Twin primes are prime numbers that are separated by 2, such as: 3 and 5, 5 and 7, 11 and 13.....etc. If you multiply any two twin primes(other that 3 and 5) and divide their product by 9, the remainder is ALWAYS 8. Give a proof that this so for all products of twin primes, with the exception above. Thank you.

Guest Jun 4, 2017

1+0 Answers


The two prime numbers can be written as n+1 and n-1. Since one of the consecutive numbers n-1, n, n+1 is divisible by 3 and n-1 and n+1 are prime (so not divisible by 3 (Exception here)) so n is divisible by 3. So n*n is divisible by 9. Now: (n-1)*(n+1)=n*n-1.= -1 mod 9 = 8 mod 9.

Guest Jun 5, 2017

6 Online Users

We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details