Distribution of Square-Prime Numbers
نویسندگان
چکیده
For $a \neq 1$ and $p$ a prime, we define numbers of the form $pa^2$ to be Square-Prime (SP) numbers. example, $75 = 3 \cdot 25$; $108 36$; $45 5 9$. These are listed in OEIS as A228056. We study properties these numbers, their distribution/density, also develop few claims on distribution/density. rely computer programs verify some conjectures up large
منابع مشابه
The Distribution of Prime Numbers
The prime number theorem tells us that π(x), the number of primes below x, is ∼ x/ logx. Equivalently, if pn denotes the n-th smallest prime number then pn ∼ n logn. What is the distribution of the gaps between consecutive primes, pn+1 − pn? We have just seen that pn+1 − pn is approximately logn “on average”. How often do we get a gap of size 2 logn, say; or of size 1 2 logn? One way to make th...
متن کاملThe Distribution of Prime Numbers
Preface These notes cover the material for the graduate course with the same title that I taught at the University of Texas at Austin during the Spring 2005 semester. They draw heavily on The Distribution of Prime Numbers by M. Huxley and Multiplicative Number Theory by H. Davenport (as revised by H. L. Montgomery). I also acknowledge the use of notes by Jeff Vaaler and numerous discussions wit...
متن کاملDistribution of generalized Fermat prime numbers
Numbers of the form Fb,n = b 2n+1 are called Generalized Fermat Numbers (GFN). A computational method for testing the probable primality of a GFN is described which is as fast as testing a number of the form 2m−1. The theoretical distributions of GFN primes, for fixed n, are derived and compared to the actual distributions. The predictions are surprisingly accurate and can be used to support Ba...
متن کاملNote on the Distribution of Prime Numbers
1. E. Cartan, " Les groupes reels simples finis et continus ", Ann. Ec Norm., 31 (1914), 263-355. 2; , " Sur certaines formes riemanniennes remarquables des geometries a groupe fondamental simple", Ann. Ec. Norm., t.44 (1927), 345-467. 3. , La thSorie des groupes finis el continus et I'analysis situs, Memorial Sc. Math. 62 (Gauthier-Villars, 1930). 4. C. Chevalley, Theory of Lie Groups (Princet...
متن کاملEvasiveness and the Distribution of Prime Numbers
A Boolean function on N variables is called evasive if its decision-tree complexity is N . A sequence Bn of Boolean functions is eventually evasive if Bn is evasive for all sufficiently large n. We confirm the eventual evasiveness of several classes of monotone graph properties under widely accepted number theoretic hypotheses. In particular we show that Chowla’s conjecture on Dirichlet primes ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Missouri Journal of Mathematical Sciences
سال: 2022
ISSN: ['0899-6180', '1085-2581']
DOI: https://doi.org/10.35834/2022/3401121