ZCubes/Mersenne Primes and Perfect Numbers

Mersenne Primes and Perfect Numbers

Mersenne prime is a prime number that is one less than a power of two. That is, it is a prime number of the form 2n − 1 for some integer n. There are also connected to perfect numbers. The largest known prime number, 282,589,933 − 1, is a Mersenne prime. Finding Mersenne prime and validating it is a computation intensive task. This video demonstrates how to generate Mersenne primes using ZCubes, and will also explore the relationship with Perfect numbers.

Video

Mersenne Primes and Perfect Numbers

Code

a=2n^(1..700);
units.on;
a.$(x=>[x,x-1n,(ISPRIME(x<>n-1n))])
  .filter(r=>r[0][2])

1..10000
  .filter(n=>SUM(PROPERDIVISORS(n))==n)

[3,7,31,127,8191,131071].$(""x*(x+1)/2"")"