Subject: Perfect numbers

Hello, I was wondering if you could help me answer a question my pre-algebra teacher asked in class the other day. He asked if we knew what the perfect numbers where.

He told us the first number is 6 the second number is 28 but the third he did not tell us. Do you know what the third perfect number is?


The only known perfect numbers are in the form 2h(2h+1 - 1) where the second factor MUST BE PRIME. (These have been known for over 2000 years. They are called "Euclid numbers" since the proof that such numbers are perfect is in Euclid's ELEMENTS.) The next largest perfect number is 496 (when h = 4), and the next is 8128 (h=6).

Perfect numbers are facinating since they are so easy to define and yet there are questions about them that no one can answer. Among other things, it is not known if there there can be odd perfect numbers; nor is it known if the list of perfect numbers is finite.

Chris and Paul
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