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I have a function that takes a number (for example, 5) and returns the first prime number after the input number (in this case, it would be 7).
This is my code:
def prime(n):
np=[]
isprime=[]
for i in range (n+1,n+200):
np.append(i)
for x in range(2,199):
for j in np:
if x%j!=0:
isprime.append(x)
return min(isprime)
However, this code doesn't work (it always returns 2). Where is the mistake?
You have a few mistakes, most notably np is clearly meant to be the potential primes (it starts at n+1 which is the first potential number that fits your critera "the first prime number after the input number"), and yet you add x to your prime list, which is from range(2,199), you should be using:
isprime.append(j)
Your primality test is also the wrong way round as a result, you should be using:
j % x != 0
Lastly, you can't append a number if that condition is true in one case, it has to be true in all cases (where x is an integer which satisfies 2 <= x < j), because of this you should switch your second set of for loops around (the x loop should be the inner loop), and you should also only loop up to j-1 (the number being tested). Additionally, you should instead choose to not add an item if j % x == 0:
for ...:
val_is_prime = True
for ...:
if j % x == 0:
val_is_prime = False
break
if val_is_prime:
isprime.append(j)
This results in the following code:
def prime(n):
np=[]
isprime=[]
for i in range (n+1,n+200):
np.append(i)
for j in np:
val_is_prime = True
for x in range(2,j-1):
if j % x == 0:
val_is_prime = False
break
if val_is_prime:
isprime.append(j)
return min(isprime)
And test run:
>>> prime(5)
7
>>> prime(13)
17
>>> prime(23)
29
Note that there's several other efficiency improvements that could be made, but this answer focuses on the mistakes rather than improvements
Try this one, the most pythonic and clear way to do this that I found (but probably not the most efficient):
def is_prime(x):
return all(x % i for i in range(2, x))
def next_prime(x):
return min([a for a in range(x+1, 2*x) if is_prime(a)])
print(next_prime(9))
https://www.geeksforgeeks.org/python-simpy-nextprime-method/
from sympy import *
# calling nextprime function on differnet numbers
nextprime(7)
nextprime(13)
nextprime(2)
Output:
11 17 3
This code working.
def prime(n):
next_prime = n + 1
prime = True
while True:
for i in range(2, next_prime):
if next_prime%i ==0:
prime = False
break
if prime:
return next_prime
else:
next_prime = next_prime + 1
if next_prime % 2 == 0:
next_prime = next_prime + 1
prime = True
if __name__=="__main__":
print(prime(5))
Here is one working sample.
inputNumber = int(input("Enter number to find next prime: "))
def nextPrime(inputNum):
for nextNumToChk in range(inputNum+1, inputNum +200):
if nextNumToChk > 1:
# If num is divisible by any number between 2 and val, it is not prime
for i in range(2, nextNumToChk):
if (nextNumToChk % i) == 0:
break
else:
#found the prime
return nextNumToChk
result = nextPrime(inputNumber)
print "Next Prime is : ",result
Output:-
Enter number to find next prime: 5
Next Prime is : 7
def is_prime(n):
# Corner case
if n <= 1:
return False
# Check from 2 to n-1
for i in range(2, n):
if n % i == 0:
return False
return True
def first_prime_over(n):
prime_number = (i for i in range(n) if is_prime(i))
try:
for i in range(0,n):
(next(prime_number))
except StopIteration:
prime_number_next = (i for i in range(n,n+1000) if is_prime(i))
print(next(prime_number_next))
first_prime_over(10)
Try this one:
def find_next_prime(n):
return find_prime_in_range(n, 2*n)
def find_prime_in_range(a, b):
for c in range(a, b):
for i in range(2, c):
if c % i == 0:
break
else:
return c
return None
def main():
n = int(input('Find the next prime number from: '))
print(find_next_prime(n+1))
if __name__ == '__main__':
main()
n = int(input("Enter a number"))
while True:
n+=1
for x in range(2,n):
if n%x==0:
break
else:
print("next prime number is",n)
break
Can someone help me and tell me why this doesn't work? The goal is to count the number of prime numbers that are produced by a given polynomial for inputs n in a specified range [a,b]:
def count_primes(poly, a, b):
primes = 0
if b >= a:
for n in range(a, b):
result = poly(n)
if result > 1:
for i in range(2, result):
if (result % i) == 0:
break
else:
primes += 1
else:
break
return primes
def poly(n):
return n**2 + n + 41
print(count_primes(poly, 0, 39))
The result should return 40 in this case.
