This number is a prime.

The square of 307 is palindromic.

El Salvador has 307 kilometers of coastline.

307 has period length 1³ + 5³ + 3³.

The Area Code for Wyoming is 307.

The smallest number that is the sum of any set of primes containing all digits: 2 + 5 + 41 + 67 + 83 + 109 = 307. [Gallardo]

In the movie The Odd Couple, when Felix checks into a hotel, the first room the desk clerk tries to assign him is 307. [Litman]

The largest number that you can type in Excel is 9.999 * 10³⁰⁷. If you type in a larger number, Excel will treat it as a character string. [Andrew]

The Grass Roots set a record for being on the Billboard charts 307 straight weeks. This was bound to happen "sooner or later."

Curious Book Shop is a used and rare book store located in downtown East Lansing, Michigan (307 East Grand River Avenue). [Frankovich]

Smallest of the first case of seven consecutive primes that remain prime if you eliminate their first digit. [Loungrides]

Smallest nonpalindromic prime with a palindromic square. The next one is 30001253. [Gaydos]

The smallest prime whose reversal is a Kaprekar number. [Loungrides]

307 permutations of the digits of 2^20 (1048576) are prime numbers. [Gaydos]

Dmitry Kamenetski found that if f(0)=307, then f(n)=3*f(n-1)-574 generates thirteen distinct primes in a row. [Rivera]

If the length of the edges of a rectangular prism are the first three odd primes, then the sum of the lengths of the edges, the area, and the volume = 307. Note that lengths 3 and 7 appear as digits. [Bergot]

307 is the smallest prime for which 2 and 3 are cubic residues. That is, the congruences x^3=2 and x^3=3 mod 307 both have three solutions. [Drost]

307 and its prime index (63) are both reverse triangular numbers. Are there any more examples of this property? [Gaydos]

If the letters in abc * de = fgh * ij each represents a different digit, then 307 is the only 3-digit prime appearing in 307 * 58 = 614 * 29. [Gaydos]

Arnault once found a composite number for which all bases less than 307 are strong liars.

"Family Circus" {tm} comic of October 23, 2022, shows a bedside digital clock display of 3:07.