Prime Number Checker & Generator

Miller-Rabin · sieve · factorization · Goldbach · twin primes · BigInt

BigInt Miller-Rabin Sieve Goldbach
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Algorithms reference
  • Primality: Deterministic Miller-Rabin for 64-bit; probabilistic for BigInt.
  • Sieve: Eratosthenes up-to-N; segmented for ranges.
  • Factorization: Trial division, 6k±1 optimization.
  • Nth prime: PNT bound n(ln n + ln ln n).
  • Goldbach: Sieve-based scan for even N.
  • GCD: Euclidean algorithm (BigInt).

Result

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Definition p > 1 with divisors 1 and p only
Fundamental theorem Unique prime factorization
PNT (approx.) π(x) ~ x / ln(x)

About this prime calculator

Check if any integer is prime (Miller-Rabin with BigInt), generate primes via the Sieve of Eratosthenes, factorize into prime factors, find the Nth prime, locate the nearest prime, test Goldbach partitions, compute GCD, highlight twin primes, and visualize gaps and density. Use Math AI for number-theory tutoring or to solve related problems (∫, algebra, matrices) in chat with the same engines as other Math Studio tools.

FAQ

How does the primality test work?
Deterministic Miller-Rabin for 64-bit integers; probabilistic Miller-Rabin with strong witnesses for larger BigInt values.
What is the Sieve of Eratosthenes?
An algorithm that marks multiples of each prime starting from 2. Range queries use a segmented sieve for primes between A and B.
How large can the numbers be?
Primality and factorization support arbitrary BigInt. Sieve generation is capped at 2 million for browser performance.
How does factorization work?
Trial division with 6k±1 optimization after dividing out 2 and 3.