#math trivia for #August23: Four substrings of #235 are prime: 2, 3, 5, 23. Find a three-digit number where all six substrings are prime.

— Burt Kaliski Jr. (@modulomathy) August 24, 2013

Let *abc* be a three-digit number. If all six substrings of *abc* are prime, then we must have:

*a*,*b*,*c*are prime*ab*,*bc*are prime*abc*is prime

It follows that *a*, *b* and *c* must each be one of the values 2, 3, 5, or 7. There are thus 16 potential values for each of *ab* and *bc*. However, only four of them are prime: 23, 37, 53, or 73. From these four values we have four potential values for *abc*: 237, 373, 537 and 737. Only of them is prime: 373.

Answer: 373.