There're two problems with the example of 13*43^n-1:

1. All candidates are divisible by 6.

2. The smallest p-value to start with srsieve is p=44, so have to be greater than the base.

What I did:

- looking the factorizations of the first values of (13*43^n-1)/6

- every n==0 mod 2 has factor 2

- every n==1 mod 3 has factor 3

- every n==3 mod 4 has factor 5

- every n==6 mod 8 has factor 17

- every n==1 mod 30 has factor 31

- every n==6 mod 22 has factor 23

Using awk with this:

Code:

BEGIN {print "44:M:1:43:258" >"t.txt"
n=1
while (n < 1000000)
{ if (n % 2 == 0) {} # factor 2
else if (n % 3 == 1) {} # factor 3
else if (n % 4 == 3) {} # factor 5
else if (n % 8 == 6) {} # factor 17
else if (n % 30 == 1) {} # factor 31
else if (n % 22 == 6) {} # factor 23
else
print "13 "n >>"t.txt"
n++
}
}

creates "t.txt" like (in seconds)

Code:

44:M:1:43:258
13 5
13 9
13 17
13 21
13 29
13 33
13 41
13 45
13 53
13 57
(...)

for n<1M.

Use sr1sieve on this to higher P.

Changing the header after sieve to

Code:

ABC ($a*43^$b-1)/6
13 41
13 101
13 149
13 165
13 173
13 185
13 233
(..)

and test it with PFGW.

I got ~26,000 candiates left (don't know the exact P-value, was only a quick test).