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

miket · 2013-05-16, 01:05

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

ET_ · 2013-05-21, 06:45

Quote:

Originally Posted by miket

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

R.D. Silverman · 2013-05-21, 11:16

Quote:

Originally Posted by miket

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

xilman · 2013-05-21, 19:11

Quote:

Originally Posted by R.D. Silverman

Gibberish

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

So what?

2013-05-16, 01:05	#1
miket May 2013 3² Posts	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 = 52^1+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*

2013-05-22, 05:26	#7
LaurV Romulan Interpreter "name field" Jun 2011 Thailand 26E9₁₆ Posts	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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2013-05-21, 01:01	#2
miket May 2013 3² Posts	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

2013-05-21, 01:25	#3
Uncwilly 6809 > 6502 """"""""""""""""""" Aug 2003 101×103 Posts 2⁴·3²·73 Posts