Sequence Of Primes Hello I have a basic number theory question.


*

*I want to find a list of primes of the form 
a, a + d, a + 2d, ... , a + 5d


*

*So a sequence of at least 6 or greater if I want to select a = 101
then what would I choose as my d to get a sequence of primes (they
don't have to be consecutive).

*I am quite lost. Maybe there isn't an answer and it's not possible? I
don't know how to find d in this case.



A well-known sequence $a_n:=a+nd$ producing at least $6$ primes with $3$-digit $a$ (this was your requirement here) is $a_n=199+210n$, i.e., 
$$
199, 409, 619, 829,1039,1249,1459,1669,1879,2089,
$$
so that the first consecutive $10$ sequence members are prime numbers. With $a=101$ you can search for such a $d$ by computer. I do not know of a conceptual way to find such a $d$.
