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Old 2020-07-20, 22:15   #20
kar_bon
 
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Mar 2006
Germany

2·3·52·19 Posts
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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).
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