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6n – 1 and 6n + 1

[communicated to me by G. L. Honaker, Jr.]

161 is a common palindrome but with an unusual property nevertheless.
Every number greater than 161 is the sum of distinct primes of the form
6n – 1

Source : "Curious and Interesting Numbers", David Wells.

Experimenting a bit certainly will deliver solutions for these first four numbers :
162 = ? | 163 = ? | 164 = ? | 165 = ?

166 = (6*10 – 1) + (6*18 – 1) = 59 + 107

Did you know ! "Euler's 6n + 1 Theorem"

Every prime of the form 6n + 1 can be written in the form x2+3y2.



A000008 Prime Curios! Prime Puzzle Richard Phillips
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