Random peaks in perlin noise?

So I know about layered noise, but what I’m trying to achieve is randomly throughout the terrain, big mountains appear. Kind of like in Minecraft, when you come across big mountains. Now I know I could use layered noise like this: zoomed-in noise with high peaks, and then use another layer for details, but all that creates is mountainous terrain. I want a mountain to appear every 1000 to 5000 blocks or so. This might not be possible, but any help/suggestions would be much appreciated!

In Minecraft and similar games this is usually done by using Fractal noise. Specifically, usually fractal simplex noise (simplex is an improvement upon perlin noise.) Fractal noise is basically the layered noise you are talking about. Generally the noise function you use will take settings for number of octaves (layers), frequency, lacunarity and gain.

The frequency is like the overall scale of the largest octave, if you increase the value, your mountain peaks get closer together. Lacunarity is how the frequency changes with each layer. So if the lacunarity is 2, the second octave will be twice as detailed, so might represent big bumps within your mountain. Further octaves will then be more and more fine details. The gain is how much effect each octave has, so with a gain of 0.5, the lumps created by your second octave will be half as tall as the first, so in my example, the first octave creates big, tall, low detail mountain shapes, and the second layer adds smaller, higher detail bumps to the mountain.

Playing with these settings can help you get the type of shapes you are after. There are various implementations of Fractal Simplex noise available online that you can try out. Usually you want settings around my example values, with 3-5 layers, depending on what you are aiming for. Getting the right gain and lacunarity will allow you to essentially control how frequent the big mountains are and how big mountains are compared to flatter areas.