Prime Factorization
Break any whole number into its prime factor building blocks.
A prime number is a natural number greater than 1 that has exactly two divisors: 1 and itself. Primes are the fundamental building blocks of all integers — every integer greater than 1 is either prime or a product of primes (Fundamental Theorem of Arithmetic).
- 1Trial division: test divisibility by all integers up to √n
- 2If n has a factor, one factor must be ≤ √n
- 3Optimisation: only test 2, 3, then numbers of the form 6k±1
- 4For large numbers, probabilistic tests like Miller-Rabin are used
17=PRIMENot divisible by 2, 3, or √17 ≈ 4.1
91=NOT PRIME91 = 7 × 13 — looks prime but isn't!
2=PRIMEThe only even prime number
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Fun Fact
As of 2024, the largest known prime is 2^136,279,841 − 1, discovered in October 2024. It has over 41 million digits.
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