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.

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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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