Prime Array
Find the 
Array of single digits which contains the maximum possible number of Primes, where allowablePrimes may lie along any horizontal, vertical, or diagonal line. For 
, 11 Primes are maximal andare contained in the two distinct arrays
giving the Primes (3, 7, 13, 17, 31, 37, 41, 43, 47, 71, 73) and (3, 7, 13, 17, 19, 31, 37, 71, 73, 79, 97), respectively.For the
array, 18 Primes are maximal and are contained in the arrays |  |  | |
 |  | ||
|  |
The best
, 
, and 
prime arrays known were found by C. Rivera and J. Ayala in 1998. They are
which contains 30 Primes,
which contains 63 Primes, and
which contains 116 Primes. S. C. Root found the a
array containing 187 primes:
In 1998, M. Oswald found five new
arrays with 187 primes: | |
 | |
 |
Rivera and Ayala conjectured and Weisstein demonstrated by direct computation in May 1999 that the 30-prime solution for
is maximal and unique. Heuristic arguments by Rivera and Ayala suggest that the maximum possible number of primes in, , and arrays are 58-63, 112-121, and 205-218, respectively.
References
Dewdney, A. K. ``Computer Recreations: How to Pan for Primes in Numerical Gravel.'' Sci. Amer. 259, 120-123, July 1988. Lee, G. ``Winners and Losers.'' Dragon User. May 1984. Lee, G. ``Gordon's Paradoxically Perplexing Primesearch Puzzle.'' http://www.geocities.com/MotorCity/7983/primesearch.html. Rivera, C. ``Problems & Puzzles (Puzzles): The Gordon Lee Puzzle.'' http://www.sci.net.mx/~crivera/puzzles/puzz_001.htm.
Weisstein, E. W. ``Prime Arrays.'' Mathematica notebook PrimeArray.m.
- Ryser Formula
- Rényi's Parking Constants
- Rössler Model
- Saalschützian
- Saalschütz's Theorem
- s-Additive Sequence
- Saddle
- Saddle-Node Bifurcation
- Saddle Point (Fixed Point)
- Saddle Point (Function)
- Saddle Point (Game)
- Safarevich Conjecture
- Safe
- Sagitta
- Saint Andrew's Cross
- Saint Anthony's Cross
- Saint Petersburg Paradox
- Sal
- Salamin Formula
- Salem Constants
- Salesman Problem
- Salient Point
- Salinon
- Salmon's Theorem
- Saltus