# [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 17:55:14 CET 2017

```Sorry my ignorance:(
several simultaneous APs!
So my Q (as my IQ) should be ignored.
Sorry again,
Zak

>Четверг,  2 февраля 2017, 11:44 +03:00 от Zak  Seidov <zakseidov at mail.ru>:
>
>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).
>>
>>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?
>>
>>
>>--
>>Seqfan Mailing list -  http://list.seqfan.eu/
>

```