I decided to crank up the power on my prime number identifier and attempt to document its efficiency in both C (GCC) and Python. I used the [very inefficient] code from the previous entry, modified it to test every integer up to 1×10^8, and let them both run on my laboratory computer overnight (an AMD Athlon 64-bit X2 Dual Core 2 GHz PC with 2GB of ram). The Python program took 3.24 processor hours, and the C program took 1.85 processor hours to complete. Each step along the way each program recorded how long it took to test the last 10,000 integers, creating a logfile with 1,000 data points, which can be easily graphed (see previous entry). On this nice, fast computer the data look very clean and curve-like. I curve-fitted the data using my new favorite website, ZunZun.com. Here’s what I came up with…

Coeffecients:

### C (GCC) ###
a =  1.4193535434065586E-03
b = -1.2708466972699874E-07
c = -4.9489218065978358E-16
d =  1.3032518272036044E-11
e =  1.3231610935638881E-06

### PYTHON ###
a =  2.6579973323520396E-03
b = -2.8299592901357803E-07
c = -1.2080374779761445E-15
d =  3.0281624700595501E-11
e =  2.4778595094623538E-06

### Generating Data Points: ###
Ys=[]
for x in range(len(values)):
     Ys.append(a*(x**.5)+b*(x)+c*(x**2)+d*(x**1.5)+e)

Note that this fitted curve is the representation of how long (in seconds, vertical axis) it takes to systematically test 10,000 integers for primeness (starting at an integer on the horizontal axis), This does NOT represent how long it takes to reach a certain X. To properly calculate this, one would need to integrate the equation. This would allow for the easy prediction of how long it would take to reach a certain integer (the solution would be the integral of the provided equation from 0 to the integer). I’ll let someone else attack that. It’s time for me to get back to work!

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