- #1
Anzas
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is it true that this function:
f(n) = 3^(n)+2
will give a prime number for any natural value of n?
f(n) = 3^(n)+2
will give a prime number for any natural value of n?
However, there exists a polynomial in 10 variables with integer coefficients such that the set of primes equals the set of positive values of this polynomial obtained as the variables run through all nonnegative integers, although it is really a set of Diophantine equations in disguise (Ribenboim 1991). Jones, Sato, Wada, and Wiens have also found a polynomial of degree 25 in 26 variables whose positive values are exactly the prime numbers (Flannery and Flannery 2000, p. 51).
Anzas said:how about the function
f(n) = 3^(2n)+2
where n is a natural number
A prime number is a positive integer that is only divisible by 1 and itself. In other words, it has exactly two factors.
The prime numbers function is a mathematical function that calculates all the prime numbers within a specified range or up to a given number.
The prime numbers function is used in cryptography to generate large prime numbers that are used as the basis for generating secure encryption keys. This is because prime numbers have unique mathematical properties that make them difficult to factorize, making them ideal for encryption.
Yes, this is known as the fundamental theorem of arithmetic. It states that every positive integer can be expressed as a unique product of prime numbers.
The prime numbers function is closely related to the Riemann Hypothesis, which is a conjecture about the distribution of prime numbers. It states that the prime numbers function can be approximated by a complex mathematical function known as the Riemann zeta function.