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# The factor problem

let us denote each number as the product of primes in a special way; for example
{2 3 5 7 11 ...}
{2 0 0 1 ...}
represents 28. (line up the primes in the first parentheses with the second one)
notice that in the prime factorization of 28, there a two 2's and one 7.
now, a further observation is that whenever we multiply two numbers, we add the number of each prime in that representation. for example 28 = [2 0 0 1] and 4 = [2 0 0 ...]. when we multiply them, we get 112 which is equal to [ 4 0 0 1]. similarly, when we raise a number to a power, we multiply each number in that "prime table" by that exponent. for example, 28^2 = [4 0 0 2], which is equal to 2x[2 0 0 1]. to summarize, multiplying numbers implies adding the corresponding prime tables and exponentiation of a number to a power implies multiplying every number in the prime table by the exponent.

now, the question is what addition of numbers translate to in the prime tables. all answers are appreciated.

Note by Sri Prasanna
1 year, 6 months ago