Big numbers, programming contest

[Hugo Pfoertner]

Ed Pegg Jr wrote:
>
[...] 
> 
> NJA and the Seq Fan list helped with defining some interesting
> problem sets.  Now, the Al Zimmermann programming contests have
> returned.  http://www.recmath.org/contest/  Not as sequency as
> the upcoming challenges.  Feel free to suggest any new challenges
> to the discussion board at the site.

At least there should be a sequence showing the first terms of the
Gordon Lee Puzzle, which is part 1 of the contest:

Given a positive integer n, fill the n*n square-grid with digits 0..9
such that as many distinct primes as possible are formed by joining
consecutive digits in any horizontal, vertical or diagonal direction,
forward or backward. Leading zeros are not taken into account.

See also: http://www.primepuzzles.net/puzzles/puzz_001.htm
http://web.archive.org/web/20041019045340/http://www.primepuzzles.net/puzzles/puzz_001.htm 

and "Prime Array" at
http://mathworld.wolfram.com/PrimeArray.html

The first terms starting at n=1 are

1, 11, 30, 63,

a(4)=63 was proved in March 2005 by Mike Oakes. The best currently known
lower bounds for the next terms are a(5)>=116, a(6)>=187, a(7)>=281 and
a(8)>=390. There is little chance that the contest will improve a(5) and
a(6), but we can hope for improvements for the higher terms.

Hugo Pfoertner