Inconclusive results¶
An inconclusive result means the question was not settled. It is not a negative answer, and Numerisect never presents it as one. This page explains where inconclusive results come from and what to do with them.
The distinction¶
Three outcomes are possible for most questions Numerisect asks:
| Outcome | Meaning |
|---|---|
| Yes | The property holds, with the strength stated. |
| No | The property definitely does not hold. |
| Inconclusive | Not determined within the budget or bound applied. |
Tools that collapse the third into the second are the reason people mistrust computational number theory. A search that ran out of time has found nothing; it has not shown there is nothing to find.
Where inconclusive results arise¶
Time budgets. Every engine call carries a timeout. The 56-class prime classifier gives each class its own budget, and a class that exceeds it is listed separately from classes that definitely do not match.
Documented search bounds. Many properties are only decidable by search. Sierpiński and Riesel candidate testing, covering-set verification, sociable-number cycles, record-number families and special-form recognition all carry documented caps. Reaching a cap is reported with the cap.
Open questions. Some classes in the catalogue are not decidable at all with current knowledge. Mills, Wilson, Wolstenholme, Higgs, cluster and Fortunate primes are the usual examples. For these, "inconclusive" is often the only honest answer that exists.
Method limits. SQUFOF exhausting its iteration limit says nothing about primality. An ECM campaign completing its curves without a split says nothing about whether a factor of that size exists. Both report inconclusive with a suggestion of what to change.
Missing external data. A catalogue with no entry for your number means the catalogue does not know.
How to act on one¶
Every inconclusive result states the bound that was reached. That tells you the lever:
- A timeout means raise the time budget, or accept that this class is expensive.
- A search cap means raise the cap, if the runtime is acceptable to you.
- An iteration limit in SQUFOF means raise it or move to SIQS.
- An ECM campaign that found nothing means raise \(B_1\) or the curve count, or move to SIQS or NFS.
- An open question means no amount of computation will settle it here.
The mistake to avoid
Do not read "no factor found" as "the number is prime". Use a primality test for that question. They are different questions and Numerisect answers them separately.
How it is enforced¶
Every engine program ends its output with a completion marker, and every count it reports is checked against the number of records parsed. A run killed by a timeout produces no marker, and Numerisect raises an error rather than returning an empty successful result. A partial run therefore cannot be mistaken for a completed search that found nothing.
Searches that stop at a cap set an explicit truncation flag alongside the results, so a truncated list is never mistaken for a complete one.