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.
Description
A first observed prime gap requires adjacent primes, not merely two primes at that distance.
A first observed prime gap requires adjacent primes, not merely two primes at that distance. A finite cutoff can leave a target gap unobserved without proving it impossible.1
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.
When to use First Occurrence Prime Gap Calculator
Use this tool to 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.
Choose the integer, sequence, coefficients or function parameters for your calculation. Follow the stated ordering, domain and size limits.
How to use First Occurrence Prime Gap 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, targetGapSize using the field table and calculation rules, then run the tool.
- Read firstObservedGapFound, firstObservedGapLeftPrime, firstObservedGapRightPrime. 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 |
| targetGapSize | Target gap size | number | Required |
Use integer gap 1–one million and sieve cutoff 0–one million. Find the first exact matching adjacent gap; return its endpoints with found true, or both endpoints −1 with found false.
target observed when adjacent prime difference = supplied gap Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.
| Output field | Meaning | Value type |
|---|---|---|
| firstObservedGapFound | First observed gap found | boolean |
| firstObservedGapLeftPrime | First observed gap left prime | number |
| firstObservedGapRightPrime | First observed gap right prime | number |
{
"input": {
"primeCutoff": 13,
"targetGapSize": 4
},
"output": {
"firstObservedGapFound": true,
"firstObservedGapLeftPrime": 7,
"firstObservedGapRightPrime": 11
}
}Limitations and assumptions
Both endpoints must lie within the cutoff. No conclusion is drawn about larger primes.
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. A successfully returned false flag is an evaluated outcome; its meaning is explained above.
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 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.
References
-
First Occurrence Prime Gap 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.
- 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.