Problems & Puzzles: Puzzles

 Puzzle 708 Find sets of k consecutive primes such that... In this puzzle you are asked to find sets of k consecutive primes, p1, p2, ..., pk such that the following concatenations are primes: p1&p2 p1&p2&p3 ... p1&p2&p3&...&pk My largest example is this one: k=6, p1=352367441 Q. Send sets of these for k>6. _____ Note: "&" means here concatenation operator.

Contributions came from J. K. Andersen, Emmanuel Vantieghem & Giovanni Resta

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Andersen wrote:

p1=352367441 is actually the first for k=6. The first 11 for k>5 are in http://oeis.org/A219271
The 4th is p1=23908162969 which is the first for k=7.

I replied him:

Thank you. BTW 6449058697 is not prime in A219271.

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Emmanuel wrote

After about 40 hours of computation my PC found a solution to puzzle 708  for  k = 7  with  p1 = 23908162969.

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Giovanni Resta wrote:

Two more solutions: starting from 23908162969 (k=7) and 483148266971 (k=8).  No more  up to 10^14.

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