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

[israel at math.ubc.ca]

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?