314

This number is a composite.

Single Curio View: (Seek other curios for this number)

  "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!

Submitted: 2026-02-02 14:51:16; Last Modified: 2026-02-05 13:44:43.