https://www.jeremykun.com/categories/prime-numbers/Recent content in Prime Numbers on Math ∩ ProgrammingHugo -- gohugo.ioen-usTue, 07 Apr 2026 06:00:00 -0700https://www.jeremykun.com/2026/04/07/deterministic-miller-rabin/Tue, 07 Apr 2026 06:00:00 -0700https://www.jeremykun.com/2026/04/07/deterministic-miller-rabin/Problem: Determine if a 32-bit number is prime (deterministically) Solution: (in C++) // Bases to test. Using the first 4 prime bases makes the test deterministic // for all 32-bit integers. See https://oeis.org/A014233. int64_t bases[] = {2, 3, 5, 7}; inline int countTrailingZeros(uint64_t n) { if (n == 0) return 64; return __builtin_ctzll(n); } int64_t modularExponentiation(int64_t base, int64_t exponent, int64_t modulus) { int64_t res = 1; int64_t b = base % modulus; int64_t e = exponent; while (e > 0) { if (e & 1) { // Doesn't overflow because we assume 32-bit integer inputs res = (res * b) % modulus; } b = (b * b) % modulus; e >>= 1; } return res; } bool isPrime(int64_t n) { if (n < 2) return false; if (n < 4) return true; if (!