Description
Trial-divide candidate prime through its square root, reject a composite, then return factor=prime^exponent as exact decimal text.
Exact integer arithmetic and finite numeric arithmetic have different range limits. A safe integer number is bounded by +/-9007199254740991, while supported decimal-integer text can represent larger values. Division and remainder also need a signed convention: truncating quotients and Euclidean nonnegative remainders can give different results.
Trial-divide candidate prime through its square root, reject a composite, then return factor=prime^exponent as exact decimal text.
When to use this tool
Use Prime Factorization One Exponent Contribution when you need this exact stated integer sign, bound, division, comparison, or factor component.
How to use the tool and how it works
- Enter prime, exponent. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read factor. Use the output convention below.
Require integer prime in 2..1000000 and exponent in 0..256. Trial-divide candidate prime through its square root, reject a composite, then return factor=prime^exponent as exact decimal text.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| prime | Prime | Required. Safe integer; minimum 2; maximum 1000000. |
| exponent | Exponent | Required. Safe integer; minimum 0; maximum 256. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| factor | Factor | Required. Text; maximum UTF-16 length 8192. |
{
"input": {
"prime": 3,
"exponent": 4
},
"output": {
"factor": "81"
}
}Limitations and assumptions
- Primality is checked even for exponent zero. This computes one prime-power contribution, not the factorization of a supplied composite or a general unbounded primality test.
- Inputs must satisfy both the field types and the cross-field conditions above. Invalid input causes an error; a successful false flag or documented placeholder is a different result.
- Numeric calculations use binary floating point unless exact decimal-integer arithmetic is explicitly stated. No hidden measurement tolerance or decimal rounding is added; nonfinite or out-of-contract results are rejected. Numeric signed-zero results are exported as zero.
Alternative or Complementary methods
Use exact decimal-integer tools when the range exceeds safe numeric integers. State the division, remainder, midpoint, and zero convention before combining results from different operations.
References
Similar or alternative tools
- Number: Factorial Trailing Zero Base Factor Term
Compute one Legendre prime valuation contribution to n! trailing zeros for an explicitly supplied prime factor and base multiplicity; does not factor a base.
- Integer Radical Exponent
Reduce supplied nonnegative prime-factor exponents to squarefree radical exponents; primality of the implicit bases is caller supplied.