Departure question
Find order without counting everythingPort 6 of 16Where two intuitions collide
The next prime appears irregularly, yet the density of primes becomes remarkably predictable from afar.
This voyage is an editorial path for understanding, not a claim of direct historical influence or sole invention.
Numbers greater than one divisible only by 1 and themselves — 2, 3, 5, 7, 11, 13, … The multiplicative atoms of the integers. RSA relies on the apparent classical difficulty of factoring large composites, while internet security combines many cryptographic methods, protocols, and implementations.
The first 25 prime numbers |
|---|
2, 3, 5, 7, 11 |
13, 17, 19, 23, 29 |
31, 37, 41, 43, 47 |
53, 59, 61, 67, 71 |
73, 79, 83, 89, 97 |
The atoms of the integers, easily found with the Sieve of Eratosthenes.
Integers greater than 1 divisible only by 1 and themselves — the multiplicative atoms of whole numbers. Euclid proved there are infinitely many; primes also support several, but not all, modern cryptographic systems.
Q.Is 6 prime?
Q.Is 13 prime?
Ports in time
Follow the scenes to see problems, notation, standards of proof, and applications changing across different times and places.
Book IX of the Elements gives an elegant contradiction proof that primes never run out — one of the earliest landmarks of pure mathematics.
No reliable place is given, so time continues without an invented pin
Continue through the world of this yearA procedure traditionally attributed to Eratosthenes crosses out successive multiples to leave primes. Later evidence preserves the attribution, not an exact ancient implementation identical to modern code.
The recorded place matches a canonical map anchor
Continue this scene on the mapRiemann connected prime distribution to zeros of the zeta function, opening a problem that remains one of the Millennium Prize Problems.
No reliable place is given, so time continues without an invented pin
Continue through the world of this yearRivest, Shamir, and Adleman created public-key cryptography from the asymmetry between multiplying large primes and factoring their product.
No reliable place is given, so time continues without an invented pin
Continue through the world of this yearRSA and several other constructions use arithmetic built from large primes or finite fields. Internet security also depends on elliptic curves, symmetric ciphers, hashes, protocols, implementations, and key management; primes are important, not the whole system.
Curated sources and problems. Bring one discovery back from OEIS, Project Euler, MathOverflow, or arXiv.
No concept belongs to one person
These are not inventor credits. They are different ports: opening a problem, sharpening a language, or carrying it into another world.
Number lenses
These numbers are editorial lenses for the voyage, not required prerequisites.
Primes are the indivisible building blocks of multiplication among natural numbers.
Open the number voyage
Extending to negative numbers changes signs while preserving divisibility structure.
Open the number voyage
Trace recurring structure through exploding possibilities, divisibility, and the apparent irregularity of primes.
Open the number voyage
Concept genealogy
Concepts arriving from before
No direct prerequisite port is curated yet.
Current port
Prime Numbers
Only direct editorial links are shown; this is not a complete learning order or historical influence line.
