The primes

4103163*2^45007-183009063*2^25003-1 is prime! (36.7389s+0.0027s)

1367721*2^45008-183009063*2^25002-1 is prime! (37.0663s+0.0046s)

1367721*2^45007-1 is prime! (10.4775s+0.0041s)

183009063*2^25002-1 is prime! (2.7422s+0.0026s)

form an AP4 with 13556, 13555, 13555 and 7535 decimal digits.

As in the previous cases of AP4s with these largest members

545510007*2^40000-464049135*2^25002-1 12050 p199 2010

522129915*2^40000-337917945*2^25002-1 12050 p199 2010

497132829*2^40000-222139713*2^25001-1 12050 p199 2010

I exploited a database of more than 10^5 25-kbit primes.

In the present case, an AP4 was found using less than 3%

of the estimated Poisson mean dose of 45-kbit primes.

David Broadhurst, 3 June 2010