Visualizing real Bitcoin public keys on an illustrative finite field F₁₀₁ · Enter a private key to shoot your own point
The actual Bitcoin curve is defined as:
y² ≡ x³ + 7 (mod p)
where p = 2²⁵⁶ − 2³² − 977, a 256-bit prime (~1.16 × 10⁷⁷). Real x/y coordinates are integers in [0, p−1], numbers around 78 digits long. You cannot plot that directly.
Each real public key has a 256-bit x-coordinate. To project onto F₁₀₁:
xproj = xreal mod 101
Then look up the precomputed table for a valid y where y²≡x³+7 (mod 101), matching parity from the key prefix (02=even, 03=odd).
Both axes are integers from 0 to 100, the elements of the finite field F₁₀₁. No physical units. The plotted curve is:
y² ≡ x³ + 7 (mod 101)
In real secp256k1, y and −y are both valid (x-axis symmetry). In F₁₀₁ the equivalent is y and 101−y, giving conjugate pairs reflected around y=50.5. That is what the paired vertical dots throughout the plot are.
★ F₁₀₁ is a toy version of the actual ~10⁷⁷-sized field. The reduction exists only so the thing can be drawn.
y² = x³ + 7 (mod 101) · Real pubkeys projected by x mod 101 · Puzzle shots computed via full secp256k1 scalar mult