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


Andersen wrote:

p1=352367441 is actually the first for k=6. The first 11 for k>5 are in
The 4th is p1=23908162969 which is the first for k=7.

I replied him:

Thank you. BTW 6449058697 is not prime in A219271.


Emmanuel wrote

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


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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