# Hashes as Numbers

• Each hash (32 byte hex string) can be interpreted as a number in the interval [0,1).
  • For example the hash FFFF...FFFF would correspond to 1-2^256 which is almost 1 and
  • the hash 0000...0000 would correspond to 0.
  • Note: A hash cannot correspond to exactly 1 but almost 1.
• For a block header h we denote
  • the verus hash interpreted as a number in [0,1) by X(h) and
  • the triple sha256 hash interpreted as a number in [0,1) by Y(h).
• We define the Janushash number J(h) = X(h)Y(h)^{0.7}.
• Similar to above where we converted a hash to a number we can do the reverse, i.e. interpret J(h) as a hash, this hash is the Janushash but we will never compute it or work with it, instead we will solely consider the number representation J(h). All theory works with numbers, so implementation only needs to convert hashes to numbers, but not numbers to hashes For convenience we will call the Janushash number also Janushash.