[2] Problem Solution
Step-1. Take in the number to be checked and store it in a variable.
Step-2. Initialize the count variable to 0.
Step-3. Let the for loop range from 2 to half of the number (excluding 1 and the number itself).
Step-4. Then find the number of divisors using the if statement and increment the count variable each time.
Step-5. If the number of divisors is lesser than or equal to 0, the number is prime.
Step-6. Print the final result.
Step-7. Exit.
The problem is that the else clause in the nested loop refers to the if, when it should be activated only if the loop finished without break. Just change the identitation to:
if result > 1:
for i in range(2, result):
if (result % i) == 0:
break
else:
primes += 1
This is the wrong way to count primes:
if result > 1:
for i in range(2, result):
if (result % i) == 0:
break
else:
primes += 1
Should be:
if result > 1:
isPrime = True
for i in range(2, result):
if (result % i) == 0:
isPrime = False
break
if isPrime:
primes += 1
Also, it goes without saying. Easy optimizations for prime number detection. You only have to test for divisibility divisibility with 2 and all odd numbers between 3 and sqrt(result).
def count_primes(poly, a, b):
primes = 0
if b >= a:
for n in range(a, b+1):
result = poly(n)
if result > 1:
for i in range(2, result):
if (result % i) == 0:
break
else:
primes += 1
else:
break
return primes
def poly(n):
return n**2 + n + 41
print(count_primes(poly, 0, 39))
Problems:
you do primes += 1 too early. In your methods, you have to test until no possible division happens, then do the addition.
[a, b] The endpoints are both inclusive. Then you should use b+1 at your for n in range(a, b+1), which produces 40.
I have a hackkerank coding challenge to print first n non prime numbers, i have the working code but the problem is that they have a locked code which prints numbers from 1 to n along with the output, in order to pass the test i need to print only the non prime numbers not 1...n numbers along with it. I cant comment the printing part of 1...n as it is blocked. please let me know the idea to print only 1st n non prime numbers:
here is my solution:
def manipulate_generator(generator, n):
if n>1:
ls=[1]
for elm in generator:
if elm>3 and len(ls)<n:
for k in range(2,elm):
if elm%k==0 and elm not in ls:
ls.append(elm)
print(elm)
if len(ls)==n:
return ls
That's the code I added but here is the code that's locked on which I have to write the code above to make it print the number one at a time
def positive_integers_generator():
n = 1
while True:
x = yield n
if x is not None:
n = x
else:
n += 1
k = int(input())
g = positive_integers_generator()
for _ in range(k):
n = next(g)
print(n)
manipulate_generator(g, n)
the point is the for _ in range(k): already prints out number which includes numbers I don't want printed out: This is the desired kind of output I want:for n=10 I want it to print out:
output:
1
4
6
8
9
10
12
14
15
16
I can't change this code but the one above is what I wrote and can be changed... Pleae help me out... Thanks in anticipation
Why not to throw away the numbers which we don't need? Look at this solution which I implemented...
def is_prime(n):
for i in range(2, n):
if n%i == 0:
return False
return True
def manipulate_generator(generator, n):
if is_prime(n+1):
next(generator)
manipulate_generator(generator, n+1)
Note: I understand that the logic can be improved to make it more efficient. But, its the idea of skipping unnecessary number printing which is important here !
You can print all the numbers from 1 up to the first prime number and then from that first number to the next one until you reach n.
I'm not sure of your hackerrank situation, but printing the first N non-prime numbers efficiently can be done this way.
def non_prime_numbers_till_n(n):
primes = set()
for num in range(2,number + 1):
if num > 1:
for i in range(2, math.sqrt(num)):
if (num % i) == 0:
break
else:
primes.add(num)
result = []
for i in range(1, n):
if i not in primes:
result.append(i)
return result
Depending on what your online editor expects you can either print them, or store them in a list and return the list.
Also bear in mind, you can only check upto the sqrt of the number to determine if its a prime or not.
I eventually came up with this answer which I believe should solve it but id there;s a better way to solve it please add your answers:
def manipulate_generator(generator, n):
for num in range(3,100000):
for q in range(2,num):
if num%q==0 and num>n:
generator.send(num-1)
return
this link python generator helped me to understand python generator
I just solved that right now. Like Swapnil Godse said you need to deal with all special cases to optimize computations. This link might be helpful: click here.
