Help plz

I mouseslipped again... https://www.chess.com/votechess/game/206021 nobody is perfect. Only certain numbers.

A perfect number is a number where the sum of its factors (excluding itself) adds to be the number itself. Perfect numbers are VERY rare, and I only remember the first 4.

6: 1+2+3=6

28: 1+2+4+7+14=28

496: 1+2+4+8+16+31+62+124+248=496

8128: 1+2+4+8+16+32+64+127+254+508+1016+2032+4064=8128

Don't believe me on the last one? Use the calculator!

Look at the two middle factors. 

We can express any perfect number as 2^(n-1)*2^n-1, as long as 2^n-1 is a prime. In order for it to be prime, n must first be a prime. Numbers like 2^n-1 that's a prime is also known as a Mersenne prime. 

List of Mersenne Primes (For 13 numbers): <-- Not a sad face

n|(2^n-1)

1|1 (nope)

2|3 (yep)

3|7 (yep)

4|15 (nope, 3*5)

5|31 (yep)

6|63 (nope, 3^2*7)

7|127 (yep)

8|255 (nope, 3*5*17)

9|511 (nope, 7*73)

10|1023 (nope, 3*11*31)

11|2047 (nope, 23*89)

Wait! Our pattern is broken! I thought as long as n was prime, 2^n-1 is also prime!

Well, what I was trying to say was in order for 2^n-1 to be a Mersenne prime, n must be prime, but even if n is prime, it is not guaranteed 2^n-1 is prime.

12|4095 (nope, 3^2*5*7*13)

13|8191 (yep)

so the next perfect number after that is 4096*8191 ( @Penguin4096 it's 4096 be happy like the number itself). For the record, that is 33550336. These numbers get real big, real fast!

Anyways, may you please join the votechess https://www.chess.com/votechess/game/206021 (I would play Nc5)