# 48

This number is a composite.

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The smallest possible sum for a set of four distinct primes such that the sum of any three is prime: {5, 7, 17, 19}.
Questions: Is there a prime quadruplet (of the form {p, p+2, p+6, p+8}) with this property? (Click here for answer.) How about prime sextuplets, where the sum of any five are prime? (Click here for answer.) Or greater admissible prime constellations (

*k*-tuples) such that the sum of any

*k*-1 primes is prime? Update: Jens Kruse Andersen has found that due to divisibility by small primes, there is no

*k*from 7 to 50 for which there exists a prime

*k*-tuplet such that the sum of any

*k*-1 is prime.

Submitted: 2013-03-30 12:36:40; Last Modified: 2014-08-30 10:16:45.

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