For 2^(p-1)(2^p-1) to be a perfect number we need both p and 2^p-1 to be prime. Since it is not known if there are infinitely many primes of the form 2^p-1 (Mersenne primes) the fact that there are infinitely many primes does not imply that there are infinitely many perfect numbers.
Add new comment
Teo tells us about his work in artificial intelligence, his travels around the world, and how inspiration sometimes strikes in the pub.
Clouds make the weather, yet their detail isn't taken into account in weather forecasts. Artificial intelligence might be able to help.
Predicting the weather is hard. But with more data and computing power becoming available, artificial intelligence may be able to help.
How does your phone know what the weather's going to be like?
How a little insect can cause chaos.