# Bulletproofs with ranges not in power of two

I am new to bulletproofs. From what I understand, if I was to do a range proof using bulletproofs, both the start and end number have to be a power of 2.

is there any algorithm/approach which can be used to expand this to numbers that are not powers of 2?

Example: find if a number is in the range 18 to 65?

• You can use an AND statement to do this. Give your number x, prove that (x-18) > 0 AND (65-x) > 0 . Bulletproofs can be used with arithmetic circuits, so you could build the statement above – user69644 Aug 15 '19 at 16:33
• yes, that's it thanks, how do i accept your answer? don't see an option – Pranav kirtani Nov 19 '19 at 9:59
• I added it as an answer – user69644 Nov 19 '19 at 13:44

To prove that x is between a and b , you can prove that (x-a) > 0 AND (b-x) > 0