For each prime p, let p# be the product of the primes less than or equal to p. We have greatly extended the range for which the primality of n!± 1 and p#± 1 are known and have found two new primes of… Expand

In 1947 Mills proved that there exists a constant A such that bA 3 n c is a prime for every positive integer n. Determining A requires determining an efiective Hoheisel type result on the primes in… Expand

We find two new primes of the first form (6380! + 1, 6917! - 1) and one of the second (42209# + 1). We supply heuristic estimates on the expected number of such primes.Expand

2 dx (log x)2 ∼ 2C2N (log N)2 where C2, called the twin prime constant, is approximately 0.6601618. Using this we can estimate how many numbers we will need to try before we find a prime. In the case… Expand

Abstract. In this paper we consider the Fibonacci Zeta functions ζF (s) = ∑∞ n=1 F −s n and the Lucas Zeta functions ζL(s) = ∑∞ n=0 L −s n . The sequences {Aν}ν≥0 and {Bν}ν≥0, which are derived from… Expand