TY - JOUR
AU - Werner Hurlimann
PY - 2016/09/06
Y2 - 2022/12/03
TI - First digit counting compatibility II: twin prime powers
JF - Journal of Progressive Research in Mathematics
JA - JPRM
VL - 9
IS - 1
SE - Articles
DO -
UR - http://scitecresearch.com/journals/index.php/jprm/article/view/890
AB - The first digits of twin primes follow a generalized Benford law with size-dependent exponent and tend to be uniformly distributed, at least over the finite range of twin primes up to 10^m, m=5,...,16. The extension to twin prime powers for a fixed power exponent is considered. Assuming the Hardy-Littlewood conjecture on the asymptotic distribution of twin primes, it is claimed that the first digits of twin prime powers associated to any fixed power exponent converge asymptotically to a generalized Benford law with inverse power exponent. In particular, the sequences of twin prime power first digits presumably converge asymptotically to Benfordâ€™s law as the power exponent goes to infinity. Numerical calculations and the analytical first digit counting compatibility criterion support these conjectured statements.
ER -