My Math Forum Primality and Euler totient

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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(n-2)+phi(n-1)-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
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Re: Primality and Euler totient

Quote:
 Originally Posted by uta n=1037.
Sorry you are right 1037 is not prime

 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 (semi-prime). Let us call them the numbers of Bogauss
March 18th, 2012, 05:28 PM   #5
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Re: Primality and Euler totient

Quote:
 Originally Posted by Bogauss There are few exceptions (semi-prime). Let us call them the numbers of Bogauss
numbers of Bogauss up to 5000:

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 prime-abundant. We can still record it as it is.
March 18th, 2012, 06:12 PM   #7
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Re: Primality and Euler totient

Quote:
 Originally Posted by Bogauss There are few exceptions (semi-prime).
12167 is the first nonsemiprime exception.

March 18th, 2012, 06:17 PM   #8
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Re: Primality and Euler totient

Quote:
Originally Posted by CRGreathouse
Quote:
 Originally Posted by Bogauss There are few exceptions (semi-prime).
12167 is the first nonsemiprime exception.
12167 is a cube!!!!

 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? Thanks from agentredlum

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