Update README.md

README.md

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-**(In this "README" file (as well as the "README" files in the "code", "primality-certificates", "unproven-probable-primes", i.e. https://github.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/blob/main/code/README.md and https://github.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/blob/main/primality-certificates/README.md and https://github.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/blob/main/unproven-probable-primes/README.md), I always offer links to the English Wikipedia (https://en.wikipedia.org/wiki/Main_Page, https://en.wikipedia.org/wiki/English_Wikipedia), The Prime Glossary (https://t5k.org/glossary/) (which is a part of The Prime Pages (https://en.wikipedia.org/wiki/PrimePages, https://www.rieselprime.de/ziki/The_Prime_Pages)), the Prime Wiki (https://www.rieselprime.de/ziki/Main_Page), and the Wolfram MathWorld (https://mathworld.wolfram.com/, https://en.wikipedia.org/wiki/MathWorld), as well as the *OEIS* (https://oeis.org/, https://en.wikipedia.org/wiki/On-Line_Encyclopedia_of_Integer_Sequences, https://www.rieselprime.de/ziki/On-Line_Encyclopedia_of_Integer_Sequences) sequences or other references, for the proper nouns, if such page exists, also the *factordb* (http://factordb.com/, https://www.rieselprime.de/ziki/Factoring_Database) entries for the large primes or probable primes, or factoring status for the *N*−1 and *N*+1 for the large primes or probable primes, or factoring status for the numbers of certain forms, also the archived pages (only list the newest available (i.e. neither 4xx nor 5xx) archived pages) for the dead links with the wayback machine (https://web.archive.org/, https://en.wikipedia.org/wiki/Wayback_Machine), also, to avoid permanently dead links, I always use both the wayback machine (https://web.archive.org/, https://en.wikipedia.org/wiki/Wayback_Machine) and the archive today (https://archive.ph/, https://archive.is/, https://archive.li/, https://archive.vn/, https://archive.fo/, https://archive.md/, https://en.wikipedia.org/wiki/Archive.today) to save all link webpages in this "README" file (as well as all link pages in the "README" files in the "code", "primality-certificates", "unproven-probable-primes", i.e. all link pages in https://github.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/blob/main/code/README.md and https://github.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/blob/main/primality-certificates/README.md and https://github.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/blob/main/unproven-probable-primes/README.md), including use the archive today (https://archive.ph/, https://archive.is/, https://archive.li/, https://archive.vn/, https://archive.fo/, https://archive.md/, https://en.wikipedia.org/wiki/Archive.today) to save all archived pages for dead links with the wayback machine (https://web.archive.org/, https://en.wikipedia.org/wiki/Wayback_Machine), also, for the ".zip" files (https://en.wikipedia.org/wiki/ZIP_(file_format)) and the ".7z" files (https://en.wikipedia.org/wiki/7z) and the ".lz" files (https://en.wikipedia.org/wiki/Lzip) and the ".gz" files (https://en.wikipedia.org/wiki/Gzip) and the ".xz" files (https://en.wikipedia.org/wiki/XZ_Utils) and the ".exe" files (https://en.wikipedia.org/wiki/.exe) and the ".dll" files (https://en.wikipedia.org/wiki/Dynamic-link_library), I always use both the wayback machine (https://web.archive.org/, https://en.wikipedia.org/wiki/Wayback_Machine) and the megalodon (https://megalodon.jp/, https://en.wikipedia.org/wiki/Megalodon_(website)) to save (since these files cannot be saved with the archive today (https://archive.ph/, https://archive.is/, https://archive.li/, https://archive.vn/, https://archive.fo/, https://archive.md/, https://en.wikipedia.org/wiki/Archive.today)), also, for the link webpages with programs (such as the "Prime checkers" and the "Integer factorizers" and the "Prime generators" and the "Base converters" and the "Expression generators" link webpages in the bottom of this "README" file), I always use the ghost archive (https://ghostarchive.org/, https://en.wikipedia.org/wiki/Ghost_Archive) as well as the wayback machine (https://web.archive.org/, https://en.wikipedia.org/wiki/Wayback_Machine) and the archive today (https://archive.ph/, https://archive.is/, https://archive.li/, https://archive.vn/, https://archive.fo/, https://archive.md/, https://en.wikipedia.org/wiki/Archive.today) to save (since in the archived pages of these webpages with the archive today (https://archive.ph/, https://archive.is/, https://archive.li/, https://archive.vn/, https://archive.fo/, https://archive.md/, https://en.wikipedia.org/wiki/Archive.today) or the megalodon (https://megalodon.jp/, https://en.wikipedia.org/wiki/Megalodon_(website)), the programs will not work), I did not only use the wayback machine (https://web.archive.org/, https://en.wikipedia.org/wiki/Wayback_Machine) to save but also use another archive service since some webpages have been excluded from the Wayback Machine (see https://wiki.archiveteam.org/index.php/List_of_websites_excluded_from_the_Wayback_Machine and https://wiki.archiveteam.org/index.php/List_of_websites_excluded_from_the_Wayback_Machine/Partial_exclusions), for more web archive sites (https://en.wikipedia.org/wiki/Web_archiving), see https://en.wikipedia.org/wiki/Wikipedia:List_of_web_archives_on_Wikipedia and https://en.wikipedia.org/wiki/Help:Archiving_a_source, also, for the cached copy of the *pdf* files (https://en.wikipedia.org/wiki/PDF) references see https://github.com/xayahrainie4793/pdf-files-cached-copy (you can click https://github.com/xayahrainie4793/pdf-files-cached-copy/archive/refs/heads/main.zip to download all these *pdf* files by one click), and for the cached copy of the prime programs (including: The primality (or probable primality) testing (https://en.wikipedia.org/wiki/Primality_test, https://www.rieselprime.de/ziki/Primality_test, https://mathworld.wolfram.com/PrimalityTest.html, https://t5k.org/prove/index.html) programs (https://www.rieselprime.de/ziki/Primality_testing_program), the sieving (https://www.rieselprime.de/ziki/Sieving, https://www.rieselprime.de/ziki/Sieving_a_range_of_sequences, https://mathworld.wolfram.com/Sieve.html, http://www.rechenkraft.net/yoyo/y_status_sieve.php, https://www.primegrid.com/stats_psp_sieve.php, https://www.primegrid.com/stats_pps_sieve.php, https://www.primegrid.com/stats_sr5_sieve.php, https://www.primegrid.com/stats_cw_sieve.php, https://www.primegrid.com/sieving/rsp/) programs (https://www.rieselprime.de/ziki/Sieving_program), the integer factoring (https://en.wikipedia.org/wiki/Integer_factorization, https://www.rieselprime.de/ziki/Factorization, https://mathworld.wolfram.com/PrimeFactorization.html, https://mathworld.wolfram.com/PrimeFactorizationAlgorithms.html, http://www.numericana.com/answer/factoring.htm) programs (https://www.rieselprime.de/ziki/Factoring_program)) see https://github.com/xayahrainie4793/prime-programs-cached-copy (you can click https://github.com/xayahrainie4793/prime-programs-cached-copy/archive/refs/heads/main.zip to download all these programs by one click), also not only webpage references, but also ".zip" files (https://en.wikipedia.org/wiki/ZIP_(file_format)) and ".7z" files (https://en.wikipedia.org/wiki/7z) and ".lz" files (https://en.wikipedia.org/wiki/Lzip) and ".gz" files (https://en.wikipedia.org/wiki/Gzip) and ".xz" files (https://en.wikipedia.org/wiki/XZ_Utils) and ".exe" files (https://en.wikipedia.org/wiki/.exe) and ".dll" files (https://en.wikipedia.org/wiki/Dynamic-link_library), which you can download (https://en.wikipedia.org/wiki/Download), also you can download the C (https://en.wikipedia.org/wiki/C_(programming_language)) program files ".c" and ".h" (https://en.wikipedia.org/wiki/Include_directive), also C++ (https://en.wikipedia.org/wiki/C%2B%2B) program files ".cpp", also the ".ini" files (https://en.wikipedia.org/wiki/INI_file) and the text files (https://en.wikipedia.org/wiki/Text_file) and the html files (https://en.wikipedia.org/wiki/HTML), of course, you can also click https://github.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/archive/refs/heads/main.zip to download all files in this *GitHub* (https://en.wikipedia.org/wiki/GitHub, https://github.com/) page by one click)**
