Electronic Journal of Differential Equations,
Vol. 2011 (2011), No. 123, pp. 1-4.

Title: A note on Sturm-Liouville problems whose spectrum is the 
       set of prime numbers

Author: Angelo B. Mingarelli (Carleton Univ., Ottawa, Ontario, Canada)

Abstract: 
 We show that there is no classical regular Sturm-Liouville
 problem on a finite interval whose spectrum consists of
 infinitely many distinct primes numbers. In particular,
 this answers in the negative a question raised by Zettl in
 his book [9]. We also show that there may
 exist such a problem if the parameter dependence is nonlinear.

Submitted August 9, 2011. Published September 27, 2011.
Math Subject Classifications: 34B05, 34B07, 11Z05.
Key Words: Sturm-Liouville; spectrum; prime numbers