6 min read
2026-03-10
Prime numbers are the foundation of modern information security and one of the most fascinating topics in mathematics.
The RSA algorithm, which protects internet transactions, is based on the difficulty of factoring the product of two large prime numbers. Your bank transfers are protected by prime numbers.
Prime numbers are used as hash table sizes to minimize collisions. This speeds up data searches in databases and programs.
Periodical cicadas emerge every 13 or 17 years — both are prime numbers. This protects them from synchronizing with predator life cycles.
Check digit verification systems (ISBN, barcodes) use arithmetic with prime numbers to detect errors.
Pseudorandom number generators often use large prime numbers in their formulas to ensure long sequence periods.
Shor's algorithm on a quantum computer can quickly factor large numbers. This is a potential threat to RSA encryption and a stimulus for developing post-quantum cryptography.
Prime numbers are one of the fundamental objects of mathematics, and their properties continue to be discovered and find new applications.
See also: GCD and LCM, Factorials and Combinatorics, Matrix Calculator