+**(In this "README" file (as well as the "README" files in the "code", "primality-certificates", "unproven-probable-primes", i.e. https://github.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/blob/main/code/README.md and https://github.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/blob/main/primality-certificates/README.md and https://github.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/blob/main/unproven-probable-primes/README.md), I always offer links to the English Wikipedia (https://en.wikipedia.org/wiki/Main_Page, https://en.wikipedia.org/wiki/English_Wikipedia), The Prime Glossary (https://t5k.org/glossary/) (which is a part of The Prime Pages (https://en.wikipedia.org/wiki/PrimePages, https://www.rieselprime.de/ziki/The_Prime_Pages)), the Prime Wiki (https://www.rieselprime.de/ziki/Main_Page), and the Wolfram MathWorld (https://mathworld.wolfram.com/, https://en.wikipedia.org/wiki/MathWorld), as well as the *OEIS* (https://oeis.org/, https://en.wikipedia.org/wiki/On-Line_Encyclopedia_of_Integer_Sequences, https://www.rieselprime.de/ziki/On-Line_Encyclopedia_of_Integer_Sequences) sequences or other references, for the proper nouns, if such page exists, also the *factordb* (http://factordb.com/, https://www.rieselprime.de/ziki/Factoring_Database) entries for the large primes or probable primes, or factoring status for the *N*−1 and *N*+1 for the large primes or probable primes, or factoring status for the numbers of certain forms, also the archived pages (only list the newest available (i.e. neither 4xx nor 5xx) archived pages) for the dead links with the wayback machine (https://web.archive.org/, https://en.wikipedia.org/wiki/Wayback_Machine), also, to avoid permanently dead links, I always use both the wayback machine (https://web.archive.org/, https://en.wikipedia.org/wiki/Wayback_Machine) and the archive today (https://archive.ph/, https://archive.is/, https://archive.li/, https://archive.vn/, https://archive.fo/, https://archive.md/, https://en.wikipedia.org/wiki/Archive.today) to save all link webpages in this "README" file (as well as all link pages in the "README" files in the "code", "primality-certificates", "unproven-probable-primes", i.e. all link pages in https://github.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/blob/main/code/README.md and https://github.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/blob/main/primality-certificates/README.md and https://github.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/blob/main/unproven-probable-primes/README.md), including use the archive today (https://archive.ph/, https://archive.is/, https://archive.li/, https://archive.vn/, https://archive.fo/, https://archive.md/, https://en.wikipedia.org/wiki/Archive.today) to save all archived pages for dead links with the wayback machine (https://web.archive.org/, https://en.wikipedia.org/wiki/Wayback_Machine), also, for the ".zip" files (https://en.wikipedia.org/wiki/ZIP_(file_format)) and the ".7z" files (https://en.wikipedia.org/wiki/7z) and the ".lz" files (https://en.wikipedia.org/wiki/Lzip) and the ".gz" files (https://en.wikipedia.org/wiki/Gzip) and the ".xz" files (https://en.wikipedia.org/wiki/XZ_Utils) and the ".exe" files (https://en.wikipedia.org/wiki/.exe) and the ".dll" files (https://en.wikipedia.org/wiki/Dynamic-link_library), I always use both the wayback machine (https://web.archive.org/, https://en.wikipedia.org/wiki/Wayback_Machine) and the megalodon (https://megalodon.jp/, https://en.wikipedia.org/wiki/Megalodon_(website)) to save (since these files cannot be saved with the archive today (https://archive.ph/, https://archive.is/, https://archive.li/, https://archive.vn/, https://archive.fo/, https://archive.md/, https://en.wikipedia.org/wiki/Archive.today)), also, for the link webpages with programs (such as the "Prime checkers" and the "Integer factorizers" and the "Prime generators" and the "Base converters" and the "Expression generators" link webpages in the bottom of this "README" file), I always use the ghost archive (https://ghostarchive.org/, https://en.wikipedia.org/wiki/Ghost_Archive) as well as the wayback machine (https://web.archive.org/, https://en.wikipedia.org/wiki/Wayback_Machine) and the archive today (https://archive.ph/, https://archive.is/, https://archive.li/, https://archive.vn/, https://archive.fo/, https://archive.md/, https://en.wikipedia.org/wiki/Archive.today) to save (since in the archived pages of these webpages with the archive today (https://archive.ph/, https://archive.is/, https://archive.li/, https://archive.vn/, https://archive.fo/, https://archive.md/, https://en.wikipedia.org/wiki/Archive.today) or