Prime Numbers

1.6 Research problems 79
An interesting claim has been made with respect to this j = 10 example. Here
is the relevant quotation, from [Dubner et al. 1998]:
Although a number of people have pointed out to us that 10 + 1 = 11, we
believe that a search for an arithmetic progression of eleven consecutive
primes is far too difficult. The minimum gap between the primes is 2310
instead of 210 and the numbers involved in an optimal search would
have hundreds of digits. We need a new idea, or a trillion-fold increase
in computer speeds. So we expect the Ten Primes record to stand for a
long time to come.
1.88. [Honaker 1998] Note that 61 divides 67 · 71 + 1. Are there three larger
consecutive primes p