Math Is Fun Forum

You can use this script to detect if a number(int64) is perfect
[6,28,496,8128,33550336,8589869056, 137438691328, 2305843008139952128].includes(x)
The longs can't outrun you

Why is the night sky dark?
Assume we have an infinite grid of stars spaced evenly and we are not in one of them
The brightness (and tidal forces) we get is ∑∑∑1/((i-1/2)^2+(j-1/2)^2+(k-1/2)^2)
The question is,does this converge?
If we slightly tweak our model a bit,so that the universe on a polar coordinate,and the stars form a circular pattern,and the nth layer has n stars on it,we get an harmonic series of light which is unending and still less than the 3d universe.

Call Hubble to the rescue!

https://replit.com/@imcute-aaaa/Numbers#main.py(it doesn't seem to error now cuz i added that error term)
my ln results are all less than (if i should get result x,then it will be less 0.00000000076956675x)
or you can say that all my results are multiplied by 0.99999999923043323392556634123536
but why???(It's not a precision problem!i used my complex rational class which has infinite precision and the error term does not relate to the prec parameter other than going wrong under prec<10 and its not <10)

p1:No Nonnegative Numbers
p2:Or Oblong Objects
p3:Painted Purple Primes.
p4:(next sentence go on with q)
Stuff that are used to keep grammar(and punchuation) do not need to start with the correct stuff
Fun and true statements are prefered.
Oh,and no politics,religion,or swearing!
I'll start:

Abnormal Acute Angles

a double factorial products up 2 at a time not 1
2x!!=product k=1->x 2x
so x+2n!!=x!!*product k=1->n 2x
for something like a gamma function,we can take the log
L(x)=ln(x!!)
N is a huge number
so ln(N+k)-ln(N)=0 for a little k compared to N
L(N+2n)=L(N)+sum k=1->n ln(N+2k)
=L(N)+sum k=1->n ln(N)
=L(N)+nlnN
now do some substitution
L(2n)+sum k=1->N/2 ln(2n+2k)=sum k=1->N/2 ln(2k)+nlnN
move it to right and merge sums
L(2n)=sum k=1->N/2 -ln(2n+2k)+ ln(2k)+nlnN
log rule
L(2n)=sum k=1->N/2 ln(k/k+n)+nlnN
sub n for 2n and exponentiate
n!!=product k=1->N/2 k/k+n/2 +N^(n/2)
minor changes
n!!=product k=1->N/2 2k/k+n +sqrt(N^n)
done!
change the limits a bit N->2N^2 x->n
x!!=lim N->inf 4*N^n*product k=1->N^2 k/(x+2k)
idk if it actually works but i think it would cuz it based on the factorial video from lines that connect

t=1.44466786100976618
the root of "|x-logt x| has 1 root“