Section I.2
Polynomial track
A 9th-degree interpolant through the ten-node core (21, 90, 49, 55, 32, 86, 73, 76, 69, 92). At continuous step n = 11 the vector lands on 11,831 — the next computational target, and the 1419th prime.
f(n)
11,831
Step
11.00
n = 1n = 11
Declared target locked — 11,831.
Ten-node window
| n | Term | f(n) |
|---|---|---|
| 1 | 21 | 21 |
| 2 | 90 | 90 |
| 3 | 49 | 49 |
| 4 | 55 | 55 |
| 5 | 32 | 32 |
| 6 | 86 | 86 |
| 7 | 73 | 73 |
| 8 | 76 | 76 |
| 9 | 69 | 69 |
| 10 | 92 | 92 |
| 11 | target | 11,831 |
Archived expansion
The master record publishes this 9th-degree form. The observatory evaluates the unique interpolant of the ten-node core, which realizes the declared n = 11 target.
f(n) = 109 / 2016n9 − 2147 / 720n8 + 17833 / 240n7 − 112613 / 120n6 + 5218081 / 720n5 − 221975 / 6n4 + 15707743 / 120n3 − 1919869 / 7n2 + 3641328 / 10n − 192822