# Al Zimmermann's programming contests

## Primal Squares

### Gordon Lee's puzzle

**Introduction**
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

**The Scoring System**

Part 1: For every distinct prime number, you get one point.

Part 2: For every distinct prime number, you get points equal to the length of the prime number.

For example, a 3 digits prime will give you 3 points.

Every even digit in the grid gives you one extra point.

**The Task**

You must submit grids of sizes 3*3 to 19*19 with the highest possible score.

**Example**:

In the following 3*3 grid:

We can find the following 17 primes:

4 primes with 1 digit: 2, 3, 5, 7

13 primes with 2 digits: 13, 17, 29, 31, 43, 53, 59, 61, 67, 71, 79, 83, 97

There are 4 even digits.

The total score for part 1, n=3, is **17** points

The total score for part 2, n=3, is (4*1)+(13*2)+4 = **34** points

**Total Scoring**
When you submit a grid, its score is automatically computed for both parts.

Both parts are scored independently. If you do not submit for a particular value of N, you will receive a 0 for that value of N.

On both parts, your score for a particular value of N will be equal to your score divided by the best score of any competitor for that value.

Hence the best total score you can get on each part is 17.

**Prizes**

First prize for each part is **125$**,
second prize is **75$** and third prize is **50$**.

In case of a tie, the entrant who reached the tied score first wins.