Discipline: Mathematics and Statistics
Subcategory: Mathematics and Statistics
Cahron Cross - Prairie State College
Co-Author(s): Jared Morton, University of Illinois, Chicago, IL; Jorge Sanchez, University of Illinois, Chicago
The aim of the research is to investigate the sequence generated by jointly ranking prime reciprocal sums up to the nth prime with ln(ln(n)). The location of the prime-reciprocal sums determine the numbers in the sequence. The objectives are to derive a formula for it and examine its characteristics, namely the differences between consecutive terms, and the differences between said differences. They will be referred to as ‘first differences’ and ‘second differences’. The first differences were proven to tend to infinity. The distribution of the second differences showed interesting patterns, and it was proven that, after the first term, they could never have an absolute value greater than 2. It remains to be determined whether or not this data can tell us something about the distribution of prime numbers. Perhaps, future research will uncover evidence for twin-prime-numbers within the sequence. References: S., D. et al. “Approximate Formulas For Some Functions Of Prime Numbers”. Mathematics Of Computation, vol 17, no. 83, 1963, p. 307. JSTOR. Villarino, M. (2005). Mertens’ Proof of Mertens’ Theorem. Ph.D. Universidad de Costa Rica. Wójtowicz, Marek. “Another Proof On The Existence Of Mertens’S Constant”. Proceedings Of The Japan Academy, Series A, Mathematical Sciences, vol 87, no. 2, 2011, pp. 22-23. Project Euclid.
Funder Acknowledgement(s): Prairie State College ; Dr. Steve Kifowit
Faculty Advisor: Steve Kifowit, SKifowit@prairiestate.edu
Role: I was a key contributor to the proofs for both the first and second differences, as well as the development of the formula for the sequence itself. I also helped with observational analysis of the compiled data.