October 8th, 2013, 07:50 PM

Help w/ Writing Function Definitions
Hi, I am taking a class in order to learn Python. One of the exercises I need to do is write function definitions. I cannot figure out how to do one of them. To show you an example here is a similar problem:
If m is an integer, then isPrime(m) iﬀ m is prime.
The code:
# Prompts the user for an integer m and then computes and prints whether
# m is prime or not.
# isPrime(m): I > Bool
# If m is an integer, then isPrime(m) if and only if m is prime.
def isPrime(m):
return False if m <= 1 else isPrimeItr(1,0,m)
# isPrimeItr(i,a,m): I x I x I > Bool
def isPrimeItr(i,a,m):
return False if a> 2 else True if a == 2 and i == m +1 else isPrimeItr(i+1,a+1,m) if m % i == 0 else isPrimeItr(i+1,a,m)
# print a brief description of the program followed by an empty line
print("Computing Prime Numbers")
print("Prompts the user an integer value for m and then computes and")
print("prints if m is prime or not.")
print()
# prompt the user for a value for m
m = eval(input("Enter an integer value for m: "))
# print if m is prime
print("The value that", m, "is a prime integer is", isPrime(m))

These are the problems I am having problem with:
If m and n are integers, then anyPrimes(m,n) iﬀ there are any prime numbers in the interval [m,n).
If m and n are integers, then countPrimes(m,n) is the number of prime numbers in the interval [m,n).
If anyone could help that would be great. Thank you.
October 9th, 2013, 01:28 AM

maybe you could construct the other functions using this primality test.
Code:
from math import sqrt # **0.5
def isPrime(A):
'''tested for the first 62 primes'''
if A < 2: # my choice.
return False
if A in (2,3,):
return True
if (A1)%6 and (A+1)%6:
return False
for potential_divisor in range(5, 1+int(sqrt(A)), 2): # could be a list of primes found so far, could continue to use the 6 \pm 1 information
if not (A % potential_divisor):
return False
return True
for i in range(3, 300):
if isPrime(i):
print(i, end=' ')
# Let A be the vector printed by this program.
# Then the j sentence (:p:@i.@#)A confirms the primality of the values,
# and that all primes through the first 62 are included in the vector.
# www.jsoftware.com J no longer looks like line noise to me.
[code]
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