Jouart conjecture

The supplied source describes the Jouart conjecture as asserting that the indices $m$ for which $P(m)=3m+i(m)$ is prime exhibit a regular exclusion structure characterized by two families of arithmetic progressions, denoted $X_1(q)$ and $X_2(q)$ . The source does not define $i(m)$ , the families $X_1(q),X_2(q)$ , or the quantification over $q$ , so a more precise formal statement cannot be recovered from the supplied material.

References

Primary source

Zenodo

Additional references

Spectral Detection of Prime Numbers A New Paradigm for RSA Key Generation Bridging the Jouart Conjecture with Practical Cryptography — Zenodo — François JOUART

cryptography number-theory

Posted 1 month ago

Progress summary

Refreshed 1 month ago

Claimed solved

A new unrefereed manuscript claims to settle the conjecture, but the claim has not been independently checked and the conjecture's exact statement is incomplete.

The Jouart conjecture asserts a regular exclusion pattern for indices producing primes through $P(m)=3m+i(m)$ , organized into two arithmetic-progression families, $X_1(q)$ and $X_2(q)$ . The supplied material attributes it to François Jouart but does not define $i(m)$ , $X_1(q)$ , $X_2(q)$ , or the quantification over $q$ .

August 23, 2026 complete-validation claim

A Zenodo preprint by François Jouart claims a complete spectral validation of the Jouart conjecture using harmonic methods connected with prime numbers. This is an unverified claim: the deposit is unrefereed, lacks independent confirmation and formal verification, and does not establish that the incomplete formulation recorded here is the exact statement proved.

Current status (as of August 2026): A complete resolution is claimed in an unverified preprint, but the exact conjecture and the validity of the claimed proof remain unsettled.

Sources

No solutions have been posted yet.