You can think of Solomonoff induction as a weighted set of experts. At each step, each expert makes a prediction, and the overall prediction is the one that get

You can think of Solomonoff induction as a weighted set of experts. At each step, each expert makes a prediction, and the overall prediction is the one that gets the highest total weight. Then the true data comes in, and the weight of each expert is increased or decreased based on whether that expert was right or wrong. And here's the kicker, the experts are all possible prediction programs, initially weighted by 2^-(program length). So yeah, in the long run Solomonoff induction will be at least as good as you at predicting any particular sequence, including prime numbers etc., because your own prediction algorithm is somewhere in the Solomonoff mixture. That also explains why approximating Solomonoff induction takes a huge amount of computation time. It's mostly a theoretical idea.