[seqfan] Re: a+b+c, a+b-c , a-b+c and -a+b+c all prime

israel at math.ubc.ca israel at math.ubc.ca
Thu Feb 2 08:59:24 CET 2017


Dickson's conjecture implies that sequences such as this are infinite 
unless there is some congruence condition that would imply that at least 
one of the four must be divisible by a certain prime (which here would have 
to be 2 or 3).

Cheers,
Robert

On Feb 1 2017, Zak  Seidov wrote:

> Consider three distinct integers a,b,c such that all 4 numbers a+b+c, 
> a+b-c, a-b+c and -a+b+c are positive/negative primes. E.g., for a=3 and 
> b=4, c = 
> 12,30,60,270,570,600,1230,1290,1620,2340,2550,3540,4020,4650,5850,6270,6360,6570,.... 
> Is this problem the old hat? What can be said about c in this particular 
> case?



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