M. Visser

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math.NT2025

Sierpinski's Hypothesis H1

Matt Visser

Sierpinski's Hypothesis H1, formulated in 1958, is the conjecture that (provided $n \geq 2$ ), when the first $n^{2}$ counting numbers, $1, 2, 3, \dots n^{2}$ , are arranged in a square, th…

math.NT2025

Effective short intervals containing primes

Matt Visser

95 years ago Hoheisel proved the existence of primes in the sub-linear interval \[ \left[x, x+x^{1-{1\over 33000}}\right] \qquad \hbox{for $x$ sufficiently large}. \] This was impr…

math.NT2025

Behaviour of the sequence $ϑ_{n} = ϑ (p_{n})$

Matt Visser

The well-known sequence $ϑ_{n} = ϑ (p_{n}) = \sum_{i = 1}^{n} ln p_{i} = ln ([p_{n}] #)$ exhibits numerous extremely interesting properties. Since $p_n = \exp(\varthe…

Sierpinski's Hypothesis H1

Effective short intervals containing primes

Behaviour of the sequence ϑn​=ϑ(pn​)

Behaviour of the sequence $ϑ_{n} = ϑ (p_{n})$