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								---
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
							
								id: 5900f3911000cf542c50fea4
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
							
								title: 'Problem 37: Truncatable primes'
							 
						 
					
						
							
								
									
										
										
										
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								challengeType: 5
							 
						 
					
						
							
								
									
										
										
										
											2019-08-05 09:17:33 -07:00 
										
									 
								 
							 
							
								
									
										 
								
							 
							
								 
							
							
								forumTopicId: 302031
							 
						 
					
						
							
								
									
										
										
										
											2021-01-13 03:31:00 +01:00 
										
									 
								 
							 
							
								
									
										 
								
							 
							
								 
							
							
								dashedName: problem-37-truncatable-primes
							 
						 
					
						
							
								
									
										
										
										
											2018-09-30 23:01:58 +01:00 
										
									 
								 
							 
							
								
							 
							
								 
							
							
								---
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
							
								
							 
						 
					
						
							
								
									
										
										
										
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								# --description--
  
						 
					
						
							
								
									
										
										
										
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											2018-09-30 23:01:58 +01:00 
										
									 
								 
							 
							
								
							 
							
								 
							
							
								The number 3797 has an interesting property. Being prime itself, it is possible to continuously remove digits from left to right, and remain prime at each stage: 3797, 797, 97, and 7. Similarly we can work from right to left: 3797, 379, 37, and 3.
							 
						 
					
						
							
								
									
										
										
										
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								Find the sum of the only `n`  (8 ≤ `n`  ≤ 11) primes that are both truncatable from left to right and right to left.
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
							
								
							 
						 
					
						
							
								
									
										
										
										
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								NOTE: 2, 3, 5, and 7 are not considered to be truncatable primes.
							 
						 
					
						
							
								
									
										
										
										
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								# --hints--
  
						 
					
						
							
								
							 
							
								
							 
							
								 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
							
								`truncatablePrimes(8)`  should return a number. 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
							
								```js
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
							
								assert(typeof truncatablePrimes(8) === 'number');
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
							
								```
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
							
								`truncatablePrimes(8)`  should return 1986. 
						 
					
						
							
								
									
										
										
										
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								```js
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
							
								assert(truncatablePrimes(8) == 1986);
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
							
								```
							 
						 
					
						
							
								
									
										
										
										
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								`truncatablePrimes(9)`  should return 5123. 
						 
					
						
							
								
									
										
										
										
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								```js
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
							
								assert(truncatablePrimes(9) == 5123);
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
							
								```
							 
						 
					
						
							
								
									
										
										
										
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								`truncatablePrimes(10)`  should return 8920. 
						 
					
						
							
								
									
										
										
										
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								```js
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
							
								assert(truncatablePrimes(10) == 8920);
							 
						 
					
						
							
								
									
										
										
										
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								```
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
							
								
							 
						 
					
						
							
								
									
										
										
										
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								`truncatablePrimes(11)`  should return 748317. 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
							
								```js
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
							
								assert(truncatablePrimes(11) == 748317);
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
							
								```
							 
						 
					
						
							
								
									
										
										
										
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								# --seed--
  
						 
					
						
							
								
									
										
										
										
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								## --seed-contents--
  
						 
					
						
							
								
									
										
										
										
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								```js
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
							
								function truncatablePrimes(n) {
							 
						 
					
						
							
								
									
										
										
										
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								  return n;
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
							
								}
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
							
								truncatablePrimes(11);
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
							
								```
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
							
								
							 
						 
					
						
							
								
									
										
										
										
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								# --solutions--
  
						 
					
						
							
								
									
										
										
										
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								```js
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
							
								// solution required
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
							
								```