the megalodon (https://megalodon.jp/, https://en.wikipedia.org/wiki/Megalodon_(website)), the programs will not work), I did not only use the wayback machine (https://web.archive.org/, https://en.wikipedia.org/wiki/Wayback_Machine) to save but also use another archive service since some webpages have been excluded from the Wayback Machine (see https://wiki.archiveteam.org/index.php/List_of_websites_excluded_from_the_Wayback_Machine and https://wiki.archiveteam.org/index.php/List_of_websites_excluded_from_the_Wayback_Machine/Partial_exclusions and https://wiki.archiveteam.org/index.php/List_of_websites_excluded_from_the_Wayback_Machine/Former_exclusions), for more web archive sites (https://en.wikipedia.org/wiki/Web_archiving), see https://en.wikipedia.org/wiki/Wikipedia:List_of_web_archives_on_Wikipedia and https://en.wikipedia.org/wiki/Help:Archiving_a_source, also, for the cached copy of the *pdf* files (https://en.wikipedia.org/wiki/PDF) references see https://github.com/xayahrainie4793/pdf-files-cached-copy (you can click https://github.com/xayahrainie4793/pdf-files-cached-copy/archive/refs/heads/main.zip to download all these *pdf* files by one click), and for the cached copy of the prime programs (including: The primality (or probable primality) testing (https://en.wikipedia.org/wiki/Primality_test, https://www.rieselprime.de/ziki/Primality_test, https://mathworld.wolfram.com/PrimalityTest.html, https://t5k.org/prove/index.html) programs (https://www.rieselprime.de/ziki/Primality_testing_program), the sieving (https://www.rieselprime.de/ziki/Sieving, https://www.rieselprime.de/ziki/Sieving_a_range_of_sequences, https://mathworld.wolfram.com/Sieve.html, http://www.rechenkraft.net/yoyo/y_status_sieve.php, https://www.primegrid.com/stats_psp_sieve.php, https://www.primegrid.com/stats_pps_sieve.php, https://www.primegrid.com/stats_sr5_sieve.php, https://www.primegrid.com/stats_cw_sieve.php, https://www.primegrid.com/sieving/rsp/) programs (https://www.rieselprime.de/ziki/Sieving_program), the integer factoring (https://en.wikipedia.org/wiki/Integer_factorization, https://www.rieselprime.de/ziki/Factorization, https://mathworld.wolfram.com/PrimeFactorization.html, https://mathworld.wolfram.com/PrimeFactorizationAlgorithms.html, http://www.numericana.com/answer/factoring.htm) programs (https://www.rieselprime.de/ziki/Factoring_program)) see https://github.com/xayahrainie4793/prime-programs-cached-copy (you can click https://github.com/xayahrainie4793/prime-programs-cached-copy/archive/refs/heads/main.zip to download all these programs by one click), also not only webpage references, but also ".zip" files (https://en.wikipedia.org/wiki/ZIP_(file_format)) and ".7z" files (https://en.wikipedia.org/wiki/7z) and ".lz" files (https://en.wikipedia.org/wiki/Lzip) and ".gz" files (https://en.wikipedia.org/wiki/Gzip) and ".xz" files (https://en.wikipedia.org/wiki/XZ_Utils) and ".exe" files (https://en.wikipedia.org/wiki/.exe) and ".dll" files (https://en.wikipedia.org/wiki/Dynamic-link_library), which you can download (https://en.wikipedia.org/wiki/Download), also you can download the C (https://en.wikipedia.org/wiki/C_(programming_language)) program files ".c" and ".h" (https://en.wikipedia.org/wiki/Include_directive), also C++ (https://en.wikipedia.org/wiki/C%2B%2B) program files ".cpp", also the ".ini" files (https://en.wikipedia.org/wiki/INI_file) and the text files (https://en.wikipedia.org/wiki/Text_file) and the html files (https://en.wikipedia.org/wiki/HTML), of course, you can also click https://github.com/xayahrainie4793/minimal-elements-of-the-prime-numbers/archive/refs/heads/main.zip to download all files in this *GitHub* (https://en.wikipedia.org/wiki/GitHub, https://github.com/) page by one click)**
 
 **(Note: I do not offer links to the *OEIS* Wiki (https://oeis.org/wiki/Main_Page) or the PrimeGrid Wiki (http://primegrid.wikia.com/wiki/PrimeGrid_Wiki) or the Rechenkraft Wiki (https://www.rechenkraft.net/wiki/Willkommen_beim_Verein_Rechenkraft.net_e.V.), with the only one exception: the page "OEIS sequences needing factors" (https://oeis.org/wiki/OEIS_sequences_needing_factors) in the *OEIS* Wiki, since fewer people contribute the *OEIS* Wiki and the PrimeGrid Wiki, and most things in the Rechenkraft Wiki are out of date)**