freeCodeCamp/curriculum/challenges/english/10-coding-interview-prep/project-euler/problem-196-prime-triplets.md

id, title, challengeType, forumTopicId, dashedName

id	title	challengeType	forumTopicId	dashedName
5900f4301000cf542c50ff42	Problem 196: Prime triplets	5	301834	problem-196-prime-triplets

--description--

Build a triangle from all positive integers in the following way:

$$\begin{array}{rrr} & 1 \\ & \color{red}{2} & \color{red}{3} \\ & 4 & \color{red}{5} & 6 \\ & \color{red}{7} & 8 & 9 & 10 \\ & \color{red}{11} & 12 & \color{red}{13} & 14 & 15 \\ & 16 & \color{red}{17} & 18 & \color{red}{19} & 20 & 21 \\ & 22 & \color{red}{23} & 24 & 25 & 26 & 27 & 28 \\ & \color{red}{29} & 30 & \color{red}{31} & 32 & 33 & 34 & 35 & 36 \\ & \color{red}{37} & 38 & 39 & 40 & \color{red}{41} & 42 & \color{red}{43} & 44 & 45 \\ & 46 & \color{red}{47} & 48 & 49 & 50 & 51 & 52 & \color{red}{53} & 54 & 55 \\ & 56 & 57 & 58 & \color{red}{59} & 60 & \color{red}{61} & 62 & 63 & 64 & 65 & 66 \\ & \cdots \end{array}$$

Each positive integer has up to eight neighbours in the triangle.

A set of three primes is called a prime triplet if one of the three primes has the other two as neighbours in the triangle.

For example, in the second row, the prime numbers 2 and 3 are elements of some prime triplet.

If row 8 is considered, it contains two primes which are elements of some prime triplet, i.e. 29 and 31. If row 9 is considered, it contains only one prime which is an element of some prime triplet: 37.

Define S(n) as the sum of the primes in row n which are elements of any prime triplet. Then S(8) = 60 and S(9) = 37.

You are given that S(10000) = 950007619.

Find S(5678027) + S(7208785).

--hints--

primeTriplets() should return 322303240771079940.

assert.strictEqual(primeTriplets(), 322303240771079940);

--seed--

--seed-contents--

function primeTriplets() {

  return true;
}

primeTriplets();

--solutions--

// solution required