Prime Generator

Watch the Sieve of Eratosthenes eliminate composites step by step, then test, factor, and explore numbers of any size.

Range

Start

End

Grid columns

46 primes in [1, 200]

Search a number

Active primeJust eliminatedCompositePrimeNot yet determined

Sieve step6

Step 6 of 6: eliminating multiples of 13 (1 newly marked composite)

Prime distribution chart

Number Theory

n (any non-negative integer — supports arbitrary-precision expressions like 2^127-1)

Primality test

Trial division: prime
Miller–Rabin: prime

Prime factorization

97 = 97

Divisibility steps

97 ÷ 97 = 1 (97 divides 97)

Divisors (2)

1, 97

Mathematical properties

Sum of divisors σ(97) = 98
97 is deficient (the sum of its proper divisors is less than itself)

Euler’s totient φ(97) = 96

Count of integers in [1, n] coprime to n.

Next prime: 101

Previous prime: 89

GCD / LCM

gcd(48, 18) = 6 · lcm(48, 18) = 144

n-th prime

The 10th prime is 29.

Algorithm comparison

Times three ways to find every prime in the current range: trial division per candidate, the plain Sieve of Eratosthenes (sieved from 0), and a segmented sieve (sieving only this range) — the segmented sieve should win when the range starts far from 0, since it never marks anything below the range’s start.