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Twin prime. A twin prime is a prime number that is either 2 less or 2 more than another prime number—for example, either member of the twin prime pair (17, 19) or (41, 43). In other words, a twin prime is a prime that has a prime gap of two. Sometimes the term twin prime is used for a pair of twin primes; an alternative name for this is prime ...
the 33rd prime number; the next is 139, with which it comprises a twin prime, and thus 137 is a Chen prime. [ 1 ] an Eisenstein prime with no imaginary part and a real part of the form 3 n − 1 {\displaystyle 3n-1} .
A prime gap is the difference between two successive prime numbers. The n -th prime gap, denoted gn or g ( pn) is the difference between the ( n + 1)-st and the n -th prime numbers, i.e. We have g1 = 1, g2 = g3 = 2, and g4 = 4. The sequence ( gn) of prime gaps has been extensively studied; however, many questions and conjectures remain unanswered.
Agoh–Giuga conjecture. Agrawal's conjecture. Andrica's conjecture. Artin's conjecture on primitive roots.
One of the greatest unsolved mysteries in math is also very easy to write. Goldbach’s Conjecture is, “Every even number (greater than two) is the sum of two primes.”. You check this in your ...
Conjecture. The real part (red) and imaginary part (blue) of the Riemann zeta function along the critical line Re ( s) = 1/2. The first non-trivial zeros can be seen at Im ( s) = ±14.135, ±21.022 and ±25.011. The Riemann hypothesis, a famous conjecture, says that all non-trivial zeros of the zeta function lie along the critical line.
The first Hardy–Littlewood conjecture predicts there are infinitely many of these. In number theory, the first Hardy–Littlewood conjecture [1] states the asymptotic formula for the number of prime k-tuples less than a given magnitude by generalizing the prime number theorem. It was first proposed by G. H. Hardy and John Edensor Littlewood ...
A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways of writing it as a product, 1 × 5 or 5 × 1, involve 5 itself. However, 4 is composite because it is a ...