The Largest Prime Less Than the Square of a Prime

Question

The first prime is two. Two squared is four. The largest prime that is less than four is three.

The set of primes is 2,3,5,7,11,13,17,19,23,29,31...

The set of their squares is 4,9,25,49,121,169,289,361,529,841,961...

The set of numbers which I am asking about is 3,7,23,47,113,167,283,359,523,839,953...

Has this particular set of numbers been studied before?

Answer 1

So the answer to my question is no.

I very strongly believe this sequence to be of more importance than mathematicians realize. If there are no papers yet written about it, then perhaps its importance is not yet known. I have begun writing a book that will reveal a deep relationship between this sequence and the distribution of the primes.

Answer 2

Yes.

Next time you are wondering whether a sequence of integers has been considered before, look it up on the Online Encyclopedia of Integer Sequences.

Answer 3

Its OEIS A054270. Which would suggest "yes" to some extent.