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.

Description

A prime-gap record is a gap larger than every previously observed adjacent gap.

A prime-gap record is a gap larger than every previously observed adjacent gap. Equal-size later gaps do not create a new strict record.^[1]

Find strict successive prime-gap records with both endpoints ≤caller sieve cutoff; equal ties are not new records and no outside-cutoff maximality claim.

When to use Prime Gap Record Calculator

Use this tool to find strict successive prime-gap records with both endpoints ≤caller sieve cutoff; equal ties are not new records and no outside-cutoff maximality claim.

Choose the integer, sequence, coefficients or function parameters for your calculation. Follow the stated ordering, domain and size limits.

How to use Prime Gap Record 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 strictRecordGapSizes, recordGapLeftPrimes, recordGapRightPrimes. 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

Use integer sieve cutoff 0–1,000,000. Enumerate adjacent actual primes with both endpoints within the cutoff and return increasing strict-record sizes and their aligned left/right primes.

gap_i = prime[i+1]−prime[i]; retain gap_i > previous record

Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.

Output field	Meaning	Value type
strictRecordGapSizes	Strict record gap sizes	list of number
recordGapLeftPrimes	Record gap left primes	list of number
recordGapRightPrimes	Record gap right primes	list of number

json

{
  "input": {
    "primeCutoff": 13
  },
  "output": {
    "strictRecordGapSizes": [
      1,
      2,
      4
    ],
    "recordGapLeftPrimes": [
      2,
      3,
      7
    ],
    "recordGapRightPrimes": [
      3,
      5,
      11
    ]
  }
}

Limitations and assumptions

Records concern the finite observed inventory. Low cutoffs can produce empty lists; no maximality beyond the cutoff is inferred.

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 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. 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

Prime Gap Record Calculator — tool.io

Similar or alternative tools

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.
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.