I am currently working quite hard and putting in a decent amount of effort in to my first mathematical thesis. As a high school student, this is becoming increasingly difficult. Because of my fear of having my ideas stolen, I kindly will refuse to state the abstract of that thesis. I am writing it for two reasons: 1) It would look like gold on college apps and 2) I love the type of math I am focused on.
My question (sorry for the fluff): Can I have a proof or disproof that there exist finitelyAre infinitely many primes $P_{2n-1}$ primes that are expressible as a $3n-1$$3k-1$?
Note:
$P_{2n-1}$ primes denotes every other prime beginning with the first prime. This would be an example of that set of primes: $2,5,11,\cdots$. Oeis sequence
Primes represented as $3n-1$ are examples of the primes such that $3n-1=p$ has solutions. Oeis sequence
At least with an answer to your question, my thesis can go one way or another, but as this is really computational to generate a given quantity, IThe primes should get a solution$P_{2n-1}$ are every other prime beginning with any answer I get. That means that this statement could be incorrect$2$: $2,5,11,17,23,31,\cdots$.
Key point- I have 4 major roadblocks here to creating my thesis, and out The first few are of respect for the mathematical communityform $3k-1$, I will solve the other 3 on my own. Thisbut $31$ is the highest priority road block though.
I have no clue how to prove this question whatsoevernot.