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Number theory toolkit: sieve of Eratosthenes, fast modular exponentiation, and gcd.

Sieving primes, fast modular power, and Euclid's gcd are the number-theory primitives that quietly power crypto, hashing, and combinatorics problems. The signal is the O(n log log n) sieve and O(log e) binary exponentiation. Here is the answer.

Updated Aug 2026 · Grounded in real Applied AI Engineer interview loops and written to a senior-engineer editorial bar.

Sieving primes, fast modular power, and Euclid's gcd are the number-theory primitives that quietly power crypto, hashing, and combinatorics problems. The signal is the O(n log log n) sieve and O(log e) binary exponentiation. Here is the answer.

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Next in this trackMatrix exponentiation: compute the nth term of a linear recurrence in O(log n).Next in this trackDesign a time-based key-value store: set with a timestamp, get the value as of a time.Next in this trackBuild a decision tree classifier from scratch: pick splits by Gini or entropy, then predict.
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