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Patterns in prime pairs
Enumerate a finite case, inspect the method, and keep the larger question open.
v1.0 · 2026-11-03 · Demonstration content
Count before conjecturing
This demonstration enumerates unordered pairs of primes for one chosen even target. Its purpose is to make a finite computation inspectable, with the input, definition, and source available together.
Avoid counting a pair twice
For a target N, the script tests candidates only up to half the target. Each returned pair therefore satisfies p ≤ q.
An intentionally simple method
The primality test checks trial divisors through the integer square root. This is easy to audit for small inputs, though it is not intended as a high-performance implementation.
Read the prime-pair source.
Finite evidence has a boundary
A successful calculation for one target, or even many targets, does not establish a claim about every even integer. The example presents finite results only and makes no proof claim about Goldbach’s conjecture.
Files in this version
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References
- Python math module — Python Software Foundation, n.d.
- Goldbach Conjecture — Eric W. Weisstein, Wolfram MathWorld, 2026
Demonstration content (2026). Patterns in prime pairs. v1.0. Zelnick Research. https://research.zelnick.pw/work/prime-pairs/?version=v1.0
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