pith. sign in
theorem

prime_threethousandfiveeleven

proved
show as:
module
IndisputableMonolith.NumberTheory.Primes.ArithmeticFunctions
domain
NumberTheory
line
2382 · github
papers citing
none yet

plain-language theorem explainer

3511 is prime and is the second known Wieferich prime. Number theorists verifying specific primes or building prime-counting tables would reference the fact. The proof is a one-line computational check that applies native decision procedures to the primality predicate.

Claim. $3511$ is a prime number.

background

The module supplies lightweight wrappers around Mathlib arithmetic functions, beginning with the Möbius function μ. The local setting is a collection of basic number-theoretic facts that can later support Dirichlet inversion or prime-counting arguments. Upstream material includes the definition of future states in TimeEmergence and the collision-free property in OptionAEmpiricalProgram, both of which appear among the declaration’s direct dependencies.

proof idea

The proof is a one-line wrapper that invokes the native_decide tactic to evaluate the primality predicate on the concrete integer 3511.

why it matters

The declaration records a verified prime that can feed primeCounting or related arithmetic functions inside the same module. It supplies a concrete datum for any later empirical or computational checks that rely on an explicit list of primes, consistent with the module’s role as a foothold for Möbius-based arguments. No downstream uses are recorded yet.

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