The Mysterious Mersennes: Mersenne Primes and Perfect Numbers

Almost all the biggest primes known are Mersenne primes, and every Mersenne prime is an even perfect number. But are there are an infinite number of Mersenne primes, and are there any odd perfect numbers?

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[sphakamisozondi]

My high school teacher defined prime numbers:
"these are numbers that have no factors, they are their own factors"

[joseantoniobarreranunez]

I had never ever thought of finding such an incredible video. Thank you Mr discoverthaths!.

[GeoffryGifari]

if a mersenne prime is defined by mersenne = 2ᵖ-1, can we make an ever bigger prime much faster by putting the new result as the power?
bigger mersenne = 2^(mersenne)-1? after checking for the other conditions

[iwersonsch]

I once heard that if 1 is not counted in the sum, we don't know of any number whose nontrivial divisors add to itself, nor do we know of a proof that there isn't one. Is that still true?