Number of packages per repository (major distributions)
Solution 1:
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pkgs.org gives an approximate but keep in mind that it is showing only binary packages, also architectures do not have same level of support.
Usually, a source package is built and sliced into multiple deliverables.
Example Debian is estimated to have 30K source packages, 59K binary packages on pkgs.org.
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One way to get exact count without installing any, is by downloading the source packages manifest/index from official repositories/pools or their mirrors. Then pass it through an
zgrep|wc -l
filter.Free distributions like Debian/Ubuntu, Fedora, OpenSuse ... all have public repository with meta.
Example of:
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Fedora mirror: https://mirror.aarnet.edu.au/pub/fedora/linux/development/rawhide/Everything/source/tree/repodata/
Name Last modified Size [ ] 1adc7f7f68727884a1cfdd5ed6a779da153f2943529eab8e22242cafd781473d-other.xml.gz 2022-02-24 18:44 3.6M [ ] 4a7e634ca3f6fbfd7af872c5bee66d53040da1a333a7d03f9e4fc81710da194a-other.sqlite.xz 2022-02-24 18:44 4.1M [ ] 7fb9cc4420874bbe652d5a8db6e5ffedcbb96cbda355a20a2c012834570ebb15-filelists.xml.gz 2022-02-24 18:44 1.8M [TXT] 38e4373598b7d48ea0b348ec5d5e8dacdb50c9aea350ad71bc5df7f94c6f670d-other.xml.zck 2022-02-24 18:44 3.2M [ ] 2235c627ffd843ae45a32a1f502c6546e121acb848c9aa83a8e2fa163c3b16fe-primary.xml.gz 2022-02-24 18:44 6.8M [TXT] aa34aca085b179988fe455ed82a6f39b98ac24501b089a24db867d4b13827251-filelists.xml.zck 2022-02-24 18:44 1.8M [ ] b5b7b1dd42bc58a7ea7ebbd0a825f77961797d2994c10186b3745253d943e806-filelists.sqlite.xz 2022-02-24 18:44 1.7M [TXT] bc278431b67a343cff3b3794c6a422d4a6a31f9a3bbe34fbe9d8654566334a18-primary.xml.zck 2022-02-24 18:44 6.2M [ ] bd645c35a0003ea67175f31e937407cb685941e1269c3a1d47a49a32405d54d1-primary.sqlite.xz 2022-02-24 18:45 8.6M [TXT] repomd.xml 2022-02-24 18:45 4.9K
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Ubuntu mirror: https://mirrors.edge.kernel.org/ubuntu/ubuntu/dists/jammy/
../ by-hash/ 15-Oct-2021 12:15 - main/ 10-Nov-2021 22:59 - multiverse/ 11-Nov-2021 03:59 - restricted/ 10-Nov-2021 23:13 - universe/ 11-Nov-2021 00:23 - Contents-amd64.gz 26-Feb-2022 04:57 44M Contents-i386.gz 26-Feb-2022 05:24 35M InRelease 26-Feb-2022 15:25 264K Release 26-Feb-2022 15:25 263K Release.gpg 26-Feb-2022 15:25 819
Solution 2:
Wikipedia keeps the probably most comprehensive and updated list.
Another question is why it would matter to you; package count does not say much in itself, and to the largest part, all the "big" packages are available for all distributions.