[dwrhiuki] timing factorization of random 200-bit numbers

200 bit: mean= 534 ms, std= 1062 ms, n= 10000
201 bit: mean= 564 ms, std= 1112 ms, n= 10000
202 bit: mean= 599 ms, std= 1186 ms, n= 10000

all are about 61 digits (future post ahlvcwcw).

Chebyshev's inequality (because the distribution of factoring times is most definitely not a normal distribution) says 99% are within 10 standard deviations of the mean.  (can we do better than Chebyshev knowing that all values must be positive?)

to get standard error of the mean, divide standard deviation by sqrt(n) = 100.

model name : Intel(R) Core(TM) i7-4810MQ CPU @ 2.80GHz

GP/PARI CALCULATOR Version 2.15.4 (released)
amd64 running linux (x86-64/GMP-6.2.1 kernel) 64-bit version
compiled: Jul 12 2023, gcc version 12.3.0 (Debian 12.3.0-5)
threading engine: pthread

? for(bitsize=200, 202, gettime; sumt=0; s2t=0; for(i=1, 10000, s=random(2^bitsize); print("dataline ",bitsize," ",s," ",factor(s)); t=gettime; sumt+=t; s2t+=t*t; print("i ",i," t ",t," sumt ",sumt," s2t ",s2t)); print("done ",bitsize))