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.



The list of first 10 such $d$ that $101+nd$ is prime for $n=0,..,5$: $[3990,5610,98220,101640,108780,122790,176550,312210,331590,333840]$
Generated by a simple Haskell program:
isPrime :: Integer -> Bool
isPrime k = null [ x | x <- [2..floor(sqrt(fromIntegral k))], k `mod` x  == 0]

good :: Integer -> Integer -> Bool
good a d = all id [isPrime (a + n * d) | n <- [0..5]]

main = print $ take 10 $ filter (good 101) [1..]

