Problems & Puzzles: Puzzles

Puzzle 421. Staircase of consecutive primes

JM Bergot sent one more nice puzzle:

Call three consecutive primes a triplet.

269+271+277=817 NOT prime

Starting at 5 I got three levels of linked triplets.
Each triplet sums to a prime and leads to the start of
a new triplet. How many levels can you find starting
at which prime?

In a fast search I (CR) found a 7 level starting with the prime 1783841

Q. Can you find starting primes with levels greater than 7?


Results can be summarized in this table:

Levels minimal p Author
3 5 JM Bergot
4 7 CR
5 2543 CR
6 249217 CR
7 1783841 CR
8 2494517 FF, JKA, FS, JT
9 624921844601 JKA
10 507995698619 JKA

CR: C. Rivera; FF: Farideh Firoozbakht; JKA: J. K. Andersen; FS: Frederick Schneider; JT: Jacques Tramu

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