Pairs and triple semiprimes

[Jack Brennen]

> Is the semiprime cluster 213=3*71, 215=5*43,
> 217=7*31, 219=3*73, 221=13*17 the longest possible
> run or can one find larger clusters?

It seems likely there are an infinite number of clusters of
eight consecutive odd semiprimes.  The smallest is:

8129 = 11*739
8131 = 47*173
8133 = 3*2711
8135 = 5*1627
8137 = 79*103
8139 = 3*2713
8141 = 7*1163
8143 = 17*479

Other such clusters begin with 9983, 99443, 132077, 190937,
237449, 401429, 441677, 452639, 604487, 802199, 858179, 991289.


I remember a couple of years ago searching for arithmetic
progressions of semiprimes, and I seem to remember finding
an arithmetic progression of 30 or more elements; maybe I'll
try to find those files if anyone is interested.