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-   -   Prime abc conjecture b == (a-1)/(2^c) (https://www.mersenneforum.org/showthread.php?t=18197)

 miket 2013-05-16 01:05

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.

 miket 2013-05-21 01:01

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

 Uncwilly 2013-05-21 01:25

:popcorn:

 ET_ 2013-05-21 06:45

[QUOTE=miket;341060]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[/QUOTE]

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

 R.D. Silverman 2013-05-21 11:16

[QUOTE=miket;341060]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[/QUOTE]

Gibberish

 xilman 2013-05-21 19:11

[QUOTE=R.D. Silverman;341087]Gibberish[/QUOTE]Seconded.

 LaurV 2013-05-22 05:26

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 :razz:

So what?

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