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My solution uses the Python tool to implement the AKS Test for primes (slower method), because I love the Numberphile youtube channel ... https://youtu.be/HvMSRWTE2mI
All credit goes to the original authors of the 2002 paper, of course! https://www.cse.iitk.ac.in/users/manindra/algebra/primality_v6.pdf
#################################
# List all non-standard packages to be imported by your
# script here (only missing packages will be installed)
# from ayx import Package
# Package.installPackages(['pandas','numpy'])
#################################
from ayx import Alteryx
import numpy as np
import pandas as pd
import sys
#################################
def is_prime(p):
roots = [1 for _ in range(p)]
roots
poly1 = np.poly1d(roots, True)
poly1
coef = [1]
for _ in range(p-1):
coef.append(0)
coef.append(-1)
coef
poly2 = np.poly1d(coef, False)
poly2
poly3 = poly1 - poly2
poly3
return np.array_equal(poly3.c[:p-1]%p, np.zeros(p-1))
#################################
dfInput = Alteryx.read("#1")
dfAnswer = Alteryx.read("#2")
#################################
results = []
for i in range(2, dfInput['Number'][0]+1):
if is_prime(i):
results.append(i)
results
#################################
dfOutput = pd.DataFrame(results, columns=['Number'])
#################################
dfAnswer = dfAnswer.astype('int64')
#################################
if dfAnswer.equals(dfOutput):
print("SUCCESS!!! Found all primes")
else:
sys.exit("ERROR!!! Try again")
#################################
Alteryx.write(dfOutput, 1)
#################################
I learned a few things about Alteryx with this challenge. First off no Factorial function, and secondly that the mod function doesn't like numbers roughly 1124000727777607680000 and larger.
I first tried to use Wilson's Theorem to solve this challenge, but quickly found challenge #74, which asks users to create a factorial calculator, persistent I used wolfram alpha to build a table for 2->50!. After doing so I couldn't get my formula tool to process mod(1124000727777607680000,22) or beyond, so I looked to a less calculation intense solution.
Brute Force
Fun challenge on my day off! Approach is detailed in the screenshot.
My answer was essentially the same as #Jean-Balteryx though not as compact. Feels a bit brute force, and certainly not a repeatable process. I actually like #OllieClarke's approach quite a bit. That was kind of what I was thinking, but I didn't quite get there.
Uploading my solution. Have excluded 1 from divisors so that a number with a single divisor is considered as Prime number.