PFACTOR Function (Gnumeric)

• Introduced: Gnumeric 1.3.92 release notes explicitly record the addition.
• Supported in: Gnumeric 1.12.62; no retirement is established.
• Scope: Desktop Gnumeric with its Number Theory plugin. English comma-separated formulas are shown.
• Checked: October 14, 2026. Tables and the named advanced check were recalculated with 1.12.57 ssconvert. Current 1.12.62 source was inspected; the later release was not executed.

PFACTOR returns the smallest prime that divides its input integer. For 57, it returns 3 because 57=3×19 and no smaller prime divides 57. A prime input returns itself, so PFACTOR(97) is 97. Versioned function help.

=PFACTOR(n)

n is one required numeric argument. The implementation floors it, then requires at least 2. This is stricter than the positive-domain convention of some other number-theory functions: PFACTOR(1) is an error. A fractional input 9.9 is treated as 9 and returns 3.

Current implementation.

These eight native integer results were independently checked by binary arithmetic or elementary number theory.

For an integer in A2, =PFACTOR(A2) gives one factor and =A2/PFACTOR(A2) gives the complementary quotient. For 91, the smallest prime factor is 7 and the quotient is 13. The native check =MOD(91,PFACTOR(91)) returned 0, confirming divisibility.

That quotient is not guaranteed to be prime. For 60, removing the smallest prime factor 2 leaves 30, which is still composite. The function provides a first factorization step rather than a complete list of prime factors.

Repeatedly dividing by the returned smallest factor can construct a factorization for small validated integers. For 12, the steps are 12→6→3→1 with factors 2, 2 and 3. Stop at 1; calling PFACTOR again would be outside its domain.

For a valid integer n at least 2, a result equal to n indicates n is prime. The source searches candidate primes through the square-root boundary. Large prime inputs can require more work than small composites that have an early factor. The ordinary tables do not benchmark worst-case factorization time.

For the standard binary64 build, the older shared input bound is 2^52 = 4503599627370496. The pinned 1.12.62 expression raises it to 2^53 = 9007199254740992. This change is established by comparing the older bound with the current bound; it is not a native test of 1.12.62. Input acceptance and exact representability of every resulting integer are separate questions.

Inputs that floor below 2 return #VALUE!, including zero, 1 and TRUE in the retained tests. An input beyond the version-specific magnitude bound returns #LIMIT!, not #NUM!. A missing argument produces #N/A. Preserve those distinctions when diagnosing a worksheet rather than converting every failure into zero.

F5 is an actually empty cell. Listed errors are native error results, not mathematical zeroes.

• Current worksheet implementation
• Tested-version worksheet implementation
• Current calculation helper
• Tested-version calculation helper

The retained workbook contained a deliberately stale SUM cache and an uncached SUM formula, both recalculated correctly. Native evidence covers the listed 1.12.57 cases. Other worksheet layouts and mathematical interpretations are separately explained checks. GUI entry, other locales and later-release output were not tested.

MOD, ISPRIME.