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March 18th, 2012, 04:51 PM   #1
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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
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March 18th, 2012, 05:06 PM   #2
uta
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Re: Primality and Euler totient

n=1037.
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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
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March 18th, 2012, 05:23 PM   #4
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Re: Primality and Euler totient

There are few exceptions (semi-prime).
Let us call them the numbers of Bogauss
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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
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March 18th, 2012, 05:34 PM   #6
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Re: Primality and Euler totient

Anyway it was a sequence prime-abundant.
We can still record it as it is.
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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.
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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!!!!
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March 18th, 2012, 06:18 PM   #9
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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.
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May 29th, 2017, 07:53 AM   #10
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Here is a little discovery.
Maybe one of you will improve it or explain why it works?
Thanks from agentredlum
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