Twin prime

A prime number that differs from another prime number by 2. The two primes form a twin-prime pair, such as 11 and 13.

Prime number: A natural number greater than 1 with exactly two positive divisors: 1 and itself. Each member of a twin-prime pair must be prime.
Twin prime conjecture: The conjecture that infinitely many pairs of primes differ by 2. It asks whether twin-prime pairs continue without bound.
Modulo arithmetic: Arithmetic that treats integers as equivalent when they have the same remainder after division by a fixed modulus. Residue classes reveal local restrictions on possible prime pairs.
Twin prime pair: Two prime numbers whose difference is 2. Examples such as 3 and 5 are the individual instances counted by the concept.
Prime gap: The difference between consecutive prime numbers. A twin-prime pair consists of consecutive primes whose gap is 2.
Brun's theorem: A theorem stating that the sum of the reciprocals of twin primes converges. It proves a strong limitation on the density of twin primes without settling infinitude.
Prime k-tuple conjecture: A conjecture describing when a finite pattern of shifted integers occurs as primes infinitely often. Its admissible-pattern framework predicts infinitely many twin primes.
Sophie Germain prime: A prime p for which 2p+1 is also prime. A Sophie Germain prime greater than 3 generates the twin pair 2p and 2p+2 only after scaling? no
Divisibility: An integer is divisible by another nonzero integer when their quotient is an integer. Testing divisibility by smaller primes establishes whether a candidate is prime.
Bounded gaps between primes: The result that some fixed finite gap occurs between infinitely many pairs of primes. It proves infinitely many bounded prime gaps, but not specifically gaps of 2.

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