Prime Numbers: Why They Matter Beyond Math Class

Primes are numbers divisible only by 1 and themselves. They are also the reason your online banking works.

Some calculations matter for a single decision; this one matters for years. Primes are numbers divisible only by 1 and themselves. They are also the reason your online banking works.

The first few

2, 3, 5, 7, 11, 13, 17, 19, 23, 29...

The unique factorisation theorem

Every integer >1 is a product of primes in exactly one way. Building blocks of arithmetic.

RSA cryptography

Multiplying two huge primes is easy; factoring the product is computationally infeasible. That's the whole trick.

Pro tips

  • The Sieve of Eratosthenes still works — fastest classroom method for finding primes below N.
  • Twin primes (pairs like 11/13, 17/19) are infinite — conjectured, not yet proven.

Frequently asked questions

Is 1 prime? No — by definition, primes have exactly two divisors. 1 has only one.

Why are large primes valuable? They power public-key cryptography. Internet security depends on them.

Bookmark the calculator linked above — you will need it more often than you think.

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