Weak Goldbach Conjecture Checker

Find first nondecreasing prime triple summing to caller odd n>5 using actual sieve and bounded pair search; witnesses may repeat primes, distinct from existing strong two-prime Goldbach partition count.

Description

A weak Goldbach representation expresses an odd integer greater than five as three primes.

A weak Goldbach representation expresses an odd integer greater than five as three primes. A witness may repeat primes and can be ordered to avoid equivalent permutations.^[1]

When to use Weak Goldbach Conjecture Checker

Use this tool to find first nondecreasing prime triple summing to caller odd n>5 using actual sieve and bounded pair search; witnesses may repeat primes, distinct from existing strong two-prime Goldbach partition count.

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

How to use Weak Goldbach Conjecture 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 oddInteger using the field table and calculation rules, then run the tool.
Read weakGoldbachRepresentationFound, primeTripleWitness. 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
oddInteger	Odd integer	number	Required

Enter an odd integer from 7 to 100,000. Sieve actual primes and search nondecreasing triples, returning the first witness. Pair comparisons are capped at one million; no found witness returns false and an empty list.

odd n = prime a + prime b + prime c, a≤b≤c

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

Output field	Meaning	Value type
weakGoldbachRepresentationFound	Weak goldbach representation found	boolean
primeTripleWitness	Prime triple witness	list of number

json

{
  "input": {
    "oddInteger": 9
  },
  "output": {
    "weakGoldbachRepresentationFound": true,
    "primeTripleWitness": [
      2,
      2,
      5
    ]
  }
}

Limitations and assumptions

The tool supplies a local witness rather than a proof. It does not count strong two-prime Goldbach partitions.

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 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. For a complementary task, use Bertrand Postulate Checker: Enumerate actual primes in open Bertrand interval (n,2n) for supplied n>1; a finite witness check of an established theorem, not an unproved-conjecture certificate or next-prime alias.

References

Weak Goldbach Conjecture Checker — tool.io

Similar or alternative tools

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.
Bertrand Postulate Checker
Enumerate actual primes in open Bertrand interval (n,2n) for supplied n>1; a finite witness check of an established theorem, not an unproved-conjecture certificate or next-prime alias.