Function primeNumberBands

Prime Number Bands — the prime numbers immediately bracketing each bar:

${prefix}Upper = the smallest prime ≥ high
${prefix}Lower = the largest prime ≤ low
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Appends two columns and no centre — there is no "average prime" to draw, and the bar itself is the middle. Reads high and low, each named by an option defaulting to its DEFAULT_OHLCV name.

What this is

It is a step function of the price level, not a statistic: the bands hold flat while price moves inside a prime gap and jump when it crosses one, so the chart is a staircase that tightens where primes are dense and widens where they are sparse. Nothing about the series' history enters it — two instruments trading at the same price have identical bands.

The corpus lists it (assessment §6.2) and it is perfectly deterministic, which is why it ships; whether the arithmetic of the integers says anything about a market is the reader's business, and this docstring is not going to pretend otherwise. No TA-Lib function and no vendor agreement to match: the definition above (bands that contain the bar) is the one the corpus names, and the oracle is a pure-Python replication over a sieve.

Edges

• No warm-up. Each bar's bands come from its own two prices, so row 0 is defined. Length-preserving.
• A price below 2 has no bands and both columns read undefined there. Two is the smallest prime; below it there is nothing to bracket with. That is the whole domain rule, and it is the kernel's — see kernels/prime.ts. Above Number.MAX_SAFE_INTEGER likewise: past 2⁵³ a double no longer names consecutive integers.
• Non-integer prices are the normal case and nothing rounds them: the upper band searches up from ceil(high), the lower down from floor(low).
• Neither scale- nor shift-equivariant, and that is not a defect. Doubling every price does not double the bands (the primes near 2p are not twice the primes near p), and adding a constant does not translate them. This is the only study in the package with no homogeneity property at all, and the property tests assert the absence — that scaling and shifting both genuinely move the reading off the transformed one — rather than skipping the check.
• The bands always contain the bar when low ≤ high, by construction, and the upper band is ≥ the lower whenever both exist. Redirecting high/low at crossed columns can invert them; nothing reorders.
• A gap in either input costs that column on that bar only.
• Cost grows with the price LEVEL, not the series length — the one operator here that does, and steeply. Measured at 1M bars: 78 ms at ordinary equity prices, 6.5 s at ~1e7, and per bar 7.7 ms at ~1e12 and 290 ms at ~1e15 (see the kernel's table; ~1e9 is the practical ceiling). Know that number before running this over a high-priced instrument at scale; the kernel's cost note explains why there is no sieve and what would change that.