| 
									
										
										
										
											2021-05-05 10:13:49 -07:00
										 |  |  |  | --- | 
					
						
							|  |  |  |  | id: 5900f3fe1000cf542c50ff11 | 
					
						
							| 
									
										
										
										
											2021-11-23 11:06:14 -08:00
										 |  |  |  | title: '問題 146:素數模式的研究' | 
					
						
							| 
									
										
										
										
											2021-05-05 10:13:49 -07:00
										 |  |  |  | challengeType: 5 | 
					
						
							|  |  |  |  | forumTopicId: 301775 | 
					
						
							|  |  |  |  | dashedName: problem-146-investigating-a-prime-pattern | 
					
						
							|  |  |  |  | --- | 
					
						
							|  |  |  |  | 
 | 
					
						
							|  |  |  |  | # --description--
 | 
					
						
							|  |  |  |  | 
 | 
					
						
							| 
									
										
										
										
											2021-11-23 11:06:14 -08:00
										 |  |  |  | 使得數字 $n^2 + 1$、$n^2 + 3$、$n^2 + 7$、$n^2 + 9$、$n^2 + 13$ 及 $n^2 + 27$ 爲連續素數的最小正整數 $n$ 是 10。 在小於一百萬的整數中,所有滿足該條件的整數 $n$ 之和爲 1242490。 | 
					
						
							| 
									
										
										
										
											2021-05-05 10:13:49 -07:00
										 |  |  |  | 
 | 
					
						
							| 
									
										
										
										
											2021-11-23 11:06:14 -08:00
										 |  |  |  | 請求出在小於一億五千萬的整數中,所有滿足該條件的整數 $n$ 之和是多少? | 
					
						
							| 
									
										
										
										
											2021-05-05 10:13:49 -07:00
										 |  |  |  | 
 | 
					
						
							|  |  |  |  | # --hints--
 | 
					
						
							|  |  |  |  | 
 | 
					
						
							| 
									
										
										
										
											2021-11-23 11:06:14 -08:00
										 |  |  |  | `primePattern()` 應該返回 `676333270`。 | 
					
						
							| 
									
										
										
										
											2021-05-05 10:13:49 -07:00
										 |  |  |  | 
 | 
					
						
							|  |  |  |  | ```js | 
					
						
							| 
									
										
										
										
											2021-11-23 11:06:14 -08:00
										 |  |  |  | assert.strictEqual(primePattern(), 676333270); | 
					
						
							| 
									
										
										
										
											2021-05-05 10:13:49 -07:00
										 |  |  |  | ``` | 
					
						
							|  |  |  |  | 
 | 
					
						
							|  |  |  |  | # --seed--
 | 
					
						
							|  |  |  |  | 
 | 
					
						
							|  |  |  |  | ## --seed-contents--
 | 
					
						
							|  |  |  |  | 
 | 
					
						
							|  |  |  |  | ```js | 
					
						
							| 
									
										
										
										
											2021-11-23 11:06:14 -08:00
										 |  |  |  | function primePattern() { | 
					
						
							| 
									
										
										
										
											2021-05-05 10:13:49 -07:00
										 |  |  |  | 
 | 
					
						
							|  |  |  |  |   return true; | 
					
						
							|  |  |  |  | } | 
					
						
							|  |  |  |  | 
 | 
					
						
							| 
									
										
										
										
											2021-11-23 11:06:14 -08:00
										 |  |  |  | primePattern(); | 
					
						
							| 
									
										
										
										
											2021-05-05 10:13:49 -07:00
										 |  |  |  | ``` | 
					
						
							|  |  |  |  | 
 | 
					
						
							|  |  |  |  | # --solutions--
 | 
					
						
							|  |  |  |  | 
 | 
					
						
							|  |  |  |  | ```js | 
					
						
							|  |  |  |  | // solution required | 
					
						
							|  |  |  |  | ``` |