Problems & Puzzles: Puzzles

Puzzle 272.  P(n) & n

This week I contributed with three more terms to the EIS A075902, related to these prime numbers p(n) such that n is a string of p(n).

At the moment of sending my contribution I noticed and wrote this:

BTW, p(n)= 1966640443 is such that n=96664044. This is the first case where n is an internal string of p(n)

Maybe you want verify it here.

Questions:

Maybe you would like to get more terms for this sequence; or just to find the next prime as 1966640443.


Solution:

Could you believe it!... This sequence was already explored and solved in my own puzzle 217!!!

What to say?

The first of all, a public apology to the solvers of Puzzle 217, specially to J. K. Andersen and and Bill Murphy. They are the first discoverers of the three terms sent by me to EIS A075902 and I will let Neil's to know this fact. I will do the same to G. L. Honaker and the PC1966640443.

Unfortunately for me, neither these 3 terms was previously sent to EIS by anybody, not the number 1966640443 was published in the Honaker's Prime Curios site, places that I consulted before publishing this puzzle.

Moreover, I made a fast search for the number 1966640443 in my own site, using the search box of my main page, and do you know what?... this search box feature is incapable to detect any number inside of a table and -  yes, of course - 1966640443 is inside a table in the puzzle 217.

So, all my warning tools failed and I got misguided, despite all my efforts.

Am I starting getting lost in my own labyrinth?

I should be feeling now as happy as Daedelus inside my own labyrinth (prime puzzles site). Instead, sometimes Iím starting to feel my self, as a lost Theseus, without a reliable thread (and without a graceful Ariadne out there ;-) The worst, I guess the Minotaur is alive...

I'm very very sorry, my friends. Please accept my truly excuses.

Haven't said that, let's go on, hopefully free of dust and without too much repetitions in the near future (otherwise the lemma of my main page should change to 'six years on the same road')

***

Going back to the questions of this puzzle, they are still alive!

No other solution as 1966640443 has been found and we are not sure if the largest Murphy's solution published in the puzzle 217

n = 46492090901 p(n) = 1246492090901

is the next term of the sequence EIS A075902. So, the puzzle is still open...

***

 



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