Both Bitcoin and Ethereum private keys are usually a 256-bit number, isn't it possible to use the same private key for both Bitcoin wallets and Ethereum accounts?
For instance, the Bitcoin wiki states:
In Bitcoin, a private key is usually a 256-bit number (some newer wallets may use between 128 and 512 bits), which can be represented one of several ways. Here is a private key in hexadecimal - 256 bits in hexadecimal is 32 bytes, or 64 characters in the range 0-9 or A-F.
E9 87 3D 79 C6 D8 7D C0 FB 6A 57 78 63 33 89 F4 45 32 13 30 3D A6 1F 20 BD 67 FC 23 3A A3 32 62
Which is (removed the whitespaces):
With MyEtherWallet I generated the corresponding public key for Ethereum:
Now I see not every 256-bit number is a valid ECDSA private key for bitcoin. Can I use the same private key for Ethereum and Bitcoin? Is there a convenient way to generate both the ETH and BTC public key from any 256-bit random number?
This would be a cool way to store Ether and Bitcoin on the same account. Is it possible?