This excerpt from an 8-31-2010 post by Alan Starr, in reply to a question from 
R.S. who also started the current thread:

(begin quote)
I believe that the answers to your questions may be found in the Data Extent 
Block (DEB) and the murky depths of history.

Due to its age, its close connections to original S370 hardware limitations and 
downward compatibility requirements, the DEB is a messy control block. As far 
as I can tell:

1) It may never exceed 2040 bytes because the single-byte field called DEBLNGTH 
at -4 specifies the total DEB length in doublewords. Maximum value is 255, 
which represents 2040 bytes.

2) At a very minimum, a direct access EXCP / BSAM / QSAM DEB comprises
    a. 23-byte prefix (appendage vector table)
    b. 32-byte basic section 
    c. Direct Access device sections
    d. 16-byte EXCP, BSAM and QSAM dependent section 

3) Expanding upon #2, the minimum length of a DEB (with no device sections) is 
23+32+16 = 71
    The maximum DEB length of 2040 minus 71 leaves 1969 bytes for device 
sections, each of which is 16 bytes
    1969 / 16 = 123 and an odd byte

(end quote)

Full text here:
https://groups.google.com/forum/#!msg/bit.listserv.ibm-main/V3zK0zcEDPI/4DOoJbAVmgEJ

Bill

On Fri, 22 Nov 2013 09:07:10 -0500, Blaicher, Christopher Y. wrote:

>I was in a class a long time ago and the explanation at that time was as 
>follows, to the best of my recollection.
>
>They can handle up to 127 extents, but any request for secondary can take up 
>to 5 extents to satisfy it.  The comment was that the developers didn't want 
>to have to deal with the case where they were at, say, 125 extents and asked 
>for another and got 5 back.  In that case they would use 2 and have to give 3 
>back.  It had something to do with they were using a service that wasn't 
>theirs and didn't want to deal it.  This way if it was at 122 extents and 
>asked for another extend it would always fit be it 1 or 5 extents returned.
>
>As I said, this was from a long time ago and my page-in facility may have lost 
>a few bits along the way.
>
>Chris Blaicher
>Principal Software Engineer, Software Development
>Syncsort Incorporated
>50 Tice Boulevard, Woodcliff Lake, NJ 07677
>P: 201-930-8260  |  M: 512-627-3803
>E: cblaic...@syncsort.com
>
>
>-----Original Message-----
>From: IBM Mainframe Discussion List [mailto:IBM-MAIN@LISTSERV.UA.EDU] On 
>Behalf Of John Gilmore
>Sent: Friday, November 22, 2013 8:53 AM
>To: IBM-MAIN@LISTSERV.UA.EDU
>Subject: Re: Extents limit for HFS
>
>For the BLKSIZE= constraint mod(32760,8) = 0, mod(32767,8) �= 0.
>
>For the extents-per-volume question it is hard to see any basis for an 
>alignment issue, and in any case both 123 and 127 are odd.  (Of the two 123 is 
>composite and 127 = 2^7 - 1 is a Mersenne prime, but this difference too is 
>unlikely to be relevant.)
>
>Finally, my point was not a cavil.   I have no animus against the
>number 123.  I was and am seeking enlightenment.  There is presumably a 
>rationale for the number 123; but 1) what it is has eluded me; and
>2) a search of the IBM-MAIN archives was unhelpful, perhaps because my query 
>was inept.
>
>John Gilmore, Ashland, MA 01721 - USA
>

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