Everyone always asks about whether forms like, say, $x^2+1$, or $n!!-1$, or sums of digits of $\pi$, or any number of others, are prime infinitely many times.
Are there any forms of primes describable in roughly that sort of way which are known to be finite?
If anyone is seeking further clarification on what I mean by "forms of primes", this Wikipedia category is exactly the sort of thing I mean.
On
Yes any univariate integer coefficient polynomial like $3x^2+5x+2$ ( aka with even number of odd coefficients and an even constant term, Also an odd number of odd coefficients with an odd constant term, or all even coefficients and an even constant term) is alway even evaluated at integers, so only at $x=0$ could it be prime. You can turn this multivariate if you think hard. These are all examples of the trivial even primes are finite argument, this can be done with any prime constant term though.
By clicking on some of the links on the page you linked to, one finds that truncatable primes (of three sorts) and minimal primes are finite sets.