HTTP API reference
Every route below is generated from the running application, so this page cannot
drift from the code. Interactive OpenAPI documentation is also served at
/api/docs while Numerisect is running.
Authentication
All /api/ routes except /api/session require the per-launch session token,
supplied either as the X-Numerisect-Token header or the numerisect_session
cookie. Obtain it from GET /api/session. The token changes every time the process
starts.
--cookie-jar jar http://127.0.0.1:8765/api/session
--cookie jar --header 'Content-Type: application/json' \
--data '{"expression":"32416190071","mode":"proven"}' \
http://127.0.0.1:8765/api/primes/check
To avoid tokens entirely, use numerisect api, which drives the same application
in-process. See the command-line reference .
Conventions
Invalid input returns 422 with a detail message naming the problem.
A missing engine returns 503 .
A refused network action returns 403 .
Operations that produce a result save a report and return its exact
output/<filename> path.
Searches that stop at a bound set a truncation flag and give a continuation point.
Routes (208)
Engine adapters
Method
Path
Purpose
GET/api/adaptersList built-in and user-declared engine adapters.
Algebra laboratory
Method
Path
Purpose
POST/api/algebra/chebotarev
POST/api/algebra/congruence
POST/api/algebra/cornacchia
POST/api/algebra/discrete-log
POST/api/algebra/divisor-lattice
POST/api/algebra/finite-field
POST/api/algebra/number-field
POST/api/algebra/quadratic-ring
POST/api/algebra/reciprocity
POST/api/algebra/record-numbers
POST/api/algebra/smoothness
POST/api/algebra/sociable
POST/api/algebra/weird-numbers
Batch import
Method
Path
Purpose
POST/api/batch/importExpand a TXT/CSV/JSON document of integers, ranges, expressions, and families.
Result cache
Method
Path
Purpose
DELETE/api/cacheDiscard cached results, optionally for one operation path only.
GET/api/cacheReport result-cache size and hit counts.
Capabilities
Method
Path
Purpose
GET/api/capabilities
Optional catalogues
Method
Path
Purpose
GET/api/cataloguesShow local catalogue files and the current network permission state.
POST/api/catalogues/factorsLook up claimed factors locally, or remotely when explicitly permitted.
POST/api/catalogues/oeisSearch OEIS for a sequence. Disabled unless explicitly permitted.
Prime counting
Method
Path
Purpose
POST/api/counting/algorithm-comparison
POST/api/counting/nth-prime-inverses
POST/api/counting/phi
Diagnostics
Method
Path
Purpose
POST/api/diagnostics
Distributed CADO-NFS
Method
Path
Purpose
POST/api/distributed/factorQueue a factorization whose sieving is distributed by CADO-NFS.
POST/api/distributed/previewValidate a distributed configuration and report its exposure without running.
GET/api/distributed/trust-modelDescribe how distributed CADO authenticates clients, and what it does not.
Analytic distribution
Method
Path
Purpose
POST/api/distribution/approximation-error
POST/api/distribution/bateman-horn
POST/api/distribution/density-surface
POST/api/distribution/maximal-gaps
POST/api/distribution/nth-prime-bounds
POST/api/distribution/pnt-convergence
POST/api/distribution/prime-race
POST/api/distribution/progressions
POST/api/distribution/short-interval
POST/api/distribution/singular-series
POST/api/distribution/tuple-prediction
OpenAPI documentation
Method
Path
Purpose
GET/api/docs
Exports
Method
Path
Purpose
GET/api/exports/jobsExport job search results in any supported interchange format.
GET/api/exports/jobs/{job_id}Export one factorization job in any supported interchange format.
GET/api/exports/reports/{filename}Re-container a saved text report; the engine-produced body is unchanged.
Expert factorization laboratory
Method
Path
Purpose
POST/api/factor-lab/certificatesGenerate and independently verify a primality certificate per prime factor.
POST/api/factor-lab/special-formDetect special algebraic forms, algebraic factors, and SNFS suitability.
POST/api/factor-lab/squfofFactor with Shanks' square forms factorization (numerisect-squfof, C/GMP).
POST/api/factor-lab/strategyRecommend an engine and estimate the expected remaining factor size.
