Prime numbers

article
An introduction to proof by contradiction

An introduction to proof by contradiction, a powerful method of mathematical proof.
article
Public key cryptography

An introduction to coding and decoding messages and the maths behind how to secretly share information.
problem
Some cubes

Age

16 to 18

Challenge level

The sum of the cubes of two numbers is 7163. What are these numbers?
problem
A biggy

Age

14 to 16

Challenge level

Find the smallest positive integer N such that N/2 is a perfect cube, N/3 is a perfect fifth power and N/5 is a perfect seventh power.
problem
Strange numbers

Age

11 to 14

Challenge level

All strange numbers are prime. Every one digit prime number is strange and a number of two or more digits is strange if and only if so are the two numbers obtained from it by omitting either its first or its last digit. Find all strange numbers.
problem
Factor trio

Age

11 to 14

Challenge level

Which of the numbers shown is the product of exactly 3 distinct prime factors?
problem
Prime order

Age

11 to 14

Challenge level

Weekly Problem 24 - 2006
How many of the rearrangements of the digits 1, 3 and 5 give prime numbers?
problem
Little Goldbach

Age

11 to 14

Challenge level

How many of the numbers 1 to 20 are not the sum of two primes?
problem
Prime counter

Age

16 to 18

Challenge level

A short challenge concerning prime numbers.
problem
Em'power'ed

Age

16 to 18

Challenge level

Find the smallest numbers a, b, and c such that: a^2 = 2b^3 = 3c^5 What can you say about other solutions to this problem?