Sequence A000607 in the Online Encyclopedia of Integer Sequences is the number of partitions of $n$ into prime parts. For example, there are $5$ partitions of $10$ into prime parts: $10 = 2 + 2 + 2 + 2 + 2 = 2 + 2 + 3 + 3 = 2 + 3 + 5 = 3 + 7 = 5 + 5.$ The OEIS gives an asymptotic expression

$$A000607(n) \sim \exp\left(2 \pi \sqrt{\frac{n}{3 \log n}}\right). $$

Numerically, this seems to be wrong even if you take the logarithm of both sides. My conjecture is that

$$\lim_{n \to \infty} \log\left(A000607(n)\right) \bigg/ \left( 2 \pi \sqrt{\frac{n}{3 \log n}} \right) \ne 1.$$

See the following graph:

How might one prove or disprove this conjecture?

For more references please see http://oeis.org/A000607.