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A continuous distribution in which the logarithm of a variable has a normal distribution. It is a general case of Gibrat's distribution, to which the log normal distribution ...

Mills' theorem states that there exists a real constant A such that |_A^(3^n)_| is prime for all positive integers n (Mills 1947). While for each value of c>=2.106, there are ...

The prime number theorem shows that the nth prime number p_n has the asymptotic value p_n∼nlnn (1) as n->infty (Havil 2003, p. 182). Rosser's theorem makes this a rigorous ...

The conjecture that, for any triangle, 8omega^3<ABC (1) where A, B, and C are the vertex angles of the triangle and omega is the Brocard angle. The Abi-Khuzam inequality ...

Geometry

Consider three mutually tangent circles, and draw their inner Soddy circle. Then draw the inner Soddy circles of this circle with each pair of the original three, and ...

When the index nu is real, the functions J_nu(z), J_nu^'(z), Y_nu(z), and Y_nu^'(z) each have an infinite number of real zeros, all of which are simple with the possible ...

Let X_1,X_2,...,X_N be a set of N independent random variates and each X_i have an arbitrary probability distribution P(x_1,...,x_N) with mean mu_i and a finite variance ...

For a bivariate normal distribution, the distribution of correlation coefficients is given by P(r) = (1) = (2) = (3) where rho is the population correlation coefficient, ...

Elliptic curve primality proving, abbreviated ECPP, is class of algorithms that provide certificates of primality using sophisticated results from the theory of elliptic ...