The force between two protons increases by a factor of four if the distance between them is cut in half.

Here's why:

* Coulomb's Law: The force between two charged particles is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.

* Protons: Protons are positively charged particles.

* Inverse Square Law: The "inverse square" part of Coulomb's Law means that if you halve the distance, the force increases by a factor of 2², which is 4.

In summary: Cutting the distance between two protons in half results in a fourfold increase in the electrostatic force of repulsion between them.