Puzzle 1268 Primes and e

Problems & Puzzles: Puzzles

Puzzle 1268 Primes and e

On March 16, 2029, Sebastián Martín Ruiz wrote:

Let p(n) the nth prime number

Q1) Prove that Limit n->Infinity (p(n)#)^(1/p(n))=e

* p(n)#=p(1)·p(2)·p(3)·...·p(n) (primorial)

Q2) Prove that Limit n->Infinity Product(ci,ci composite<=n)^(1/p(n))=e