1. The problem asks for the 6th perfect number. 2. A perfect number is a positive integer that is equal to the sum of its proper divisors (excluding itself). 3. The formula for even perfect numbers is given by $$2^{p-1}(2^p - 1)$$ where $$2^p - 1$$ is a Mersenne prime. 4. The first few Mersenne primes correspond to $$p = 2, 3, 5, 7, 13, 17, 19, 31, ...$$ 5. The first 6 perfect numbers are: - For $$p=2$$: $$2^{1}(2^2 - 1) = 2 \times 3 = 6$$ - For $$p=3$$: $$2^{2}(2^3 - 1) = 4 \times 7 = 28$$ - For $$p=5$$: $$2^{4}(2^5 - 1) = 16 \times 31 = 496$$ - For $$p=7$$: $$2^{6}(2^7 - 1) = 64 \times 127 = 8128$$ - For $$p=13$$: $$2^{12}(2^{13} - 1) = 4096 \times 8191 = 33550336$$ - For $$p=17$$: $$2^{16}(2^{17} - 1) = 65536 \times 131071 = 8589869056$$ 6. Therefore, the 6th perfect number is $$8589869056$$.