Prime number

Key people

• Charles-Jean de la Vallée PoussinBelgian mathematician (1866–1962)
• Johann Gustav HermesGerman mathematician (1846–1912)
• Stanislaw KnapowskiPolish mathematician (1931-1967)

Timeline

• 1550 BCHistory From around 1550 BC, the Rhind Mathematical Papyrus has Egyptian fraction expansions of different forms for fractions with prime and composite denominators.
• 300 BCThere are infinitely many primes, as demonstrated by Euclid around 300 BC.
• 1912Often having an elementary formulation, many of these conjectures have withstood proof for decades: all four of Landau's problems from 1912 are still unsolved.
• 1951Since 1951 all the largest known primes have been found using these tests on computers.
• 1992This is why since 1992 (as of October 2024) the largest known prime has always been a Mersenne prime.

Read

• La solitudine dei numeri primiPaolo Giordano · 2008Book
• The distribution of prime numbersA. E. Ingham · 1932Book
• Prime numbers and computer methods for factorizationHans Riesel · 1994Book
• Color Prime NumbersFrancis Gurtowski · 2016Book

Listen

• Prime NumbersUnknownPodcast
• The Prime Numbers PodcastPrime NumbersPodcast
• 素数ラジオ（primeNumberポッドキャスト）primeNumberPodcast
• Prime Factorisation | Real Number | CBSE | Class 10 | MathShiksha AbhiyanPodcast

Debates

• Is the Riemann Hypothesis true?One view: The hypothesis suggests a specific pattern for the distribution of prime numbers, which has been supported by extensive computational evidence. · Another: Despite strong evidence, no definitive proof exists, and some mathematicians explore alternative distributions or counterexamples.Open question
• Are there infinitely many twin primes?One view: The Twin Prime Conjecture proposes that twin primes (primes differing by 2) continue indefinitely, supported by observations of their frequency. · Another: While many twin primes are known, there is no mathematical proof to confirm their infinite existence, making it an open problem.Open question

Glossary

• Prime NumberA natural number greater than 1 that has no positive divisors other than 1 and itself.
• Composite NumberA natural number greater than 1 that is not prime, meaning it has at least one divisor other than 1 and itself.
• FactorA number that divides another number exactly, leaving no remainder.
• DivisorA number that divides an integer evenly, identical to a factor.
• Sieve of EratosthenesAn ancient algorithm for finding all prime numbers up to a specified integer by iteratively marking multiples of primes as composite.
• Fundamental Theorem of ArithmeticEvery integer greater than 1 is either a prime number itself or can be represented as a unique product of prime numbers.

Careers

Roles this can lead toward

Threads 4

Where this connects to other fields — and why it's worth knowing.

• Money, Banking & Credit Economics

  Banks exist partly so two strangers can trust a payment. Prime-number math does the same job without any middleman: it lets people who've never met send money safely, building trust out of pure arithmetic instead of a bank vouching for them.

• Epistemology Philosophy

  There's a clever trick called a zero-knowledge proof: you can prove you know a password without ever revealing the password. That turns a deep question, 'how do I know you know?', into pure math. You pass along the certainty without passing along the secret itself.

• Writing Systems Literature

  Cracking a lost ancient script and cracking a secret code are the same puzzle: hunt for patterns in symbols. That's why Champollion decoding Egyptian hieroglyphs and Turing breaking Nazi codes were really doing one craft, two centuries apart.

• Elections & Voting Politics

  Voting seems stuck with a trade-off: keep your ballot secret, or let people verify the count, but not both. Clever math from internet security can do both at once, proving your vote was counted without revealing who you picked. It dissolves a problem democracy long thought was unavoidable.