28657

28657 is a natural number that sits between 28656 and 28658. In mathematics it is notable for its role in the Fibonacci sequence and as a prime number.

As a Fibonacci number, 28657 equals F(23) when the sequence is defined by F(0) = 0, F(1) = 1 and F(n) = F(n−1) + F(n−2). Therefore, 28657 is the 23rd term in the standard Fibonacci sequence. The value is relatively modest in size but carries significance within number theory due to its primality.

28657 is a prime number, making it one of the Fibonacci primes. Fibonacci primes are Fibonacci numbers that are prime, and they occur sporadically within the sequence. The identification of 28657 as prime has made it a point of reference in discussions of primality among Fibonacci numbers. In this context, the next known Fibonacci prime after 28657 is F(29) = 514,229.

Beyond its place in the Fibonacci sequence, 28657 does not have widely recognized applications in everyday mathematics or applied sciences. It is primarily noted for its status within number theory and for illustrating the intersection of Fibonacci numbers and primality. See also Fibonacci numbers and Fibonacci primes for related context.