Number Theory

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Elementary number theory on arbitrary-precision integers — GCD and LCM, prime factorization, primality testing, Euler's totient, and modular exponentiation.

UtilityBasex402 v2exactnumtheory.openverbs.com ↗︎
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Endpoints (6 live)

  • POST /v1/totient — Euler's totient φ(n) — the count of integers in [1, n] coprime to n — for a positive integer ≤ 10^15 (it is computed from the prime factorization). (0.004 USDC on Base)
  • POST /v1/modpow — Compute (base ^ exponent) mod modulus efficiently for arbitrary-precision integers. The modulus must be positive. (0.004 USDC on Base)
  • POST /v1/is-prime — Miller-Rabin primality test (with witnesses that are exact for all 64-bit integers) on an arbitrary-precision integer. Returns { prime }. (0.004 USDC on Base)
  • POST /v1/lcm — Least common multiple of two or more positive integers (arbitrary precision). (0.004 USDC on Base)
  • POST /v1/factorize — Prime-factorize a positive integer (≤ 10^15 so the computation is always fast). Returns the prime factors with exponents, the divisor count, and whether n is prime. (0.004 USDC on Base)
  • POST /v1/gcd — Greatest common divisor of two or more non-negative integers (arbitrary precision). (0.004 USDC on Base)

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