Sloane's OEIS: A007697 lists odd numbers with at least n Goldbach representations.
Leonhard Euler observed that as numbers get larger, they have more representations of the form
, suggesting that there may be a largest number with no such representations; i.e., the above list of Stern primes might be not only finite, but complete.
Goldbach once incorrectly conjectured that all Stern numbers are prime.
(See OEIS: A060003 for odd Stern numbers) Christian Goldbach conjectured in a letter to Leonhard Euler that every odd integer is of the form p + 2b2 for integer b and prime p. Laurent Hodges believes that Stern became interested in the problem after reading a book of Goldbach's correspondence.