Primes 1000 3D 02 [A3 size art print]


Shipping to United States: $23.82

If the universe is a mystery it is at least partially because prime numbers are a mystery. Prime numbers are the building blocks of reality. Anything that can be measured or counted is ultimately built out of the irreducible building blocks of prime numbers.

Their secrets have occupied the thoughts - the entire lives - of mathematicians. And though many of those secrets have been yielded up, the mystery remains. Searching for primes is as old as mathematics.

Probably the simplest and earliest method is ‘The Sieve of Eratosthenes’ where the span of integers to be searched has all the even numbers removed first then, successively, those divisible by the next lowest primes, namely 3, 5, 7, 11 and so on. The process continues through the list of the first primes until the next prime is larger than the square root of the largest number in the list being searched. Searching for primes in the first 1000 integers, for instance, means removing multiples of every prime number up to 31 – and no further. Searching for multiples of the next highest prime number, 37, is redundant because the square of 37 is 1369. There will be many numbers between 1 and 1000 which are multiples of 37 but they will have at least one other prime factor which is less than 37 and so will already have been removed.

My design Primes 1008 is based on this approach. Numbers divisible by 2 are not removed but are allocated a colour and, once coloured, are left unchanged. So the number 6, for instance, is coloured as divisible by 2 and is not changed, even though it is divisible by 3 as well. Primes 1008 is designed to be quite highly patterned, revealing simple insights like the fact that all prime numbers nestle next to a number divisible by 6.

This design, Primes 1000, takes a different approach. While still using only the prime numbers up to 31 – for the simple reason that there is a practical limit to the number of colours in a design – the same process of searching takes place but the largest prime factor dictates the colour or shade used. In the case of 30, for instance, it is divisible by the prime numbers 2, 3 & 5. Using the sieve method it would be coloured as a multiple of 2 and then left alone – as if it had been sieved out. For Primes 1000 it would be coloured as a multiple of 5. This results in a less highly patterned – and perhaps more intriguing – design. As an experiment, this version has an added 3D effect.

Whatever process is used to create a design based on primes it will always be enigmatic, suggesting patterns which are either totally misleading or at least partly so. Of course, if you can detect a real predictive pattern which persists beyond the chosen upper limit, your name will never be forgotten – not least because you may well have destroyed the global financial system, whose encryption methods are partly based on the fact that primes are unpredictable.

Designed by David Lawrence, d/dx art prints are created to order on heavyweight Canson Infinity Museum Rag produced at the centuries-old Arches paper mill in France. This superb art board is acid-free and uses no optical brighteners to degrade over time.

Ultrachrome K3 inks provide vivid colours which will last without fading for many decades in normal conditions. The robustness of the paper makes DIY framing a simple matter and frames of the correct size are widely available.

This print is standard European A3 (297 * 420 mm) in size and is unframed. It will be packed flat in a crystal envelope with cardboard stiffener and posted in a rigid protective container.

Shipping & Policies

Payment Methods

  • Accepts Etsy gift cards


We accept credit card, debit card, etsy gift cards, and PayPal payments through Etsy.

Shipping from United Kingdom

We post items wherever possible within 2 working days. Prints are posted in rigid boxes via Royal Mail (First Class within the UK).


Returns & Exchanges

I gladly accept returns and exchanges

Just contact me within: 14 days of delivery

Ship items back to me within: 30 days of delivery

I don't accept cancellations

But please contact me if you have any problems with your order.

The following items can't be returned or exchanged

Because of the nature of these items, unless they arrive damaged or defective, I can't accept returns for:

  • Custom or personalized orders
  • Perishable products (like food or flowers)
  • Digital downloads
  • Intimate items (for health/hygiene reasons)

Returns and exchange details

In the unlikely event that there is a flaw in your print we are happy to exchange it or refund the price on return. In the event of damage in transit, it helps if you can provide photographic or other evidence so that we can claim from Royal Mail.


The colours you are seeing on your monitor are inevitably not precisely the colours you would see if you were looking at the same design in printed form. There is simply no way around that, since the internet places limits on the range of colours that can be displayed and, even if that were not the case, every monitor is subtly (sometimes wildly!) different in the way it displays colours.

But you can be reassured that the quality of our equipment is such that colours and quality are consistent over time and the print you receive will be identical to other prints sold in galleries and art fairs to buyers who have every opportunity to handle and assess them.

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