Bateman-Horn Conjecture Checker
Bounded off line reference: Bateman-Horn open conjecture statement/scope, no decidability claim. Topics: statement, scope. Not live/exhaustive reference, a proof of an open assertion, diagnosis or safe-use approval.
Description
The Bateman-Horn conjecture concerns asymptotic joint prime values of polynomial families and local root factors.
The Bateman-Horn conjecture concerns asymptotic joint prime values of polynomial families and local root factors.1
This tool returns a stored statement and scope note without evaluating a singular-series model or proving the conjecture.
When to use Bateman-Horn Conjecture Checker
Read a bounded educational reference for one of the supported topics.
How to use Bateman-Horn Conjecture Checker and how it works
- Choose a supported exact topic from the table below.
- Enter that topic token and run the tool.
- Read result.text and its scope or precision limitations.
- Correct an unsupported token before rerunning; use an independently applicable reference when more detail or current evidence is required.
| Input field | Meaning | Value type | Requirement |
|---|---|---|---|
| topic | One exact case-sensitive supported topic token from the table below. | string | Required; other constraints below |
Choose one exact case-sensitive topic: statement, scope. The implementation matches that token to a stored text record and returns result.text unchanged. Unknown tokens, blank strings and wrong input types are errors; no case folding or live lookup occurs. These are bounded educational records, not a calculation from observations, a proof search, a site or equipment assessment or an arbitrary-precision value. The supported topic inventory below identifies the available records.
text=storedInventory[exactTopic] Apply the input ordering, units and branch conditions stated above.
| Exact topic token | Record selected |
|---|---|
| statement | Stored statement reference. |
| scope | Stored scope reference. |
| Output field | Meaning | Value type |
|---|---|---|
| result | Object containing the calculated or selected fields below. | object |
| result.text | Exact stored educational text selected by the topic token. | string |
{
"input": {
"topic": "statement"
},
"output": {
"result": {
"text": "For primitive irreducible integer polynomials with no fixed prime divisor, joint prime values have a conjectural asymptotic governed by local root factors."
}
}
}Limitations and assumptions
This is a stored text inventory. It does not calculate from measurements, obtain live data, prove an infinite assertion, evaluate an installation or certify arbitrary precision.
All fields require explicit values. Unexpected fields, wrong types, nonfinite numbers and sparse arrays are rejected. Alignment, bounds and supported-token rules are explained above; extremely large inputs or nonfinite results can also fail. Input errors differ from successful false comparisons, unavailable-domain flags and empty match lists.
Alternative or Complementary methods
Use Elliptic Curve Rank Calculator for a complementary operation: Elliptic-curve rank requires an identified nonsingular curve and independently certified arithmetic evidence.
Use Dickson Conjecture Checker for a complementary operation: Dickson's conjecture concerns simultaneous prime values of suitable linear forms infinitely often.
References
-
Bateman-Horn Conjecture Checker — tool.io
Similar or alternative tools
- Elliptic Curve Rank Calculator
Elliptic-curve rank requires an identified nonsingular curve and independently certified arithmetic evidence.
- Dickson Conjecture Checker
Dickson's conjecture concerns simultaneous prime values of suitable linear forms infinitely often.