Exercise · ZW-PERFECT-NUMBER-008 · ★★☆ Intermediate

If \(2^p-1\) is prime with \(p=7\), which perfect number does Euclid's formula give?

Choose one option.

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  • A. 8128

Explanation

With \(p=7\), \(2^7-1=127\) is prime and \(2^{6}\cdot 127=8128\). The number 254 is \(2\cdot 127\), and 127 is only the Mersenne prime itself.

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Review the concept: Perfect number

A perfect number is a positive integer \(n\) equal to the sum of its proper divisors, those smaller than \(n\); with the divisor-sum function \(\sigma\), the sum of all its divisors is twice \(n\).

\[\sigma(n)=2n\]

More practice problems: perfect number

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