Corrigenda: ‘‘Statistics on certain large primes”

Large Sophie Germain primes

If P is a prime and 2P+1 is also prime, then P is a Sophie Germain prime. In this article several new Sophie Germain primes are reported, which are the largest known at this time. The search method and the expected search times are discussed.

Generating large primes

1 A simple paradigm Generating a large prime is an important step in the RSA algorithm. We can generate a large prime by repeatedly selecting a large random integer and testing it for primality. We stop when a prime number is found. Therefore, assume that a large integer n is given, and choose a rational number α < 1 to perform the following algorithm: repeat generate a random integer p ∈ [n α ...

On Certain Large Additive Functions

pα||n α. As usual p will denote primes, pα||n means that p divides n but p does not, and a function f(n) is additive if f(mn) = f(m)+f(n) whenever (m,n) = 1. From the pioneering works of Alladi and Erdős [1]-[2], P. Erdős’s perspicacity and insight have been one of the main driving forces in the research that brought on many results on summatory functions of large additive functions and P (n). ...

Entropy Properties of Certain Record Statistics and Some Characterization Results

In this paper, the largest and the smallest observations are considered, at the time when a new record of either kind (upper or lower) occurs based on a sequence of independent random variables with identical continuous distributions. We prove that sequences of the residual or past entropy of the current records characterizes F in the family of continuous distributions. The exponential and the ...

Searching for Large Elite Primes