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?

score 2 · Answer 1 · answered Sep 27 '14 at 05:03

2

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

answered Sep 27 '14 at 05:03

user164587

1,509

score 1 · Answer 2 · answered Sep 27 '14 at 05:03

1

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.

answered Sep 27 '14 at 05:03

Yuval Filmus

57,157

2

It is listed as A054270. But I can't see that it has been "studied"? I cannot find any reference to a paper there. – miracle173 Sep 27 '14 at 05:18
1

If the sequence had been studied further, I would imagine there would be mention of it in the OEIS. Certainly it has been "noted" before. – Yuval Filmus Sep 27 '14 at 05:19
1

Note also sequence A054271. – Charles Dec 19 '22 at 14:38

Jeffrey Young · Accepted Answer · 2014-10-02T06:52:34.940

0

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.

edited Oct 02 '14 at 06:52

answered Sep 27 '14 at 07:24

Jeffrey Young

841

Can you elaborate on why this sequence is so important? That would be interesting to read. – Joonas Ilmavirta Sep 29 '14 at 14:16
@JoonasIlmavirta I am planning to write a book about this because the information takes up so much space. – Jeffrey Young Oct 02 '14 at 06:51

The Largest Prime Less Than the Square of a Prime

3 Answers3