CullenWilliams primes and WoodallWilliams primes
The [B]CullenWilliams number[/B] base b is (b1)*b^(b1)+1, which is both Cullen number base b (n*b^n+1, some author requires n>=b1, and for this number n is exactly b1) and 2nd Williams number base b ((b1)*b^n+1)
The [B]WoodallWilliams number[/B] base b is (b1)*b^(b1)1, which is both Woodall number base b (n*b^n1, some author requires n>=b1, and for this number n is exactly b1) and 1st Williams number base b ((b1)*b^n1) The [B]CullenWilliams number[/B] base b, (b1)*b^(b1)+1 is prime for b = 2, 3, 4, 10, 11, 15, 34, 37, ... (they are exactly the smallest Cullen prime base b for b = 2, 3, 11, 37, and they are exactly the smallest 2nd Williams prime base b for b = 2 and 11) The [B]WoodallWilliams number[/B] base b, (b1)*b^(b1)1 is prime for 3, 4, 8, 15, 44, 82, ... (they are exactly the smallest Woodall prime base b for b = 82, and they are exactly the smallest 2nd Williams prime base b for b = 15 and 82) What are the next CullenWilliams prime and the next WoodallWilliams prime? 
Do you have search limits for these forms?

Must not be too deeply searched. A pfgw script to b = 1000 yields the PRPs (9441)*944^(9441)1 and (16221)*1622^(16221)1
Here is the script. Use f to trial factor before PRP testing. ABC2 ($a1)*$a^($a1)+1  ($a1)*$a^($a1)1 a: from 1 to <whatever limit you want> Running to a higher value to see if anything else shows up. 
Faster still is to use plain ABC.
[C]ABC2 ($a1)*$a^($a1)+1[/C] uses generic FFT. Instead, run something like this: [C]cat > a1.abc ABC $a*$b^$c$d ^D seq 1 20000  awk '{print $11,$1,$11,"+1"}' >> a1.abc pfgw64 N f l a1.abc[/C] OEIS: [OEIS]271718[/OEIS] , [OEIS]191568[/OEIS] 
I stopped searching at b=12000 and am stopping. Someone else can take it further.
There *might* be value in someone using sr1sieve with a script to find factors rather than using pfgw to find factors. 
Continuing WoodallWilliams from b=12000.

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