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Prime Number Problems

The Prime Puzzles website starts with the Gordon Lee Puzzle, in which a 6 by 6 array of numbers is to be constructed with as many primes hidden in it as possible. The numbers 0 - 9 are used in the array and numbers can be read from the array in any direction (vertically, horizontally or diagonally in both directions). The same type of question can be asked of a hexagonal array.

Problem 1

We have placed digits in each of the triangles that make this hexagon, and can now begin to look for prime numbers. You can read the lines or part of them, in horizontal or diagonal orientation and in both directions.

How many different prime numbers can you find in the arrangement that we have chosen?

 

Problem 2

Using the H-hexagon of side 2 as the base, how can the numbers 0 - 9 be placed in the hexagons to make as many different prime numbers as possible?

Note: There are 37 numbers that can be made from this arrangement of digits. The question is how many of these can be be different prime numbers?

Problem 3

The original Gordon Lee puzzle has 36 positions that need to be filled, and can be shown to generate 187 prime numbers. The T-hexagon of side 2 has spaces for 24 numbers. How many different primes can it be used to generate?