When I started this little project, I hadn't expected the Batalov Effect. We are grateful to Serge for his huge crunching efforts and he has been rewarded with finding those 4 primes for base 10 and expoenent 388080. It is a pity about the dearth for exponent 471240.
The use of generic modular reduction for such large exponents and bigger ones is a big disadvantage to the project. However I have a few ideas about what to do next:
(A) Shelve the project.
(B) Do another sub-million exponent for base 10 -- will require a few weeks of Ksieve.
(C) Do a mega exponent for base 10 using the magic formula which leaves a lot in the sieve -- will require quite a while with Ksieve.
(D) Do base 10 with exponent 1000000.
(E) Do a base 2 search using the magic formula -- can be engineered to leave a lot in the sieve; has a bigger domain to search, with more primes per exponent. Fast at sub-semi-mega bigger-than-PG-twin-search.
(F) Choose another base such as 3 or 2015 etc.
(G) Go for a world record prime -- fanciful.
(H) Search for NeRDs which use only special modular reduction.
My favourites are (A) or (E).
