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March 18th, 2012, 04:51 PM  #1 
Senior Member Joined: Jan 2011 Posts: 560 Thanks: 1  Primality and Euler totient
Conjecture? If phi(n2)+phi(n1)phi(n) < or =0 then n is prime. Phi is Euler totient and n>2 Here are the first few : 3 5 7 11 17 23 37 41 47 71 101 107 137 167 191 197 233 257 281 317 401 431 457 587 617 647 677 761 821 827 857 911 937 947 971 977 
March 18th, 2012, 05:06 PM  #2 
Newbie Joined: Feb 2012 Posts: 18 Thanks: 0  Re: Primality and Euler totient
n=1037.

March 18th, 2012, 05:16 PM  #3  
Senior Member Joined: Jan 2011 Posts: 560 Thanks: 1  Re: Primality and Euler totient Quote:
 
March 18th, 2012, 05:23 PM  #4 
Senior Member Joined: Jan 2011 Posts: 560 Thanks: 1  Re: Primality and Euler totient
There are few exceptions (semiprime). Let us call them the numbers of Bogauss 
March 18th, 2012, 05:28 PM  #5  
Newbie Joined: Feb 2012 Posts: 18 Thanks: 0  Re: Primality and Euler totient Quote:
1037 1157 1457 1541 1927 2147 2501 2627 3551 3977 4061 4097 4181 4187 4307 4577 4601 4727 4811  
March 18th, 2012, 05:34 PM  #6 
Senior Member Joined: Jan 2011 Posts: 560 Thanks: 1  Re: Primality and Euler totient
Anyway it was a sequence primeabundant. We can still record it as it is. 
March 18th, 2012, 06:12 PM  #7  
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: Primality and Euler totient Quote:
 
March 18th, 2012, 06:17 PM  #8  
Senior Member Joined: Jan 2011 Posts: 560 Thanks: 1  Re: Primality and Euler totient Quote:
 
March 18th, 2012, 06:18 PM  #9 
Senior Member Joined: Jan 2011 Posts: 560 Thanks: 1  Re: Primality and Euler totient
There are a lot of numbers finishing either by 1 or 7. Are the numbers finishing by 3 and 9 all prime? The answer is no. 
May 29th, 2017, 07:53 AM  #10 
Banned Camp Joined: Dec 2013 Posts: 1,117 Thanks: 41 
Here is a little discovery. Maybe one of you will improve it or explain why it works? 

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euler, primality, totient 
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