Apa itu Bilangan Sempurna?

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The first four perfect numbers: divisor portraits

Euclid–Euler theorem: even perfect numbers ↔ Mersenne primes

n is even perfect  ⟺  n = 2^(p−1) · (2^p − 1)

where 2^p − 1 is a Mersenne prime

Euclid proved the → direction. Euler proved ← . All 51 known perfect numbers are even and come from this formula. Whether odd perfect numbers exist is unknown.

Perfect numbers on a log scale: they grow faster than exponentially

Values shown as log10. Even on a log scale each jump is dramatically larger. The 51st perfect number has over 49 million digits.

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