data/problems/196.yml
---
:id: 196
:name: Prime triplets
:url: https://projecteuler.net/problem=196
:content: "Build a triangle from all positive integers in the following way:\n\n 1
\ \n 2 3 \n 4 5 6 \n 7 8 9
10 \n11 12 13 14 15 \n16 17 18 19 20 21 \n22 23 24 25 26 27 28 \n29 30 31 32
33 34 35 36 \n37 38 39 40 41 42 43 44 45 \n46 47 48 49 50 51 52 53 54 55 \n56
57 58 59 60 61 62 63 64 65 66 \n. . .\n\nEach positive integer has up to eight
neighbours in the triangle.\n\nA set of three primes is called a _prime triplet_
if one of the three primes has the other two as neighbours in the triangle.\n\nFor
example, in the second row, the prime numbers 2 and 3 are elements of some prime
triplet.\n\nIf row 8 is considered, it contains two primes which are elements of
some prime triplet, i.e. 29 and 31. \nIf row 9 is considered, it contains only
one prime which is an element of some prime triplet: 37.\n\nDefine S(<var>n</var>)
as the sum of the primes in row <var>n</var> which are elements of any prime triplet.
\ \nThen S(8)=60 and S(9)=37.\n\nYou are given that S(10000)=950007619.\n\nFind
S(5678027) + S(7208785).\n\n"