Prime Triplet Checker
Check supplied prime-triplet patterns (p,p+2,p+6) or (p,p+4,p+6), plus exceptional (3,5,7); not any three primes or a twin-pair alias.
Description
Prime triplets are closely spaced prime patterns.
Prime triplets are closely spaced prime patterns. This tool uses (p,p+2,p+6), (p,p+4,p+6), and the exceptional triple (3,5,7).1
Check supplied prime-triplet patterns (p,p+2,p+6) or (p,p+4,p+6), plus exceptional (3,5,7); not any three primes or a twin-pair alias.
When to use Prime Triplet Checker
Use this tool to check supplied prime-triplet patterns (p,p+2,p+6) or (p,p+4,p+6), plus exceptional (3,5,7); not any three primes or a twin-pair alias.
Choose the integer, sequence, coefficients or function parameters for your calculation. Follow the stated ordering, domain and size limits.
How to use Prime Triplet Checker and understand its results
- Choose the integer, sequence, coefficients or function parameters for your calculation. Follow the stated ordering, domain and size limits.
- Enter candidateTriplet using the field table and calculation rules, then run the tool.
- Read allThreeArePrime, allowedTripletGapPattern, isPrimeTriplet. 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 |
|---|---|---|---|
| candidateTriplet | Candidate triplet | list of number | Required |
Enter exactly three strictly increasing integers from 2 to one million. Test each for primality, audit the permitted gaps and return the two component flags and their conjunction.
triplet flag = all members prime and one allowed gap pattern Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.
| Output field | Meaning | Value type |
|---|---|---|
| allThreeArePrime | All three are prime | boolean |
| allowedTripletGapPattern | Allowed triplet gap pattern | boolean |
| isPrimeTriplet | Is prime triplet | boolean |
{
"input": {
"candidateTriplet": [
5,
7,
11
]
},
"output": {
"allThreeArePrime": true,
"allowedTripletGapPattern": true,
"isPrimeTriplet": true
}
}Limitations and assumptions
Other triples of primes validly fail the pattern check. This is a local classification without an infinitude claim.
Numeric inputs and returned numeric values must be finite; an unrepresentable returned value produces an error. Numeric lists are limited to 100,000 entries; the rules above may require smaller limits. 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 Twin Prime Constant Approximation: Compute finite twin-prime constant Euler product over odd primes ≤cutoff using log1p; omitted factors mean finite value is not exact constant or proof of twin-prime infinitude. For a complementary task, use Brun Constant Approximation: Compute finite Brun reciprocal sum over actual twin pairs with both primes ≤cutoff; shared prime 5 contributes in both pairs, no extrapolated Brun constant or tail estimate.
References
-
Prime Triplet Checker — tool.io
Similar or alternative tools
- Twin Prime Constant Approximation
Compute finite twin-prime constant Euler product over odd primes ≤cutoff using log1p; omitted factors mean finite value is not exact constant or proof of twin-prime infinitude.
- Brun Constant Approximation
Compute finite Brun reciprocal sum over actual twin pairs with both primes ≤cutoff; shared prime 5 contributes in both pairs, no extrapolated Brun constant or tail estimate.