POST/api/factor-lab/traceProduce a bounded, educational step trace of a factoring algorithm.
POST/api/factor-lab/tuneMeasure this machine's SIQS/NFS crossover with YAFU's own tune.
Method
Path
Purpose
POST/api/forms/class-group
POST/api/forms/compose
POST/api/forms/continued-fraction
POST/api/forms/pell
POST/api/forms/prime-form
POST/api/forms/reduce
POST/api/forms/reduced-forms
POST/api/forms/represent
Performance history
Method
Path
Purpose
GET/api/history/performanceAggregate completed-job runtimes by engine and decimal-digit bucket.
Factorization jobs
Method
Path
Purpose
GET/api/jobsList jobs, optionally filtered and sorted (roadmap item 135).
POST/api/jobs
POST/api/jobs/batch
POST/api/jobs/batch-export
POST/api/jobs/reorderReorder queued jobs; the supplied order becomes the dispatch order.
GET/api/jobs/{job_id}
POST/api/jobs/{job_id}/cancel
POST/api/jobs/{job_id}/certificatesCertify every prime factor of a completed factorization (roadmap item 13).
POST/api/jobs/{job_id}/continue-cofactor
GET/api/jobs/{job_id}/export
GET/api/jobs/{job_id}/log
POST/api/jobs/{job_id}/pauseSuspend a running job's process group with SIGSTOP.
POST/api/jobs/{job_id}/priorityChange one job's scheduling priority; higher runs sooner.
POST/api/jobs/{job_id}/resume
POST/api/jobs/{job_id}/resume-pausedContinue a paused job's process group with SIGCONT.
Number theory
Method
Path
Purpose
POST/api/number-theory/aliquot
POST/api/number-theory/arithmetic-functions
POST/api/number-theory/crt
POST/api/number-theory/cunningham-chain
POST/api/number-theory/cyclotomic
POST/api/number-theory/discrete-log
POST/api/number-theory/divisor-classification
POST/api/number-theory/eisenstein
POST/api/number-theory/factor-strategy
POST/api/number-theory/hensel-roots
POST/api/number-theory/modular-roots
POST/api/number-theory/ntt-primes
POST/api/number-theory/order-distribution
POST/api/number-theory/perfect-power
POST/api/number-theory/polynomial
POST/api/number-theory/power-residues
POST/api/number-theory/primality-lab
POST/api/number-theory/prime-approximations
POST/api/number-theory/quadratic-decomposition
POST/api/number-theory/special-form-test
POST/api/number-theory/special-prime-family
POST/api/number-theory/summatory-functions
POST/api/number-theory/symbols
POST/api/number-theory/tonelli-shanks
POST/api/number-theory/unit-group
POST/api/number-theory/valuation
Report download
Method
Path
Purpose
GET/api/outputs/{filename}
/api/primality-lab
Method
Path
Purpose
POST/api/primality-lab/bitwin-chains
POST/api/primality-lab/carmichael
POST/api/primality-lab/chernick
POST/api/primality-lab/compare
POST/api/primality-lab/constrained-prime
POST/api/primality-lab/covering-set
POST/api/primality-lab/deterministic-witnesses
POST/api/primality-lab/ecpp-steps
POST/api/primality-lab/lucas-lehmer-steps
POST/api/primality-lab/lucas-sequence
POST/api/primality-lab/pocklington
POST/api/primality-lab/pratt
POST/api/primality-lab/prime-ladder
POST/api/primality-lab/proth
POST/api/primality-lab/proth-search
POST/api/primality-lab/repunit
POST/api/primality-lab/sierpinski
POST/api/primality-lab/taxonomy
POST/api/primality-lab/verify-certificate
Method
Path
Purpose
POST/api/primes/absolute
POST/api/primes/after
POST/api/primes/batch-check
POST/api/primes/before
POST/api/primes/check
POST/api/primes/classify
POST/api/primes/contiguous-digits
POST/api/primes/coprimes
POST/api/primes/count
POST/api/primes/digit-constrained
POST/api/primes/distribution
POST/api/primes/factor-count-distribution
POST/api/primes/gap-statistics
POST/api/primes/gaps
POST/api/primes/gaussian/check
POST/api/primes/gaussian/range
POST/api/primes/generate
POST/api/primes/generate-special
POST/api/primes/goldbach
POST/api/primes/indicator-constant
POST/api/primes/integer-profile
POST/api/primes/miller-rabin-witnesses
POST/api/primes/modular
POST/api/primes/modular-wheel
POST/api/primes/nth
POST/api/primes/nth-near
POST/api/primes/palindrome-derived
POST/api/primes/paterson
POST/api/primes/perfect
POST/api/primes/polynomial
POST/api/primes/primorials
POST/api/primes/problems
POST/api/primes/progression
POST/api/primes/pyramid
POST/api/primes/random-range
POST/api/primes/range
POST/api/primes/reciprocal
POST/api/primes/reptend
POST/api/primes/sieve-intervalEnumerate primes in an interval of any magnitude.
