Hello everybody,
I've just found the following example of 3 titanic palindromic primes in
arithmetic progression:
10^1000+13186668131*10^495+1
10^1000+14266666241*10^495+1
10^1000+15346664351*10^495+1
Its common difference is 107999811*10^496. In fact, this progression is
the smallest of its kind.
I started searching by using PrimeForm to generate the first few hundreds
of the smallest titanic palindromic probable primes. This could be done
with the technic similar to the one I recently described to the PrimeForm
list; see
http://www.onelist.com/messages/primeform?archive=101
Then, I used a self-written program to look for any AP lurking in these
primes in much the same way that I used to find examples of 4 large primes
in AP and the smallest progressions of palindromic primes; see
http://www.utm.edu/~primes/Primes-L/msg00415.html
http://www.ping.be/~ping6758/palprim2.htm#warut
The final step is to rigorously prove their primality with the N-1 mode of
PrimeForm.
Best regards,
Warut