Re: Re: Conjecture: 2n+1= 2^i+p ; 6k-2 or 6k+2 = 3^i+p

*To*: mathgroup at smc.vnet.net*Subject*: [mg97156] Re: [mg97047] Re: [mg97037] Conjecture: 2n+1= 2^i+p ; 6k-2 or 6k+2 = 3^i+p*From*: Andrzej Kozlowski <akoz at mimuw.edu.pl>*Date*: Fri, 6 Mar 2009 04:28:18 -0500 (EST)*References*: <200903031056.FAA02950@smc.vnet.net> <200903041209.HAA27014@smc.vnet.net> <47F63136-6342-4418-8AF4-AE3231F9A099@mimuw.edu.pl>

On 4 Mar 2009, at 22:40, Andrzej Kozlowski wrote: > On the other hand, the OP question was a bit different as he > included the possibility of "negative prime", in other words his > question was: is it true that for every obstinate number x one can > find an integer n such that 2^n-x is prime. Actually, one could ask > an even stronger question: is it true that for every odd number a > there exists an integer n such that 2^n - a is prime? It seems very > likely that the answer is yes, and probably the proof is easy but I > can't spend any more time on this... Actually, on reflection I have changed my mind. I don't think it will be easy to prove that for every odd a there is an n such that 2^n-a is prime. When I wrote that I expected that for every odd a there would be infinitely many n such that 2^n -a is prime, but, of course, this is not even known for a=1. In view of that I now tend to think the conjecture is probably true but very hard to prove. Andrzej Kozlowski

**References**:**Conjecture: 2n+1= 2^i+p ; 6k-2 or 6k+2 = 3^i+p***From:*Tangerine Luo <tangerine.luo@gmail.com>

**Re: Conjecture: 2n+1= 2^i+p ; 6k-2 or 6k+2 = 3^i+p***From:*DrMajorBob <btreat1@austin.rr.com>