I have been fascinated with prime numbers ever since I was very young and actually setup a "Sieve of Eratosthenes" long before I ever knew that something like that existed. As I have gotten older and more exposed to methods of evaluating the "primeness" of numbers, I more and more wonder whether the ways that we are taught to count "on our fingers" and the pervasive use of Base-10 number systems affect our ability to actually find and prove theorems on Prime Numbers and Factorization.

Sorry for taking so long to come to my question: Has there been any research into how counting and the human need to find patterns may hinder our ability to determine the best way to factor numbers? Is there a practical approach to overcoming these limitations?

Please forgive me for not being able to express this in a more technical fashion. I am very much an amateur mathematician and have had little formal training in higher mathematics. My background is in computer programming and it seems to me that one of the basic challenges is that the programmer must be able to define and understand a solution before he/she can instruct a computer to do something with it.


I don't think that our use of base 10 to represent numbers has inhibited our factorization algorithms. I don't know of any that use base 10 at all, aside from quick tests for divisibility by small numbers. Pollard's rho, SQUFOF, ECM, the quadratic sieve (single- or multiple-polynomial), and the NFS don't take advantage of decimal.

To answer the question asked: No, I'm not aware of any such research.


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