| 
									
										
										
										
											2018-10-10 18:03:03 -04:00
										 |  |  |  | --- | 
					
						
							|  |  |  |  | id: 5900f3fe1000cf542c50ff11 | 
					
						
							| 
									
										
										
										
											2021-11-23 11:06:14 -08:00
										 |  |  |  | title: '问题 146:素数模式的研究' | 
					
						
							| 
									
										
										
										
											2018-10-10 18:03:03 -04:00
										 |  |  |  | challengeType: 5 | 
					
						
							| 
									
										
										
										
											2021-02-06 04:42:36 +00:00
										 |  |  |  | forumTopicId: 301775 | 
					
						
							| 
									
										
										
										
											2021-01-13 03:31:00 +01:00
										 |  |  |  | dashedName: problem-146-investigating-a-prime-pattern | 
					
						
							| 
									
										
										
										
											2018-10-10 18:03:03 -04:00
										 |  |  |  | --- | 
					
						
							|  |  |  |  | 
 | 
					
						
							| 
									
										
										
										
											2020-12-16 00:37:30 -07:00
										 |  |  |  | # --description--
 | 
					
						
							|  |  |  |  | 
 | 
					
						
							| 
									
										
										
										
											2021-11-23 11:06:14 -08:00
										 |  |  |  | 使得数字 $n^2 + 1$、$n^2 + 3$、$n^2 + 7$、$n^2 + 9$、$n^2 + 13$ 及 $n^2 + 27$ 为连续素数的最小正整数 $n$ 是 10。 在小于一百万的整数中,所有满足该条件的整数 $n$ 之和为 1242490。 | 
					
						
							| 
									
										
										
										
											2020-02-18 01:40:55 +09:00
										 |  |  |  | 
 | 
					
						
							| 
									
										
										
										
											2021-11-23 11:06:14 -08:00
										 |  |  |  | 请求出在小于一亿五千万的整数中,所有满足该条件的整数 $n$ 之和是多少? | 
					
						
							| 
									
										
										
										
											2018-10-10 18:03:03 -04:00
										 |  |  |  | 
 | 
					
						
							| 
									
										
										
										
											2020-12-16 00:37:30 -07:00
										 |  |  |  | # --hints--
 | 
					
						
							| 
									
										
										
										
											2018-10-10 18:03:03 -04:00
										 |  |  |  | 
 | 
					
						
							| 
									
										
										
										
											2021-11-23 11:06:14 -08:00
										 |  |  |  | `primePattern()` 应该返回 `676333270`。 | 
					
						
							| 
									
										
										
										
											2018-10-10 18:03:03 -04:00
										 |  |  |  | 
 | 
					
						
							|  |  |  |  | ```js | 
					
						
							| 
									
										
										
										
											2021-11-23 11:06:14 -08:00
										 |  |  |  | assert.strictEqual(primePattern(), 676333270); | 
					
						
							| 
									
										
										
										
											2018-10-10 18:03:03 -04:00
										 |  |  |  | ``` | 
					
						
							|  |  |  |  | 
 | 
					
						
							| 
									
										
										
										
											2021-01-13 03:31:00 +01:00
										 |  |  |  | # --seed--
 | 
					
						
							|  |  |  |  | 
 | 
					
						
							|  |  |  |  | ## --seed-contents--
 | 
					
						
							|  |  |  |  | 
 | 
					
						
							|  |  |  |  | ```js | 
					
						
							| 
									
										
										
										
											2021-11-23 11:06:14 -08:00
										 |  |  |  | function primePattern() { | 
					
						
							| 
									
										
										
										
											2021-01-13 03:31:00 +01:00
										 |  |  |  | 
 | 
					
						
							|  |  |  |  |   return true; | 
					
						
							|  |  |  |  | } | 
					
						
							|  |  |  |  | 
 | 
					
						
							| 
									
										
										
										
											2021-11-23 11:06:14 -08:00
										 |  |  |  | primePattern(); | 
					
						
							| 
									
										
										
										
											2021-01-13 03:31:00 +01:00
										 |  |  |  | ``` | 
					
						
							|  |  |  |  | 
 | 
					
						
							| 
									
										
										
										
											2020-12-16 00:37:30 -07:00
										 |  |  |  | # --solutions--
 | 
					
						
							| 
									
										
										
										
											2020-08-13 17:24:35 +02:00
										 |  |  |  | 
 | 
					
						
							| 
									
										
										
										
											2021-01-13 03:31:00 +01:00
										 |  |  |  | ```js | 
					
						
							|  |  |  |  | // solution required | 
					
						
							|  |  |  |  | ``` |