Problems & Puzzles: Puzzles

 Puzzle 788. P&p(i)^2&RP Vicente F. Izquierdo sent the following nice puzzle: Find the smallest prime P such that the first k equations are simultaneously prime numbers. P&2^2&RP P&3^2&RP P&5^2&RP ... P&p(k)^2&RP Where RP is the reversible of P. The symbol & means concatenation. Vicente found the minimal P for k=6: 123638027&{2,3,5,7,11,13}^2&720836321 are the following prime numbers: 1236380274720836321 1236380279720836321 12363802725720836321 12363802749720836321 123638027121720836321 123638027169720836321 As a mater of fact he found the minimal P for k=1 to 6: 11,17,1097,7949,780587, 123638027,... Q1. Find more terms Q2. Show that this sequence is finite or infinite.

Contributions came from Vicente F. Izquierdo, Abhiram R. Devesh and Emmanuel Vantieghem. They found the next term on the sequence for Q1. Nobody posted anything about Q2.

VIcente:

"Acabo de encontrar el elemento 7º: 3.259.714.649  para 2,3,5,7,11,13 y 17", May 30, 2015

Abhiram:

"For Q1: The next in series is 3259714649 [325971464949464179523, 325971464999464179523, 3259714649259464179523, 3259714649499464179523,32597146491219464179523, 32597146491699464179523,
32597146492899464179523]- In this case 9464179523 (Reverse of 3259714649 )  is also prime like 11,17,1097 and 7949". May 31, 2015

Emmanuel:

Here is what I could find about puzzle 788 : The smallest prime for  k = 7  is  3259714649. If there is a smallest prime for  k = 8  then it is bigger than  33*10^9.

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On June 10, 2015, Hans Havermann wrote:

"Next two terms are 3259714649 and 76526081651." ...Oops. I just refreshed your page and see that the first one was already submitted. So just 76526081651.

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Vicente Felipe Izquierdo wrote on July 4, 2015:

He subido la secuencia de tu puzzle 788 a OEIS y he puesto tu referencia.
es la A259744 está en borrador todavía,

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