TITLE: Properties of prime numbers proven as finite
QUESTION [6 upvotes]: Many modern proofs/conjectures concerning prime numbers (twin primes, infinite primes not containing one specific digit) intend to show that some property of prime numbers is infinite.
Are there any similar, nontrivial properties of prime numbers that have been proven to only appear within the first n, but not the rest (finite)? As a rough guideline to nontriviality, there should be at least ~3 somewhat spread out instances of the property that discontinue after reaching some number above ~50. The property cannot solely involve a simple operator such as < or >, and ideally should not involve repeated deletion of digits (truncatable primes) as this makes proof via exhaustion easier.

REPLY [3 votes]: Some possible solutions after digging into this problem a bit deeper:

Primes where you can repeatedly delete any number and still have a prime:
2, 3, 5, 7, 23, 37, 53 and 73

Left truncatable primes

Right truncatable primes

Left and right truncatable primes


https://en.wikipedia.org/wiki/Truncatable_prime
However, all of these involve some sort of deletion of numbers, which make proof via exhaustion easy. The most interesting solution would not involve deletion.
EDIT with sufficient answer:
Upon consulting Wikipedia's list of prime numbers, it appears a few more candidate sequences exist including supersingular primes, minimal primes, Wilson primes, Wolstenholme primes, Fermat primes, and Stern primes.
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