Math & Statistics · 质数 · Updated 2026-10-25
What Is Prime Number?
Definition
A prime is >1 with no divisors besides 1 and itself. Unique factorization makes primes the atoms of multiplication; RSA security rests on the hardness of factoring large numbers.
Formula
Trial-divide by primes ≤ √n; π(n) ≈ n/ln n
Worked Example
91 = 7×13 (composite); 97 survives trial division (prime). RSA-2048 pairs two ~617-digit primes.
Common Misconception
"1 is prime" - it is not; excluding 1 is the premise for unique factorization. "Primes thin out until they run out" - Euclid proved 2,000 years ago that they are infinite.
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