Let's run the numbers. You're saying 2^{-256} ~ P_rare_day^{365}, so that would make P_rare_day 2^{-256/365} ~ 61%. Not rare at all... If we put P_rare_day at

Let's run the numbers. You're saying 2^{-256} ~ P_rare_day^{365}, so that would make P_rare_day 2^{-256/365} ~ 61%. Not rare at all... If we put P_rare_day at a more realistic 1 in a billion, or ~ 2^{-30}, then it only takes 8.53 rare days in a row...