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

Zak Seidov zakseidov at mail.ru
Thu Feb 2 09:44:25 CET 2017

Is Dickson's conjecture valid for two APs: a+b*n and c+d*n
(or 3,4,5 simultaneous APs), AP = arithmetic progression?

>Четверг,  2 февраля 2017, 10:59 +03:00 от 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).
>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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