Quick Questions About Primes
(thanks to Tony Gardiner, author of Mathematical Puzzling)
1. Find a prime number which is one less than
a perfect square.
2. Find another prime number which is one
less than a perfect square.
3. Find a prime number which is one more
than a perfect square.
4. Find another prime number which is one
more than a perfect square.
5. Find a prime number which is one less than
a perfect cube.
6. Find another prime number which is one
less than a perfect cube.
7. Find a prime number which is one more
than a perfect cube.
8. Find another prime number which is one
more than a perfect cube.
9. What can you say about n when 2n − 1 is
a prime?
10. What can you say about n when 2n + 1 is
a prime?
A Prime Puzzler
Can you make six prime numbers which together use each of the nine digits 1-9 exactly
once? How many ways can you do this?
Instructions for writeups:
1. State the question in your own words.
2. Describe the process you used in tackling
the problem.
3. State the results you obtained.
4. Propose a related question. You need not
solve your new problem.
Some extensions of the Prime Puzzler
Note: All of these were contributed by students.
• Write five primes using the digits 1 - 9 each
once.
• Make three three-digit primes using the digits 1 - 9 each once.
• How many single-digit primes are there? 2digit? 3-digit? 4-digit? Is there a pattern?
• Write six primes using all nine digits exactly
twice.
A Geometry Puzzler
thanks to Ed Barbeau
By means of two straight cuts, subdivide a
9 × 16 rectangle into three pieces that can be
reassembled into a square.