Prime Suspects and lucky numbers

Keywords: Fibonnaci Sequence, Mersenne prime, Eratosthenes sieve, Prime number theorem, Markov Chain, Primality test, Lucky numbers

Overall ideas:

• How to represent any sequence $(a_n{)}_{n\in {\mathbb{Z}}^{+}}$ as the spectrum of an Hamiltonian
• Representing the distribution of primes as a Markov Chain

Results shared:

• The energy level for any Hamiltonian satisfies $E_n\le n^2$, with this bound being attained using the Single well.