POST/api/primes/special-numbers
POST/api/primes/tuples
POST/api/primes/verify-certificate
Job queue
Method
Path
Purpose
GET/api/queueShow queued and running jobs in dispatch order.
Saved reports
Method
Path
Purpose
GET/api/reportsSearch the index of saved report files.
Session
Method
Path
Purpose
GET/api/session
Engine setup
Method
Path
Purpose
GET/api/setup
POST/api/setup/install
GET/api/setup/log
Integer structure
Method
Path
Purpose
POST/api/structure/factorint-strategies
POST/api/structure/lenstra-divisors
POST/api/structure/predicates
Independent verification
Method
Path
Purpose
POST/api/verify/primalityDecide primality with independent implementations and compare them.
POST/api/verify/prime-countCompute pi(x) with every independent method available and compare them.
POST/api/verify/self-testAsk each installed engine questions with published answers.
Visualization
Method
Path
Purpose
POST/api/visual/complexity
POST/api/visual/eisenstein-lattice
POST/api/visual/gap-timeline
POST/api/visual/modular-wheel
POST/api/visual/prime-race
POST/api/visual/residue-heatmap
POST/api/visual/sieve-trace
POST/api/visual/spiral
Workspaces
Method
Path
Purpose
GET/api/workspacesList saved workspaces, newest first.
POST/api/workspacesSave a named workspace referencing jobs, reports, and interface state.
DELETE/api/workspaces/{workspace_id}Delete one workspace. Jobs and reports are not affected.
GET/api/workspaces/{workspace_id}Load one workspace.
POST/api/workspaces/{workspace_id}Update selected fields of one workspace.
Zeta and L-functions
Method
Path
Purpose
POST/api/zeta/backlund-sCertified S(T) with an exploratory plot across an ordinate range.
POST/api/zeta/charactersDirichlet character table modulo q with conductor, parity and order.
POST/api/zeta/chebyshev-psiChebyshev ψ(x) reconstructed from certified zeros (FLINT/Arb).
POST/api/zeta/count
POST/api/zeta/dedekindDedekind zeta of a bounded number field through PARI/GP.
POST/api/zeta/euler-productTruncated Euler products against ζ(s) with a rigorous tail bound.
POST/api/zeta/evaluate
POST/api/zeta/explicit-prime-countRiemann's explicit formula for π(x) from certified zeros (FLINT/Arb).
POST/api/zeta/functional-equation
POST/api/zeta/gram
POST/api/zeta/gram-blocksGram's-law verdicts, exceptions and Gram blocks over an index range.
POST/api/zeta/hardy
POST/api/zeta/heatmap
POST/api/zeta/l-functionRigorous L(s, χ) enclosure with an independent Hurwitz cross-check.
POST/api/zeta/l-zerosCertified critical-line sign changes, or exploratory
POST/api/zeta/line
POST/api/zeta/pair-correlationPair correlation of certified zeros against the GUE prediction.
POST/api/zeta/riemann-siegelRiemann–Siegel main sum with K corrections against acb_dirichlet_zeta.
POST/api/zeta/stieltjes
POST/api/zeta/xi-eta
POST/api/zeta/zero-spacingNormalized nearest-neighbour spacing histogram of certified zeros.
POST/api/zeta/zeros