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November 20th, 2013, 09:46 AM  #1 
Member Joined: Jul 2010 Posts: 83 Thanks: 2  Conjecture about primes of a special form In other words, some primes and all composites fail the test. The first 10 integers in the sequence are 5, 11, 59, 107, 347, 587, 1019, 1307, 2027, and 2459. Is this a wellknown conjecture or theory? Also, I get the feeling that this could be generalized somehow. Any thoughts on this? Counterexamples? 
November 20th, 2013, 09:13 PM  #2 
Member Joined: Jul 2010 Posts: 83 Thanks: 2  Re: Conjecture about primes of a special form
I just realized something else: all of the above appear to be a subset of the safe primes!

November 21st, 2013, 12:11 AM  #3 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: Conjecture about primes of a special form
I think it's likely to be false, but the first counterexample might be large since even most primes fail these conditions. Indeed, there is no counterexample below 2^64.

November 21st, 2013, 01:09 AM  #4  
Member Joined: Jul 2010 Posts: 83 Thanks: 2  Re: Conjecture about primes of a special form Quote:
 
November 21st, 2013, 11:25 AM  #5 
Member Joined: Jul 2010 Posts: 83 Thanks: 2  Re: Conjecture about primes of a special form
Whoops, there was an error in my safe prime identification code. Having fixed it, it turns out that n=32140859 passes the SpecialPrime test but in that case (n1)/2 is not a SophieGermaine, so the assumption that every value in the sequence is a safe prime is false. Still haven't found any composites that pass the SpecialPrime test, so the original assertion of the conjecture still stands though.

November 21st, 2013, 11:46 AM  #6  
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: Conjecture about primes of a special form Quote:
 
November 21st, 2013, 11:54 AM  #7  
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: Conjecture about primes of a special form Quote:
 
November 21st, 2013, 01:00 PM  #8  
Member Joined: Jul 2010 Posts: 83 Thanks: 2  Re: Conjecture about primes of a special form Quote:
 
November 21st, 2013, 01:16 PM  #9  
Member Joined: Jul 2010 Posts: 83 Thanks: 2  Re: Conjecture about primes of a special form Quote:
 
November 22nd, 2013, 03:38 PM  #10  
Member Joined: Jul 2010 Posts: 83 Thanks: 2  Re: Conjecture about primes of a special form
[quote=Sebastian Garth] Quote:
Oh, right...2^64.  

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