Geodesic
A note on Sturm-Liouville problems whose spectrum is the set of prime numbers
Electronic journal of differential equations, Tome 2011 (2011)
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.
Classification : 34B05, 34B07, 11Z05
Keywords: Sturm-Liouville, spectrum, prime numbers 
@article{EJDE_2011__2011__a91,
     author = {Mingarelli,  Angelo B.},
     title = {A note on {Sturm-Liouville} problems whose spectrum is the set of prime numbers},
     journal = {Electronic journal of differential equations},
     year = {2011},
     volume = {2011},
     zbl = {1231.34045},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2011__2011__a91/}
}
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Mingarelli,  Angelo B. A note on Sturm-Liouville problems whose spectrum is the set of prime numbers. Electronic journal of differential equations, Tome 2011 (2011). http://geodesic.mathdoc.fr/item/EJDE_2011__2011__a91/