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.

• 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.