Kevin Ford

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math.NT2024

Primes with small primitive roots

Kevin Ford, Mikhail R. Gabdullin, Andrew Granville

Let $δ (p)$ tend to zero arbitrarily slowly as $p \to \infty$ . We exhibit an explicit set $S$ of primes $p$ , defined in terms of simple functions of the prime factors of $p-…

math.NT2024

Poisson Approximation of prime divisors of shifted primes

Kevin Ford

We develop an analog for shifted primes of the Kubilius model of prime factors of integers. We prove a total variation distance estimate for the difference between the model and ac…

math.NT2024

On the theory of prime producing sieves

Kevin Ford, James Maynard

We develop the foundations of a general framework for producing optimal upper and lower bounds on the sum $\sum_{p} a_{p}$ over primes $p$ , where $(a_{n})_{x /2 < n \leq x}$ is an arbitrary n…

math.NT2023

Long strings of consecutive composite values of polynomials

Kevin Ford, Mikhail R. Gabdullin

We show that for any polynomial $f$ from the integers to the integers, with positive leading coefficient and irreducible over the rationals, if $x$ is large enough then there is a…