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∑MathIntermediate

Legendre's Formula

Legendre's formula gives the exponent of a prime p in n! by summing how many multiples of p, p^2, p^3, ... are ≤ n.

#legendre's formula#p-adic valuation#binomial divisibility+10
∑MathIntermediate

Prime Factorization

Prime factorization expresses any integer greater than 1 as a product of primes raised to powers, uniquely up to ordering.

#prime factorization
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#sieve of eratosthenes
#trial division
#spf sieve
+12
∑MathIntermediate

Sieve of Eratosthenes

The Sieve of Eratosthenes marks multiples of each prime to find all primes up to n in O(n log log n) time.

#sieve of eratosthenes#segmented sieve#linear sieve+11