# Base-prime numbers system.

Base-prime numeral system is a notation for representing numbers with prime numbers as a base.

Base-prime numbers are encoded with `0`, `1`, `(` and `)` symbols. Each digit of base-prime number must contain either `0`, `1` or braced base-prime number recursively. Each N-th digit in base-prime number corresponds to power of N-th prime number, except of first digit which must be `0` in all base-prime numbers except of `1`.

Examples:
• `0 = 0`
• `1 = 1`
• `110 = 31*21 = 6`
• `100(110)0 = 7*2base-prime 110 = 7*26 = 448`
• `100000000000000000000 = 20-th prime = 71`

The problem of base-prime notation is that we have no effective algorithms to copmare, add, multiply or divide numbers in base-prime notation without converting them to base-ten (i.e. finding exact prime numbers for each digit in base-prime number recursively).

For example guess which number is bigger: `10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000010` or `(1010)0` without finding 97-th prime.

Base-prime number:

Base-ten number: