I think

split out between keyspace on puzzle and bitcoin real

1.
keyspace on puzzle
by puzzle each range

2
bitcoin address it can use from number 1 to 2^256
but number under 2^256 is not safety it is risk with  bruteforce attack
like number under 65 bit it is can bruteforce by bitcrack
and number under 115 bit it is can bruteforce by kangaroo
so do not use low bit with bitcoin private key, low bit easy to guess and bruteforce
other not safety  is brainwallet don't use

puzzle use low bit, some part puzzle already solve


3.
bitcoin real use , reference from first bitcoin program from satoshi it use 256 bit number from begin use
may be safety number is between 2^255-2^256
real bitcoin keyspace is 2^256

4.
number over 256 bit when sha256 to use private key is duplicate with number on range 2^256