Jumping Champion Calculator
Return all tied finite prime-gap frequency champions below actual sieve cutoff; not largest-gap record, asymptotic jumping champion or conjecture proof.
Description
A jumping champion is a most frequent adjacent prime-gap size in an observed range.
A jumping champion is a most frequent adjacent prime-gap size in an observed range. A frequency champion is different from the largest or record-setting gap.1
Return all tied finite prime-gap frequency champions below actual sieve cutoff; not largest-gap record, asymptotic jumping champion or conjecture proof.
When to use Jumping Champion Calculator
Use this tool to return all tied finite prime-gap frequency champions below actual sieve cutoff; not largest-gap record, asymptotic jumping champion or conjecture proof.
Choose the integer, sequence, coefficients or function parameters for your calculation. Follow the stated ordering, domain and size limits.
How to use Jumping Champion Calculator and understand its results
- Choose the integer, sequence, coefficients or function parameters for your calculation. Follow the stated ordering, domain and size limits.
- Enter primeCutoff using the field table and calculation rules, then run the tool.
- Read mostFrequentObservedGapSizes, observedMaximumGapFrequency, totalObservedAdjacentGaps. The explanation below defines the units, signs, ordering and any flags or placeholder values.
- If the tool reports an input issue, correct the values and run it again. Apply the stated assumptions when interpreting a successfully returned result.
| Input field | Meaning | Value type; see rules below | Requirement |
|---|---|---|---|
| primeCutoff | Prime cutoff | number | Required |
Enter integer prime cutoff 0–one million. Sieve primes, tally adjacent gaps and return all tied champions in ascending size order, maximum frequency and total adjacent-gap count. No gaps returns empty champions and zero frequency.
champions = gap sizes attaining maximum observed frequency Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.
| Output field | Meaning | Value type |
|---|---|---|
| mostFrequentObservedGapSizes | Most frequent observed gap sizes | list of number |
| observedMaximumGapFrequency | Observed maximum gap frequency | number |
| totalObservedAdjacentGaps | Total observed adjacent gaps | number |
{
"input": {
"primeCutoff": 13
},
"output": {
"mostFrequentObservedGapSizes": [
2
],
"observedMaximumGapFrequency": 3,
"totalObservedAdjacentGaps": 5
}
}Limitations and assumptions
The finite result makes no asymptotic champion claim.
Numeric inputs and returned numeric values must be finite; an unrepresentable returned value produces an error. Missing required fields, extra fields, wrong value types and violations of the calculation rules are input errors.
Alternative or Complementary methods
Use Prime Gap Record Calculator: Find strict successive prime-gap records with both endpoints ≤caller sieve cutoff; equal ties are not new records and no outside-cutoff maximality claim. For a complementary task, use First Occurrence Prime Gap Calculator: Find first exact target gap between adjacent actual primes in complete sieve up to caller cutoff; missing observation is found=false/-1 rather than proof target never occurs.
References
-
Jumping Champion Calculator — tool.io
Similar or alternative tools
- Prime Gap Record Calculator
Find strict successive prime-gap records with both endpoints ≤caller sieve cutoff; equal ties are not new records and no outside-cutoff maximality claim.
- First Occurrence Prime Gap Calculator
Find first exact target gap between adjacent actual primes in complete sieve up to caller cutoff; missing observation is found=false/-1 rather than proof target never occurs.