Prime number
A prime number is an integer greater than one whose only positive divisors are one and itself.
Hacking Cryptography
A prime number is an integer greater than one that has no positive divisors other than one and itself.
- How it is used
- Supports asymmetric key generation and explains why integer factorization can serve as a public-key cryptographic trapdoor.
- How deep it goes
- Defines primes, demonstrates factorization, and explains probabilistic testing, but defers detailed asymmetric algorithms.
- Examples
- Uses 13, 37, 42, and the worked factorization of 764,512 to distinguish primes from composite numbers.
- What you can do after
- Evaluate candidate integers, follow cryptographic prime generation, and understand its relationship to RSA factorization hardness.
Real-World Cryptography
A prime number is an integer greater than one with no positive divisors other than one and itself, used in finite-field Diffie-Hellman as the modulus.
- How it is used
- Supplies the modulus and group size for finite-field Diffie-Hellman key exchange.
- How deep it goes
- Defines primality, relates size to discrete-logarithm security, and stops short of proving primality or deriving DH attacks.
- Examples
- Uses small primes, a modulus-5 clock, probable-prime generation, ROCA, and historical broken DH parameter sets.
- What you can do after
- Configure DH with appropriately sized, carefully specified prime groups and recognize risks from faulty parameter generation.
Elliptic Curve Cryptography for Developers
A prime number is a positive integer greater than one that has no positive divisors other than one and itself.
- How it is used
- Defines the modulus for finite-field arithmetic used throughout elliptic-curve cryptography.
- How deep it goes
- Develops prime numbers through field rules, modular arithmetic, cryptographic scale, and implementation-oriented GMP routines.
- Examples
- Uses a modulo-43 clock, 256-bit field sizes, and a largest-prime curve cardinality to ground the concept.
- What you can do after
- Evaluate/understand how prime moduli support finite-field operations and cryptographic elliptic-curve parameters.
Read how Elliptic Curve Cryptography for Developers explains prime number →
Learn C++ by Example
A prime number is a positive integer greater than one that has no positive divisors other than one and itself.
- How it is used
- Uses primality testing to constrain random targets in a number-guessing game.
- How deep it goes
- Explains a tested modulo algorithm through square-root bounds, while deferring further optimizations and the sieve of Eratosthenes.
- Examples
- Demonstrates primes through 2, 3, 4, 6, and 35, then applies them to a five-digit guessing game.
- What you can do after
- Build a C++ primality predicate and use rejection sampling to generate prime game targets.
Regular Expression Puzzles and AI Coding Assistants
A prime number is a natural number greater than one that has no positive divisors other than one and itself.
- How it is used
- Uses prime sequences to test whether regular expressions can recognize arithmetic structure rather than merely imitate its surface pattern.
- How deep it goes
- Contrasts prime definition, sieve mechanics, encoded examples, and regex failure without developing a formal impossibility proof.
- Examples
- Uses @-encoded prefixes such as 2 3 5 7 11 and counterexamples that skip 5 or include 4.
- What you can do after
- Evaluate prime-recognition solutions by checking correctness, edge cases, algorithmic fit, and explanations instead of trusting executable-looking code.
Read how Regular Expression Puzzles and AI Coding Assistants explains prime number →
Related concepts
- crypto/rand packageproduced by · The crypto/rand package is Go’s standard-library package for generating cryptographically secure random data from system-provided entropy sources.
- public key cryptographyuses · Public-key cryptography is asymmetric cryptography that uses mathematically related public and private keys for encryption, decryption, signing, and verification.
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