It's interesting to notice that 2784623964023 is a prime number, which very likely is not a coincidence, it's moderately large prime. However, as someone said it's probably to small (0x1098FFBC) to be a direct private key in the ECDSA sense of the word, or "secret exponent" as Brainwallet.org calls it. Such "small" numbers are almost certainly in hash tables of people who brute force private keys and would be collected until now. It may be a part of the custom ECDSA implementation as order of ECDSA curve or something, but writing such a custom implementation would require bigger award then 1 BTC so this may be a blind alley.