23 December

This number is a prime number. If you treble it and add 16, the result is also prime. Repeating this will give 11 prime numbers in total (including the number itself).

14 December

What is the only palindromic three digit prime number which is also palindromic when written in binary?


Let \(S=\{3n+1:n\in\mathbb{N}\}\) be the set of numbers one more than a multiple of three.
(i) Show that \(S\) is closed under multiplication.
ie. Show that if \(a,b\in S\) then \(a\times b\in S\).
Let \(p\in S\) be irreducible if \(p\not=1\) and the only factors of \(p\) in \(S\) are \(1\) and \(p\). (This is equivalent to the most commonly given definition of prime.)
(ii) Can each number in \(S\) be uniquely factorised into irreducibles?

Show answer & extension


Show me a random puzzle
 Most recent collections 

Advent calendar 2020

Advent calendar 2019

Sunday Afternoon Maths LXVII

Coloured weights
Not Roman numerals

Advent calendar 2018

List of all puzzles


games money elections doubling graphs grids symmetry shape prime numbers clocks unit fractions christmas speed triangle numbers quadrilaterals 2d shapes products sums proportion palindromes quadratics digital clocks time cryptic crossnumbers tiling star numbers cards dodecagons multiplication people maths sport geometry combinatorics probability books floors integration range triangles regular shapes gerrymandering square numbers complex numbers crossnumbers bases sum to infinity coins area scales calculus dominos remainders means integers coordinates dates rugby crossnumber chalkdust crossnumber sequences rectangles odd numbers logic cryptic clues algebra irreducible numbers averages shapes arrows surds mean squares lines partitions crosswords addition balancing ellipses volume factorials perfect numbers planes numbers number factors median pascal's triangle colouring fractions perimeter chocolate chess trigonometry taxicab geometry parabolas multiples advent angles polygons wordplay menace dice hexagons folding tube maps differentiation digits functions probabilty 3d shapes circles square roots cube numbers the only crossnumber spheres percentages routes ave indices division


Show me a random puzzle
▼ show ▼
© Matthew Scroggs 2012–2021