# Databases for perfect numbers

So I have been trying to find a database that offers perfect numbers. I need this to help me and a friend with a project that we have been working on for a while involving the odd perfect number conjecture and I haven't had any luck finding any such database. If anybody knows of such a database or could suggest how to get hold of a wide array of perfect numbers that I could then use for analysis, it would be greatly appreciated.

• – sranthrop Mar 8 '15 at 3:36

## 4 Answers

Some links to help you out with finding data:-

There is a few, http://web.mit.edu/adorai/www/perfectnumbers.html and http://www.mersenne.org/primes/ has a note on the sides about perfects

The even perfect numbers are specific multiples of Mersenne primes: if $2^p - 1$ is prime, then $(2^{p - 1})(2^p - 1)$ is a perfect number.

So if you can't find a database of perfect numbers, the next best thing is a database of Mersenne primes, such as this one: http://www.mersenne.org/primes/ (notice that it has a column for perfect numbers).

If you meant to include numbers with abundancy index $$I(x) = \dfrac{\sigma(x)}{x}$$ equal to an integer which is at least $3$, then you can check out The Multiply Perfect Numbers Page, last updated by Achim Flammenkamp on 2014-01-25 19:35 UTC+1.