314

This number is a composite.

Besides being one of the most standard approximations for π (divided by 100), 314² + 1 is prime. [Patterson]

The smallest pisemiprime, i.e., a semiprime formed by the initial digits of the decimal expansion of π. The sequence begins 314, 314159265358, 314159265358979323, 3141592653589793238462643383279502, ... . [Najafi]

314 is the first even number in the decimal expansion of π. When halved, we obtain the 37th prime. Note that in the Bible gematria ('wisdom') has a value of 37, indicating that God and π are linked. [Homewood]

  "314" first occurs at Order-13

  9  5  3  5  2  7  1  3  2  2  8  5  0
  4  9  7  6  0  7  1  1  2  4  3  5  5
  0  8  3  2  9  5  4  4  9  4  7  2  5
  8  2  0  4  8  8  2  0  5  9  9  8  9
  1  1  7  1  2  3  9  7  9  7  0  4  0
  2  4  8  9  3  5  1  4  8  2  2  3  6
  8  8  1  7  8  9  3  1  5  3  8  0  4
  4  0  6  1  4  2  6  5  3  8  5  8  4
  8  8  4  6  6  2  6  4  3  3  0  2  8
  1  6  0  9  3  9  9  3  7  5  1  6  3
  1  5  6  2  8  6  2  0  8  9  9  8  9
  1  1  3  2  8  2  3  0  6  6  4  7  0
  7  4  5  0  2  8  4  1  0  2  7  0  1

  [Honaker, 3/14/15 @ 9 PM EST]

Consider an n-by-n Ulam spiral of digits using the decimal expansion of π, as depicted above. Using the standard word search rules (i.e., reading forward or backward along any row, column or diagonal), at what spiral size does the prime number 314159 first appear? Order-421 (solved by Mike Keith). The sequence (starting at n = 1) giving the minimal square size for first appearence of n-digits of π is: 1, 3, 13, 23, 87, 421, 1343, 4639, 21323, ... . An "Ulam Pi-Square" including the 38th term would be picturesque!