What functions can create infinite primes?

Recentlly iv'e been thinking on functions that create an infinite amount of primes, so for example looking at the function f(n) = n its clear this function creates an infinite amount of primes in fact all of the primes can be generated from this function, another example is f(n) = 3n + 1 which generates an infinte amount of primes and loosely speaking around a half of all primes can be generated by this function. The problem is to find a test for a function f:N -> N to find whether it can create an infinte amount of primes. A good place to start is with a finite polinomial with integer coefficient, a specific example i curentlly struggle with is f(n) = n^2 + 7.

Note: if you can find a solution to a general infinite polynomial it might be possible to extend the solution via taylor series to all function from the natural numbers to the natural numbers.

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Comments

Any f(n)=an+b while gcd(a,b)=1

alon maayan - 8 months, 3 weeks ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$