id	title	challengeType	forumTopicId	dashedName
5900f4ea1000cf542c50fffc	Problem 381: (prime-k) factorial	5	302045	problem-381-prime-k-factorial

--description--

For a prime p let S(p) = (\sum (p - k)!)\bmod (p) for 1 ≤ k ≤ 5.

For example, if p = 7,

(7 - 1)! + (7 - 2)! + (7 - 3)! + (7 - 4)! + (7 - 5)! = 6! + 5! + 4! + 3! + 2! = 720 + 120 + 24 + 6 + 2 = 872

As 872\bmod (7) = 4, S(7) = 4.

It can be verified that \sum S(p) = 480 for 5 ≤ p < 100.

Find \sum S(p) for 5 ≤ p < {10}^8.

--hints--

primeKFactorial() should return 139602943319822.

assert.strictEqual(primeKFactorial(), 139602943319822);

function primeKFactorial() {

  return true;
}

primeKFactorial();

// solution required