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Old 2013-05-16, 01:05   #1
miket
 
May 2013

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Default Prime abc conjecture b == (a-1)/(2^c)

Prime numbers generated by the prime abc conjecture when c=4: suppose a is positive, odd and not a multiple of 3 and b is the cycle length of a as defined below. Then if b == (a-1)/(2^c) for some positive integer c then a is prime.
The cycle length of 2n-1 is OEIS A179382(n).

Example:
11 = 5*2^1+1
11 (1,3, 7, 9, 5)

Prime numbers generated by the prime abc conjecture when c=4,see OEIS A225759.

Last fiddled with by ewmayer on 2013-05-21 at 19:32 Reason: remove annoying xtra-large font
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Old 2013-05-21, 01:01   #2
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Conjecture on cycle length and primes prime abc conjecture final version: Suppose a is positive odd, and b=A179382((a+1)/2), if b=(a-1)/(2^c) for some c>0, as a approaches infinity, the possibility of a is prime approaches 1.

Counter seq: 92673,143713,3579553,4110529,28688897,127017857,141127681,157648097,212999489,663414881
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Old 2013-05-21, 01:25   #3
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Old 2013-05-21, 06:45   #4
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Quote:
Originally Posted by miket View Post
Conjecture on cycle length and primes prime abc conjecture final version: Suppose a is positive odd, and b=A179382((a+1)/2), if b=(a-1)/(2^c) for some c>0, as a approaches infinity, the possibility of a is prime approaches 1.

Counter seq: 92673,143713,3579553,4110529,28688897,127017857,141127681,157648097,212999489,663414881

You said:

1 - if a is a positive odd
2 - and b = A179382, c>0
3 - then the possibility of a is prime approaches 1 as a approaches infinity.

Did you mean that, as a grows, the possibility that a is prime approaches 1?
In that case, what is the use of A179382?

Luigi
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Old 2013-05-21, 11:16   #5
R.D. Silverman
 
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Quote:
Originally Posted by miket View Post
Conjecture on cycle length and primes prime abc conjecture final version: Suppose a is positive odd, and b=A179382((a+1)/2), if b=(a-1)/(2^c) for some c>0, as a approaches infinity, the possibility of a is prime approaches 1.

Counter seq: 92673,143713,3579553,4110529,28688897,127017857,141127681,157648097,212999489,663414881
Gibberish
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Old 2013-05-21, 19:11   #6
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Quote:
Originally Posted by R.D. Silverman View Post
Gibberish
Seconded.
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Old 2013-05-22, 05:26   #7
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Why make it so complicate? Let x be a 2-prp, the probability of x to be prime approaches 1 as x goes to infinity

So what?

Last fiddled with by LaurV on 2013-05-22 at 05:26
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