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I cannot seem to find the formal statement of the theorem if there are infinite perfect numbers in Wikipedia or online. I searched this site but the closest is the generalization of perfect numbers question dealing with group theory.

Where can I find resources relating to the computability aspect of perfect numbers?

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    It is not known whether there are infinitely many perfect numbers.2012-03-31
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    You seem to be asking if there are infinitely many (or an infinite number of) perfect numbers. This is different from trying to define an infinite perfect number.2012-03-31

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