My Math Forum All primes are in form of 10nk+c

 Number Theory Number Theory Math Forum

 August 11th, 2016, 07:09 PM #1 Newbie   Joined: Aug 2016 From: Hong Kong Posts: 5 Thanks: 0 All primes are in form of 10nk+c Prove: For positive integer n, and any positive integer c that 0 < c < 10n and c is coprime with 10n, all primes larger than 10n can be expressed in form of 10nk+c where k is a positive integer. Remark: c may have various values. For example, when n=2, possible values of c are: 1,3,7,9,11,13,17,19
 August 11th, 2016, 11:53 PM #2 Math Team   Joined: Nov 2014 From: Australia Posts: 689 Thanks: 244 Let $m = nk$. Then setting $n = 1$, it is clear that $m$ can be any natural number. It is a consequence of the division algorithm that any positive number (including primes) can be represented by $10m + c$, where $0 < c < 10$. This proves the result.
 August 12th, 2016, 08:31 AM #3 Global Moderator     Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,935 Thanks: 1129 Math Focus: Elementary mathematics and beyond But if $c$ is coprime to $10n$ how would you represent, say, 12? Thanks from Joppy
 August 12th, 2016, 08:59 AM #4 Global Moderator   Joined: Dec 2006 Posts: 20,629 Thanks: 2077 If $c$ isn't coprime to $10n$, $10n + c$ isn't a prime. Thanks from greg1313 and Joppy
 August 12th, 2016, 03:26 PM #5 Math Team   Joined: Nov 2014 From: Australia Posts: 689 Thanks: 244 Ah. I didn't read the question very well it seems. It is still trivial however, since 1, 3, 7 and 9 are all coprime to $10n$. This means that all odd numbers not ending in 5 (and thus not divisible by 5) can be represented in this way. Thanks from greg1313 and Joppy

 Tags 10nk, coprime, form, primes

 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post mobel Number Theory 21 October 16th, 2015 07:45 AM caters Number Theory 67 March 19th, 2014 04:32 PM Sebastian Garth Number Theory 9 November 22nd, 2013 02:38 PM WheepWhoop Number Theory 7 October 20th, 2011 05:09 PM johnmath Number Theory 8 April 29th, 2011 08:45 AM

 Contact - Home - Forums - Cryptocurrency Forum - Top