Video art cycle by Artem Tarkhanov
Artist statement
Aesthetics of formal systems (mathematics, logic, discrete games)

Properties of a rigorous abstract object in the role of an artwork

Paths to a contradiction, infinity, undecidable propositions

Nature of curiosity
beweistheorie I
The first part of the beweistheorie cycle explores turning points in culture in the beginning of the 20th century – modernism in art and foundational crisis in mathematics.

In spite of the different context of these events, they can be compared in terms of an impact to the basis of each field. As a result, art has significantly stepped forward by plenty of new directions but lost grounds of its definition and naming ("what is art"). At the same time similar questions arose, as it seemed, in the most defined field – mathematics. Trying to overcome paradoxes of set theory, mathematicians have developed different approaches to axiomatic systems what eventually made foundations of math uncertain and subjective.

Besides historical parallels, the work could be considered as an autonomous visual system. In this connection a key theme of the video could be described as a search for new methods of symbol construction transformed to rule systems.
Director | Visual art: Artem Tarkhanov
Director of photography | Effects | Color: Andrey Nikolaev
Line producer: Anastasiya Sovashchenko
Music: Plaster (Stroboscopic Artefacts) and Akkord (Houndstooth)
Selected exhibitions and screenings
- Los Angeles Short Film Festival (USA), Best experimental film award
- Euregion Film Festival (Netherlands)

- Nunnery Gallery (London, UK), "Visions" Moving Image Exhibition
- Hong Kong Design Institute, 20th Microwave New Media Arts Festival
- ARFF International (Berlin, Germany), Best experimental film of 2016
- 19th Annual Media Art Festival "Antimatter" (Canada)
- 6th Cineramabc Festival (Balneário Camboriú, Brazil)
- 9th Lviv International Short Film Festival "Wiz-Art" (Lviv, Ukraine)
- CICA Museum (South Korea), "Abstract Mind" Exhibition
- Vienna Independent Film Festival (Vienna, Austria)
- 7th Annual New Media Film Festival (Los Angeles, USA)
- Chromatic Festival 2016 (Canada), Exhibition Program
The video work presents several mathematical questions and original sequences of prime numbers. These questions are more likely of an aesthetic kind since related to the decimal numeral system and can't be an appropriate subject for the professional study (the writing of the number is not related to the number itself). However, there are no claims for an academic research or science art, and the main role here is played by the process of artistic search.

In the video number six is used as a general selected symmetry. And it is possible to consider prime numbers constructed by digits from 1 to 6 only (base-ten).
Sequence of prime numbers in a row
The first question is how often these prime numbers (with digits 1-6) go in a row in the series of all prime numbers.
It turns out that for six-digit prime numbers there is the only one maximum sequence – six times in a row:
562613, 562621, 562631, 562633, 562651, 562663.

What would be the longest sequence of that type for other prime numbers?
Base 10-7-10 iteration process
At the same time prime numbers with digits 1-6 also can be interpreted as numbers in septenary system. And it is possible to generate an iteration process when a prime number in decimal system is converted to septenary system, and if its writing in decimal system is also a prime number, an iteration process continues.
Here is an example for three steps:
(241)10 is prime in base-ten, conversion to base-seven = (463)7
(463)10 is prime in base-ten, conversion to base-seven = (1231)7
(1231)10 is prime in base-ten, conversion to base-seven = (3406)7
(3406)10 is not prime (even), stop.

What would be the longest sequence for this iteration process?
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