freeCodeCamp/curriculum/challenges/english/10-coding-interview-prep/project-euler/problem-123-prime-square-remainders.md

---
id: 5900f3e71000cf542c50fefa
title: 'Problem 123: Prime square remainders'
challengeType: 5
forumTopicId: 301750
dashedName: problem-123-prime-square-remainders
---

# --description--

Let pn be the nth prime: 2, 3, 5, 7, 11, ..., and let r be the remainder when (pn−1)n + (pn+1)n is divided by pn2.

For example, when n = 3, p3 = 5, and 43 + 63 = 280 ≡ 5 mod 25.

The least value of n for which the remainder first exceeds 109 is 7037.

Find the least value of n for which the remainder first exceeds 1010.

# --hints--

`euler123()` should return 21035.

```js
assert.strictEqual(euler123(), 21035);
```

# --seed--

## --seed-contents--

```js
function euler123() {

  return true;
}

euler123();
```

# --solutions--

```js
// solution required
```
-												feat(challenge-md): Add initial markdown challenge files

											
										
										
											2018-09-30 23:01:58 +01:00
+								---
 								id: 5900f3e71000cf542c50fefa
 								title: 'Problem 123: Prime square remainders'
-												Feat: add new Markdown parser (#39800)

and change all the challenges to new `md` format.
											
										
										
											2020-11-27 19:02:05 +01:00
+								challengeType: 5
-												fix(curriculum): Added forumTopicId to remaining 1200 challeng… (#36558)


											
										
										
											2019-08-05 09:17:33 -07:00
+								forumTopicId: 301750
-												feat(curriculum): restore seed + solution to Chinese (#40683)

* feat(tools): add seed/solution restore script

* chore(curriculum): remove empty sections' markers

* chore(curriculum): add seed + solution to Chinese

* chore: remove old formatter

* fix: update getChallenges

parse translated challenges separately, without reference to the source

* chore(curriculum): add dashedName to English

* chore(curriculum): add dashedName to Chinese

* refactor: remove unused challenge property 'name'

* fix: relax dashedName requirement

* fix: stray tag

Remove stray `pre` tag from challenge file.

Signed-off-by: nhcarrigan <nhcarrigan@gmail.com>

Co-authored-by: nhcarrigan <nhcarrigan@gmail.com>
											
										
										
											2021-01-13 03:31:00 +01:00
+								dashedName: problem-123-prime-square-remainders
-												feat(challenge-md): Add initial markdown challenge files

											
										
										
											2018-09-30 23:01:58 +01:00
+								---
-												Feat: add new Markdown parser (#39800)

and change all the challenges to new `md` format.
											
										
										
											2020-11-27 19:02:05 +01:00
+								# --description--
-												feat(challenge-md): Add initial markdown challenge files

											
										
										
											2018-09-30 23:01:58 +01:00
+								Let pn be the nth prime: 2, 3, 5, 7, 11, ..., and let r be the remainder when (pn−1)n + (pn+1)n is divided by pn2.
-												Feat: add new Markdown parser (#39800)

and change all the challenges to new `md` format.
											
										
										
											2020-11-27 19:02:05 +01:00
-												feat(challenge-md): Add initial markdown challenge files

											
										
										
											2018-09-30 23:01:58 +01:00
+								For example, when n = 3, p3 = 5, and 43 + 63 = 280 ≡ 5 mod 25.
-												Feat: add new Markdown parser (#39800)

and change all the challenges to new `md` format.
											
										
										
											2020-11-27 19:02:05 +01:00
+								The least value of n for which the remainder first exceeds 109 is 7037.
-												feat(challenge-md): Add initial markdown challenge files

											
										
										
											2018-09-30 23:01:58 +01:00
-												Feat: add new Markdown parser (#39800)

and change all the challenges to new `md` format.
											
										
										
											2020-11-27 19:02:05 +01:00
+								Find the least value of n for which the remainder first exceeds 1010.
-												feat(challenge-md): Add initial markdown challenge files

											
										
										
											2018-09-30 23:01:58 +01:00
-												Feat: add new Markdown parser (#39800)

and change all the challenges to new `md` format.
											
										
										
											2020-11-27 19:02:05 +01:00
+								# --hints--
-												feat(challenge-md): Add initial markdown challenge files

											
										
										
											2018-09-30 23:01:58 +01:00
-												Feat: add new Markdown parser (#39800)

and change all the challenges to new `md` format.
											
										
										
											2020-11-27 19:02:05 +01:00
+								`euler123()` should return 21035.
-												feat(challenge-md): Add initial markdown challenge files

											
										
										
											2018-09-30 23:01:58 +01:00
-												Feat: add new Markdown parser (#39800)

and change all the challenges to new `md` format.
											
										
										
											2020-11-27 19:02:05 +01:00
+								```js
 								assert.strictEqual(euler123(), 21035);
-												feat(challenge-md): Add initial markdown challenge files

											
										
										
											2018-09-30 23:01:58 +01:00
+								```
-												Feat: add new Markdown parser (#39800)

and change all the challenges to new `md` format.
											
										
										
											2020-11-27 19:02:05 +01:00
+								# --seed--
-												feat(challenge-md): Add initial markdown challenge files

											
										
										
											2018-09-30 23:01:58 +01:00
-												Feat: add new Markdown parser (#39800)

and change all the challenges to new `md` format.
											
										
										
											2020-11-27 19:02:05 +01:00
+								## --seed-contents--
-												feat(challenge-md): Add initial markdown challenge files

											
										
										
											2018-09-30 23:01:58 +01:00
 								```js
 								function euler123() {
-												fix: remove Good luck! comment from challenge seed code (#39575)


											
										
										
											2020-09-15 09:57:40 -07:00
-												feat(challenge-md): Add initial markdown challenge files

											
										
										
											2018-09-30 23:01:58 +01:00
+								  return true;
 								}
 								euler123();
 								```
-												Feat: add new Markdown parser (#39800)

and change all the challenges to new `md` format.
											
										
										
											2020-11-27 19:02:05 +01:00
+								# --solutions--
-												feat(challenge-md): Add initial markdown challenge files

											
										
										
											2018-09-30 23:01:58 +01:00
 								```js
 								// solution required
 								```