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July 21, 2026Open Access

Maynard's Sieve Refines Prime Gaps to 246, Not Yet Twin Primes — E8 Intelligence Research

Andrew Stewart Caldin

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Key Points

This research aims to refine the GPY sieve and prove bounded gaps between prime numbers.
Utilized Maynard's theorem to analyze gaps between consecutive primes.
Employed a multidimensional sieve weight to maximize the ratio of sums.
Solved a variational problem involving the Selberg sieve to establish bounds.
Achieved a bound reduction to 246 for gaps between primes.
Showed that infinitely many prime pairs exist with gaps ≤ 246.
Confirmed that the method does not reach the gap of 2 required for twin primes.

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Implication

Finding reveals bounded prime gaps of 246, while not yet proving twin primes.

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Cite This Study

Andrew Stewart Caldin (2026) studied this question.

synapsesocial.com/papers/6a61b0f6faa9903c5116b4fb https://doi.org/10.5281/zenodo.21467303

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