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Mathematics of Computation
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 ofExpand
Determining Mills' Constant and a Note on Honaker's Problem
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 inExpand
On the primality of n! +- 1 and 2 x 3 x 5 x ... x p +- 1
TLDR
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
Prime Curios!: The Dictionary of Prime Number Trivia
On the primality of n!±1 and 2d3d5cp±1
AN AMAZING PRIME HEURISTIC
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 caseExpand
Powers of Sierpiński Numbers Base b
TLDR
A Sierpiński number is a positive odd integer k such that k · 2 n + 1 is composite for all integers n > 0. Expand
FRACTION EXPANSIONS OF FIBONACCI AND LUCAS DIRICHLET SERIES 2 . Fibonacci-type Zeta Functions
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 fromExpand
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