smallest_prime_factor

std.elementwise.smallest_prime_factor · Level L4

The smallest prime factor of each n ≥ 2, by trial division (factor_summary).

min{p prime : p | n}

Signature

smallest_prime_factor(n: i64[s]) → i64[s]

Structure

The function as NOVA stores it: one box per input, operation and output, and arrows that carry values. A double border marks another library function this one runs — called once, or by Scan once per element; select it to open that function.

input
operation
constant
call
output

Verification

Signature proven by NOVA’s shape solver, for every size.
Equal to the reference the first factor found by trial division in exact rational arithmetic, on all 40 test cases.
All 149 int64 results are exact: the error is zero.
Interpreter and NumPy backend return bit-identical results.
At float32 too: the 40 test cases rounded to float32, and 40 of them exact, with zero error.

Accuracy in detail

correctly rounded (the int64 nearest the exact value): 100%
bit-equal to the NumPy formula in int64: 100%
largest error, in units in the last place: 0

Identity

Calls

factor_summary

Called by

—

sha256:ad631bd6c724e8bbe7a28f5110139ca5a52537c6ea0c88995c9a7069097d986b

The semantic hash of the graph. It changes when the program changes, and never when only its documentation does.

Control handle

Symbol: Ω:std.elementwise.smallest_prime_factor · Ω:smallest_prime_factor
Pins: sha256:d0e839290d8f390dd51e8feba2eb50bb80c72325afbb92dff706c3535e1af0b7this graph and the 3 it reaches through calls
Evidence: sha256:45856542e642c1c2d4f1dc5a173c09ca6608de489e1eff8173f07a60b4cfe446the hash of its verification record
Needs: no capability: a pure function

Through NOVA’s control layer, the symbol launches this function only while the program still matches what it pins: a change to this graph, or to any graph it reaches, needs a migration first.