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 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 = 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
 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 101ร103 Posts 211·5 Posts
2013-05-21, 06:45   #4
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"Luigi"
Aug 2002
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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

2013-05-21, 11:16   #5
R.D. Silverman

Nov 2003

164448 Posts

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

2013-05-21, 19:11   #6
xilman
Bamboozled!

"๐บ๐๐ท๐ท๐ญ"
May 2003
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22×112×23 Posts

Quote:
 Originally Posted by R.D. Silverman Gibberish
Seconded.

 2013-05-22, 05:26 #7 LaurV Romulan Interpreter     "name field" Jun 2011 Thailand 71×139 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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