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When a prime is divided by 60, the remainder is a composite number.  When a second prime is divided by 60, the remainder is a prime.  Find the smallest possible value of the second prime.

 
 Oct 30, 2024
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When a prime is divided by 60, the remainder is a composite number.  When a second prime is divided by 60, the remainder is a prime.  Find the smallest possible value of the second prime.  

 

2 is the smallest prime.  2 / 60 = 0 R 2 so the remainder is a prime as well.  

 

However, I think that is not the intent of the problem.  Let's go larger than 60.    

 

Note the smallest primes – 2, 3, 5, 7, 11, etc – and then add to 60    

 

                             62 not prime   

                             63 not prime   

                             65 not prime   

                             67 prime and 67 / 60 = 1 R 7 and the remainder is prime as well.    

.   

 Oct 30, 2024

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