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Primality quiz
#!/usr/bin/env python3
# Primality quiz
# Use the commandline argument "p" to show the list
#
# http://sekika.github.io/2016/12/13/Primality/
### Parameters
rep=10 # Numbers of questions
# Control the numbers for questions
# The numbers from first to last, excluding obvious numbers will be shown.
# Obvious numbers include
# (1) Multiple of 2 and 5
# (2) Multiple of 3 (when three=True)
# or Numbers where all digits are multiple of 3 (when three=False)
# (3) Numbers in the obvious list
first=29 # Smallest number
last=400 # Largest number
three=False # Make multiple of 3 as obvious
obvious=[7,11,13,21,27,49,77,81,777] # Obvious numbers
########################
import math, random, sys
# Sieve of Eratosthenes; divisor[n] is the minimum divisor
divisor = [i for i in range(0,last+1)]
lastprime=1
for prime in divisor:
if prime > math.sqrt(last): break
if prime <= lastprime: continue
lastprime=prime
for non_prime in range(2 * prime, last+1, prime):
divisor[non_prime] = min(prime, divisor[non_prime])
# factorize(n) shows factorization
def factorize(n):
n = int(n)
if n == divisor[n]:
return str(n)
else:
return str(divisor[n])+' * '+factorize(n/divisor[n])
# Prepare primes and nonprimes for questions
prime=[]
nonprime=[]
for n in range(first, last+1):
if three:
modthree=n % 3
else:
modthree=sum([int(c)%3 for c in str(n)]) # All the digits are multiple of 3?
if (n % 2)*(n % 5)*modthree != 0 and not n in obvious:
if n==divisor[n]:
prime.append(n)
else:
nonprime.append(n)
# Read command line argument
if len(sys.argv) > 1:
arg = sys.argv[1]
else:
arg = ""
##### Print mode (command line argument = "p")
if arg == "p":
print ('List of primes')
print (prime)
print ('List of composite numbers')
for n in nonprime:
print (n, '=', factorize(n))
sys.exit()
##### Primality quiz
# Prepare the questions
while len(prime)<rep:
prime.extend(prime)
random.shuffle(prime)
while len(nonprime)<rep:
nonprime.extend(nonprime)
random.shuffle(nonprime)
question=prime[:rep]
question.extend(nonprime[:rep])
random.shuffle(question)
question=question[:rep]
# Main loop
print (rep, 'questions for primality.')
print (question)
for n in question:
key=input(str(n)+' is prime? Type return to show the answer. ')
if n==divisor[n]:
print ('Prime!')
else:
print ('Composite.',n, '=', factorize(n))
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