Talk:Jordan-Pólya numbers: Difference between revisions
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== Factoring the 1050th number == |
== Factoring the 1050th number == |
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The 1050th jp number is 139,345,920,000. |
The 1050th jp number is 139,345,920,000. It factors as 7! * 5!^3 * 2!^4 or 8! * 5!^3 * 2! but the <del>Phix</del>/Julia/Wren entries are not getting that. Update: new algorithm posted. --[[User:Petelomax|Petelomax]] ([[User talk:Petelomax|talk]]) 05:31, 10 June 2023 (UTC) |
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<pre> |
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92,160 = 6! * 2!^7, or |
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92,160 = 5! * 3! * 2!^7 |
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18,345,885,696 = 4!^7 * 2!^2, or |
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18,345,885,696 = 3!^7 * 2!^16 |
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139,345,920,000 = 7! * 5!^3 * 2!^4 (only one?) |
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18,345,885,696 = 4!^7 * 2!^2, or |
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18,345,885,696 = 3!^7 * 2!^16 |
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724,775,731,200 = 6! * 5! * 2!^23, or |
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724,775,731,200 = 5!^2 * 3! * 2!^23 |
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9,784,472,371,200 = 6!^2 * 4!^2 * 2!^15, or |
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9,784,472,371,200 = 5!^2 * 3!^4 * 2!^19 |
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439,378,587,648,000 = 14! * 7! (only one?) |
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7,213,895,789,838,336 = 4!^8 * 2!^16, or |
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7,213,895,789,838,336 = 3!^8 * 2!^32 |
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</pre> |
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There are probably only a few ways to do each, maybe show them all? --[[User:Petelomax|Petelomax]] ([[User talk:Petelomax|talk]]) 23:52, 9 June 2023 (UTC) |
Revision as of 05:31, 10 June 2023
Isn't that like N-smooth_numbers using n! instead of primes?
In N-smooth numbers one can change p1..pn by 2! to n!
I think , only using 2!,3!,5!,..pn! is sufficient.
4! = (2!)^2*3!, 6! = 5!*3!... so no extra numbers will be created.
7213895789838336 =(4!)^8 * (2!)^16 == ((2!)^2 *(3!))^8 * (2!)^16 = (2!)^32*(3!)^8
Horst (talk) 08:48, 9 June 2023 (UTC)
- There may, of course, be more than one way to decompose a J-P number into a product of factorials but the idea is to choose the way which uses the largest factorials and present these in highest to lowest order. I've added a sentence to the task description to try and clarify this. --PureFox (talk) 09:57, 9 June 2023 (UTC)
- I believe (bicbw) there is no way to make 439,378,587,648,000 = 14! * 7! with only prime factorials. --Petelomax (talk) 02:53, 10 June 2023 (UTC)
Factoring the 1050th number
The 1050th jp number is 139,345,920,000. It factors as 7! * 5!^3 * 2!^4 or 8! * 5!^3 * 2! but the Phix/Julia/Wren entries are not getting that. Update: new algorithm posted. --Petelomax (talk) 05:31, 10 June 2023 (UTC)