Number theory / Computational certificate
Exact totient trajectory
Start at 400,000,287,233,629. Repeatedly apply φ(n) + 1 until the first prime. This released trajectory takes exactly 104 steps.
φ(n), Euler’s totient function, counts the positive integers up to n that are coprime to n. This explorer presents the released certificate data; a visualization is not a replacement for its verification.
Explore the certificate
Certificate explorer
Use the slider or arrow keys for each exact step; Home and End select the endpoints. The plot’s vertical axis is logarithmic.
400,000,287,233,629
Composite · continue the iteration
- Factorization from the certificate
- 1,399,663 × 285,783,283
- φ(n)
- 400,000,000,050,684
- Next integer: φ(n) + 1
- 400,000,000,050,685
Claim and boundary
Result and scope
The certificate establishes F(400000287233629) = 104 under the first-prime stopping convention. Therefore the supremum of stopping times is at least 104.
This is a pointwise certificate and a lower bound on the supremum; the global Erdős Problem #409 remains open. Different accounting conventions can shift displayed step counts; this page follows the release’s index-0 starting value and index-104 first prime.
Reproducibility
Reproduction
The displayed values come from certificates/F104/trajectory.csv at commit ee62d68d16f187b808c814108fd53881c4e3e614. The embedded CSV preserves the source text; the source file is identified by its Git blob below.
Source Git blob: d8d3c17f12b0b0264a26b22d791c696dca54764b
The browser uses exact integer strings for the numerical details and floating-point coordinates only for drawing the graph. The original release contains the factorization and primality verification programs.
The original verification programs and release repository are not currently public. The exact trajectory is available above for inspection.