Using some smart factorisation is probably the quickest way to crack this problem.

3²⁴- 2¹⁶ =

(3¹² + 2⁸)(3¹² – 2⁸) =

(3¹² + 2⁸) (3⁶ + 2⁴)(3⁶ – 2⁴) =

(3¹² + 2⁸) (3⁶ + 2⁴)(3³ + 2²)(3³ – 2²)

(3³ + 2²)(3³ – 2²) = (27 + 4)(27 – 4) = 31 x 23

So we have two prime factors here.

To find more prime factors we’ll need to do some longer calculations.

3⁶ + 2⁴ = 81 x 9 + 16 = 729 + 16 = 745 = 5 x 149

We know that 5 is prime, and a quick check of the divisibility of 149 shows us that this is also prime.

So 5, 23, 31 and 149 are four prime factors of 3²⁴- 2¹⁶.

(There are definitely others! If you find any, let us know your non-tech method!)

Challenge 274: Find Four