5041/5040: Difference between revisions

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{{Infobox Interval
| Name = third brown pair comma, 19th highly compositema
| Comma = yes
}}
5041/5040, the '''third brown pair comma''', or the '''19th highly compositema''' is a 71-limit superparticular interval measuring about 343 millicents.
5041/5040, the '''third brown pair comma''', or the '''19th highly compositema''' is a 71-limit superparticular interval measuring about 343 millicents.


== Theory ==
== Theory ==
5041/5040 represents the difference between 72/71 and 71/70. It is also the naswer to the Brocard's problem question of n! + 1 = m^2, to which there's only three known so far - [[25/24]], [[121/120]], and this.
5041/5040 represents the difference between 72/71 and 71/70. It is also the answer to the Brocard's problem question of n! + 1 = m^2, to which there's only three known so far - [[25/24]], [[121/120]], and this.


== References ==
== References ==


* Wikipedia Contributors, [[Wikipedia:Brocard's problem|Brocard's problem]].
* Wikipedia Contributors, [[Wikipedia:Brocard's problem|Brocard's problem]].
[[Category:71-limit]]
[[Category:Superparticular]]

Revision as of 18:34, 27 October 2022

Interval information
Ratio 5041/5040
Subgroup monzo 2.3.5.7.71 [-4 -2 -1 -1 2
Size in cents 0.3434647¢
Names third brown pair comma,
19th highly compositema
FJS name [math]\displaystyle{ \text{P1}^{71,71}_{5,7} }[/math]
Special properties square superparticular,
reduced
Tenney norm (log2 nd) 24.5987
Weil norm (log2 max(n, d)) 24.599
Wilson norm (sopfr(nd)) 168
Comma size unnoticeable
S-expression S71
Open this interval in xen-calc

5041/5040, the third brown pair comma, or the 19th highly compositema is a 71-limit superparticular interval measuring about 343 millicents.

Theory

5041/5040 represents the difference between 72/71 and 71/70. It is also the answer to the Brocard's problem question of n! + 1 = m^2, to which there's only three known so far - 25/24, 121/120, and this.

References