Signature series
Sacks Spiral
Mathematics · Prime distribution · 1994
- Original infographic and mathematical visualisations by Simon Tyler
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A prime number art print placing every integer from 1 to 250,000 on a single polar spiral, with 22,044 primes marked in black. Ordered in a list they look like scatter; ordered by square root they fall into long curved arcs.
About this print
About this print
This Sacks spiral art print places every integer from 1 to 250,000 on a single spiral, each number set at a distance proportional to its square root, with one full turn per perfect square. The 22,044 primes among them - 8.82% of the total - are marked in black.
The square-root spacing is what makes the image work. Because every perfect square lands on the same ray, the primes fall into sweeping curves rather than the diagonals of a square spiral, and quadratics that are unusually rich in primes show up as long unbroken arcs. The print holds 2,588 twin-prime pairs, and a largest gap of 86 consecutive composite numbers.
Robert Sacks devised the layout in 1994, working outward from the older Ulam spiral of 1963. Where Ulam used a square grid, Sacks used polar coordinates - the same primes, a different geometry, and a noticeably different picture of how they distribute.
Part of the Signature series of mathematical art prints.
The Signature series
The Signature series
Signature is a collection of mathematical, scientific and infographic visualisations - prime number distributions, evolutionary trees, geological timescales, and other structures that become something unexpected when rendered at print scale.
Each piece begins as a data-driven computational process and is developed into a finished artwork through a combination of custom code and design refinement. The aim is not to illustrate mathematics but to make the underlying structures visible - to find the image that was always inside the data.
The series draws on fields including number theory, evolutionary biology, palaeontology, topology, and information design.
Paper and printing
Paper and printing
All prints are produced to order on 250gsm archival matte paper using pigment-based inks, chosen for colour accuracy and long-term stability.
Each print is rolled in acid-free tissue and shipped in a rigid cardboard tube, sealed for moisture protection, ready for framing on arrival.
Dimensions
Dimensions
Large · 50 × 70 cm · 20 × 28 in
XLarge · 70 × 100 cm · 28 × 40 in
Delivery
Delivery
UK: Free · 3-5 working days
Europe: €8.50 · 3-7 working days · No customs charges
USA & Canada: $8.95 / $12.00 CAD · 5-10 working days
Australia: $14.00 AUD · 5-10 working days
Rest of World: £14.95 · 7-14 working days
All prints are produced to order and dispatched within 1-3 working days. Orders placed before 5pm GMT ship the same day. You'll receive tracking information by email once dispatched.
Orders outside Europe may be subject to local customs charges on delivery - these are the responsibility of the recipient.
Returns
Returns
Returns accepted within 30 days. Email returns@axisophy.com with your order number and we'll provide return instructions.
Return postage is the customer's responsibility except where the print arrives damaged or there's been an error - in which case we'll arrange a replacement or refund immediately, no return needed.