[seqfan] Re: Runs of semiprimes of the same parity

[Silvester Resnik]

On Fri, Apr 20, 2018 at 5:54 PM, Zak Seidov via SeqFan <
seqfan at list.seqfan.eu> wrote:

>
>
> Runs of semiprimes of the same parity
> {4, 6}, {9}, {10, 14}, {15, 21}, {22}, {25}, {26}, {33}, {34}, {35}, {38},
> {39},
> {46}, {49, 51, 55, 57}, {58, 62}, {65, 69}, {74}, {77}, {82}, {85},
> {86}, {87, 91, 93}, {94},...
> What are maximal lengths of runs?
> Up to now I have 7 for even and 82 for odd runs.
> Thx,
> Zak.
>
>
I found two runs of even semiprimes with length 7 using brute force.

7: 1096669582 1096669594 1096669598 1096669606 1096669622 1096669642
1096669646
7: 3146898362 3146898374 3146898382 3146898386 3146898394 3146898406
3146898418

Given that semiprimes are denser than primes, finding longer runs of even
semiprimes could be difficult.  Conversely, runs of odd semiprimes get
longer and longer.  For example, taking the prime gap between
a=1425172824437699411 and b=1425172824437700887 (b - a = 1476), we get a
range (2a+1,2b-1) that doesn't contain any even semiprimes, but it does
contain 269 odd semiprimes.