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`

.

`0 = 0`

`1 = 1`

`110 = 3`

^{1}*2^{1}= 6`100(110)0 = 7*2`

^{base-prime 110}= 7*2^{6}= 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: