Hi Andreas,
Regarding output,
non-human-readable output of uptime is not modified.
I had to modify code flow a little bit to not change upminutes and uphours 
after initial calculation in case of "-p", thus I hid it under 
if(!human_readable).
Code flow for !human_readable should stay exactly as before.

Regarding 60s fix, it looks like it should be a fairly one line change. I 
proposed following change
    if (upminutes || (!upminutes && uptime_secs < 60)) { // change < to <=
      pos += sprintf(buf + pos, "%s%d %s", comma > 0 ? ", " : "", upminutes,
                     upminutes != 1 ? "minutes" : "minute");
      comma += 1;
    }
I'll wait for a feedback from upstream

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https://bugs.launchpad.net/bugs/2035061

Title:
  uptime -p reports incorrect output after 52 weeks

Status in procps package in Ubuntu:
  New
Status in procps source package in Focal:
  New
Status in procps source package in Jammy:
  New

Bug description:
  [ Impact ]

  uptime -p will provide incorrect data for 24 hours after exactly 52 weeks. 
Users and tools utilizing this command will receive example output "up 2 hours" 
instead of "up 52 weeks, 2 hours". After 24 hours since 52 weeks, uptime -p 
will report "up 1 year" which is correct output.
  Issue is already fixed in upstream 
https://gitlab.com/procps-ng/procps/-/commit/0496b39876d569fe1cecb76ad5ef212cd14c0374.
  Latest procps releases already include this patch (procps 4.0.3 lunar/mantic)
  The fix is needed for following set of packages:
  procps | 2:3.3.17-6ubuntu2   | jammy
  procps | 2:3.3.16-1ubuntu2   | focal

  [ Test Plan ]

  Reproduction:
  UPTIME="31528920 31528800"; mkfifo uptime_fifo; while true; do cat <<<$UPTIME 
> uptime_fifo; done & sudo mount -obind uptime_fifo /proc/uptime
  uptime -p
  Running above commands will result in incorrect uptime output.
  Testing:
  In attached uptime_test_results file there is modified print_uptime function 
which has been used to test multiple corner cases.

  [ Where problems could occur ]

  Proposed changes modifies output format of "uptime -p". Issue has been 
already fixed in latest version of procps package available in lunar/mantic 
however older releases are based on different code base and patch cannot be 
directly cherry-picked. Due to backport requirements some code of "uptime" 
(without -p) has been also changed but this should not impact logic for that 
usage.
  As the change focuses on modifying "uptime -p" output format any potential 
issues will impact this command.
  I have also looked for a reverse dependencies on procps package to check for 
potential uses of uptime -p, however I was not able to find any. Internally 
within procps package this functionality is used in "top" application, however 
for that case "uptime" (without -p) is used.

  [ Other Info ]
  Bug upstream: https://gitlab.com/procps-ng/procps/-/issues/217
  Following patch is needed for older releases: 
https://gitlab.com/procps-ng/procps/-/commit/0496b39876d569fe1cecb76ad5ef212cd14c0374
  Old commit on which upstream patch is based: 
https://gitlab.com/procps-ng/procps/-/commit/8827c6763f79f77a126968e200b0e402de7cb749
  Small change on top of proposed patch (already included in debdiff): 
https://gitlab.com/procps-ng/procps/-/commit/10824b0655f3eeaeac87ae6e4e3881429a237f3e

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