IBM Ponder This #332 · December 2025

This puzzle was suggested by Giorgos Kalogeropoulos - thanks!

Given a natural number 𝑛, take the first 𝑛 odd primes (3, 5, 7, 11, …) and the first 𝑛 positive even integers (2, 4, …, 2𝑛).

Compute all possible pairwise sums between these two sets (𝑛² sums in total, all odd).

We denote by 𝑓(𝑛) the number of these sums that are prime. For example, 𝑓(5) = 16.

Your goal: Find 𝑓(10⁸).

A bonus "*" will be given for finding 𝑓(10⁹).

Solution

Best opened after a real attempt

To be added.