---
id: 5900f4831000cf542c50ff95
challengeType: 5
title: 'Problem 278: Linear Combinations of Semiprimes'
forumTopicId: 301928
---

## Description
<section id='description'>
Given the values of integers 1 < a1 < a2 <... < an, consider the linear combinationq1a1 + q2a2 + ... + qnan = b, using only integer values qk ≥ 0.


Note that for a given set of ak, it may be that not all values of b are possible.
For instance, if a1 = 5 and a2 = 7, there are no q1 ≥ 0 and q2 ≥ 0 such that b could be
1, 2, 3, 4, 6, 8, 9, 11, 13, 16, 18 or 23.

In fact, 23 is the largest impossible value of b for a1 = 5 and a2 = 7. We therefore call f(5, 7) = 23. Similarly, it can be shown that f(6, 10, 15)=29 and f(14, 22, 77) = 195.


Find ∑ f(p*q,p*r,q*r), where p, q and r are prime numbers and p < q < r < 5000.
</section>

## Instructions
<section id='instructions'>

</section>

## Tests
<section id='tests'>

```yml
tests:
  - text: <code>euler278()</code> should return 1228215747273908500.
    testString: assert.strictEqual(euler278(), 1228215747273908500);

```

</section>

## Challenge Seed
<section id='challengeSeed'>

<div id='js-seed'>

```js
function euler278() {
  // Good luck!
  return true;
}

euler278();
```

</div>



</section>

## Solution
<section id='solution'>

```js
// solution required
```

</section>