Problems & Puzzles: Puzzles

Puzzle 421. Staircase of consecutive primes JM Bergot sent one more nice puzzle: Call three consecutive primes a triplet. 5+7+11=23 23+29+31=83 83+89+97=269 269+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?

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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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