Circular Primes
The number, $197$, is called a circular prime because all rotations of the digits: $197$, $971$, and $719$, are themselves prime. There are thirteen such primes below...
-
John Rhodes
-
August 15, 2023
Digit Factorials
$145$ is a curious number, as $1! + 4! + 5! = 1 + 24 + 120 = 145$. Find the sum of all numbers which are...
-
John Rhodes
-
August 15, 2023
Digit Cancelling Fractions
The fraction $49/98$ is a curious fraction, as an inexperienced mathematician in attempting to simplify it may incorrectly believe that $49/98 = 4/8$, which is correct, is...
-
John Rhodes
-
August 15, 2023
Pandigital Products
We shall say that an $n$-digit number is pandigital if it makes use of all the digits $1$ to $n$ exactly once; for example, the $5$-digit number,...
-
John Rhodes
-
August 15, 2023
Coin Sums
In the United Kingdom the currency is made up of pound (£) and pence (p). There are eight coins in general circulation: 1p, 2p, 5p, 10p, 20p,...
-
John Rhodes
-
August 15, 2023
Distinct Powers
Consider all integer combinations of $a^b$ for $2 \le a \le 5$ and $2 \le b \le 5$: \begin{matrix} 2^2=4, &2^3=8, &2^4=16, &2^5=32\\ 3^2=9, &3^3=27, &3^4=81, &3^5=243\\...
-
John Rhodes
-
August 15, 2023
Number Spiral Diagonals
Starting with the number $1$ and moving to the right in a clockwise direction a $5$ by $5$ spiral is formed as follows: 21 22 23 24...
-
John Rhodes
-
August 15, 2023
Quadratic Primes
Euler discovered the remarkable quadratic formula: $n^2 + n + 41$ It turns out that the formula will produce $40$ primes for the consecutive integer values $0...