The Twin Prime Conjecture is a longstanding problem

The gap

Evidence profile

Stated in the inline gaps and cells research gap and cells future research sections of the source papers, classified as general, all from Zenodo (CERN European Organization for Nuclear Research).

Supporting evidence — 5 representative gaps

• COUNTING PRIMES IN A NEW LIGHT:SQUARE ROOT SPIRALS AND THEIR IMPLICATIONS FOR THE RIEMANN HYPOTHESIS (2026) · Zenodo (CERN European Organization for Nuclear Research) · doi

  Future investigations could explore additional geometric constructs or alternative mathematical frameworks that may yield further breakthroughs in this fundamental area of mathematics. This work not only bridges the gap between number theory and geometric representation but also opens new avenues for further research into prime number theory.

  generalstated in inline gapsevidence 5/5
  Keywords: geometric further number theory future investigations explore additional constructs alternative mathematical frameworks yield breakthroughs fundamental
• Prime Conch Geometry and Riemann Zeta Zero Analysis Based on Modulo-210 Periodic Vortex Topology (PDSM Framework) (2026) · Zenodo (CERN European Organization for Nuclear Research) · doi

  Traditional number-theoretic research has inherent barriers to converting the disordered discrete distribution of primes into quantifiable and derivable continuous geometric field evolution laws. - A self-consistent and intuitive geometric topological interpretation system is still lacking.

  generalstated in cells research gapevidence 5/5
  Keywords: traditional number-theoretic research has inherent barriers converting disordered
• COUNTING PRIMES IN A NEW LIGHT:SQUARE ROOT SPIRALS AND THEIR IMPLICATIONS FOR THE RIEMANN HYPOTHESIS (2026) · Zenodo (CERN European Organization for Nuclear Research) · doi

  The lack of a geometric approach to counting prime numbers. - The need for a new theorem that corrects the numerator and denominator of the prime number theorem.

  generalstated in cells research gapevidence 5/5
  Keywords: lack geometric approach counting prime numbers need new
• A Proof of the Star-Moon Conjecture via Fixed-Window Tower Sieve (2026) · Zenodo (CERN European Organization for Nuclear Research) · doi

  Future research can apply the technique used in the paper to other problems in number theory. - Future research can explore the implications of the Star-Moon Conjecture for other areas of mathematics.

  generalstated in cells future researchevidence 5/5
  Keywords: future research apply technique used paper other problems
• A Primorial-Shift Conjecture for Twin Primes (2026) · Zenodo (CERN European Organization for Nuclear Research) · doi

  The Twin Prime Conjecture is a longstanding problem in number theory. - There is a need for a new approach to resolve the conjecture.

  generalstated in cells research gapevidence 4/5
  Keywords: twin prime conjecture longstanding problem number theory there

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