Generating private key/bitcoin address based on a "password"

Generating private key/bitcoin address based on a "password"

Since the private key is basically a random large number, would I be able to pick a password and have that converted into an address?

For example: pick "mysecretpwd". Have it sha256ed, obtain a large integer that is the private key from which I can easily derive the public key and the bitcoin address.

Then for spending any funds received at that address I only need to remember "mysecretpwd", no private key storage on paper, mnemonics or anything, basically the funds are stored in my brain.

What are the security/privacy implications?

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