Hidden symmetry in the primes
An independent research project mapping structure where the prime numbers were thought to be random — through conjecture, computation, and visualisation.
Read the Martini Glass Conjecture · See the field visualisations
What is DaveField?
DaveField treats the integers not as a static list but as a field — a structure that can be grown under simple, symmetric rules and then photographed. Seen this way, the primes stop looking scattered. Twin primes settle into stable lattices. The midpoints between prime pairs line up along clean geometric axes. Patterns that are invisible in a table of numbers become plain in a projection of the field.
The project is the work of Dr Michael Maughan, an independent researcher. It is non-commercial, unfunded, and entirely open: the conjectures, the code, the data, and the images are all here to be examined, tested, and argued with.
The Martini Glass Conjecture
A claim about the midpoints between prime pairs: that they are divisible by twin-prime midpoints in a way that is constrained, not random — tested computationally past 108 with no counterexample.
Read the conjecture →Martini Quartets
Sets of four primes locked into a single symmetry. The largest published example here has a twin midpoint of 5,547 digits, verified with gmpy2 and PFGW. One example is recorded on the PrimePages.
See the quartets →Field Visualisations
Mollweide “starscapes” of twin primes, thermodynamic surfaces, and flythroughs of grown prime crystals — symmetry breaking emerging from perfectly symmetric rules.
Explore the images →