Here is the solution:
from math import sqrt
def is_prime(n):
if (n <= 1):
return False
if (n == 2):
return True
if (n % 2 == 0):
return False
i = 3
while i <= sqrt(n):
if n % i == 0:
return False
i = i + 2
return True
def manipulate_generator(g, n):
if is_prime(n+1):
next(g)
manipulate_generator(g, n+1)
prime = int(input('Please enter the range: '))
prime_number = []
for num in range(prime):
if num > 1:
for i in range(2,num):
if num % i == 0:
break
else:
prime_number.append(num)
print(f'Prime numbers in range {prime} is {prime_number}')
all_number = []
for i in range(2,prime+1):
all_number.append(i)
Non_prime_number = []
for element in all_number:
if element not in prime_number:
Non_prime_number.append(element)
print(f'Non Prime numbers in range {prime} is {Non_prime_number}')
I am trying to implement a function primeFac() that takes as input a positive integer n and returns a list containing all the numbers in the prime factorization of n.
I have gotten this far but I think it would be better to use recursion here, not sure how to create a recursive code here, what would be the base case? to start with.
My code:
def primes(n):
primfac = []
d = 2
while (n > 1):
if n%d==0:
primfac.append(d)
# how do I continue from here... ?
A simple trial division:
def primes(n):
primfac = []
d = 2
while d*d <= n:
while (n % d) == 0:
primfac.append(d) # supposing you want multiple factors repeated
n //= d
d += 1
if n > 1:
primfac.append(n)
return primfac
with O(sqrt(n)) complexity (worst case). You can easily improve it by special-casing 2 and looping only over odd d (or special-casing more small primes and looping over fewer possible divisors).
The primefac module does factorizations with all the fancy techniques mathematicians have developed over the centuries:
#!python
import primefac
import sys
n = int( sys.argv[1] )
factors = list( primefac.primefac(n) )
print '\n'.join(map(str, factors))
This is a comprehension based solution, it might be the closest you can get to a recursive solution in Python while being possible to use for large numbers.
You can get proper divisors with one line:
divisors = [ d for d in xrange(2,int(math.sqrt(n))) if n % d == 0 ]
then we can test for a number in divisors to be prime:
def isprime(d): return all( d % od != 0 for od in divisors if od != d )
which tests that no other divisors divides d.
Then we can filter prime divisors:
prime_divisors = [ d for d in divisors if isprime(d) ]
Of course, it can be combined in a single function:
def primes(n):
divisors = [ d for d in range(2,n//2+1) if n % d == 0 ]
return [ d for d in divisors if \
all( d % od != 0 for od in divisors if od != d ) ]
Here, the \ is there to break the line without messing with Python indentation.
I've tweaked #user448810's answer to use iterators from itertools (and python3.4, but it should be back-portable). The solution is about 15% faster.
import itertools
def factors(n):
f = 2
increments = itertools.chain([1,2,2], itertools.cycle([4,2,4,2,4,6,2,6]))
for incr in increments:
if f*f > n:
break
while n % f == 0:
yield f
n //= f
f += incr
if n > 1:
yield n
Note that this returns an iterable, not a list. Wrap it in list() if that's what you want.
Most of the above solutions appear somewhat incomplete. A prime factorization would repeat each prime factor of the number (e.g. 9 = [3 3]).
Also, the above solutions could be written as lazy functions for implementation convenience.
The use sieve Of Eratosthenes to find primes to test is optimal, but; the above implementation used more memory than necessary.
I'm not certain if/how "wheel factorization" would be superior to applying only prime factors, for division tests of n.
While these solution are indeed helpful, I'd suggest the following two functions -
Function-1 :
def primes(n):
if n < 2: return
yield 2
plist = [2]
for i in range(3,n):
test = True
for j in plist:
if j>n**0.5:
break
if i%j==0:
test = False
break
if test:
plist.append(i)
yield i
Function-2 :
def pfactors(n):
for p in primes(n):
while n%p==0:
yield p
n=n//p
if n==1: return
list(pfactors(99999))
[3, 3, 41, 271]
3*3*41*271
99999
list(pfactors(13290059))
[3119, 4261]
3119*4261
13290059
Here is my version of factorization by trial division, which incorporates the optimization of dividing only by two and the odd integers proposed by Daniel Fischer:
def factors(n):
f, fs = 3, []
while n % 2 == 0:
fs.append(2)
n /= 2
while f * f <= n:
while n % f == 0:
fs.append(f)
n /= f
f += 2
if n > 1: fs.append(n)
return fs
An improvement on trial division by two and the odd numbers is wheel factorization, which uses a cyclic set of gaps between potential primes to greatly reduce the number of trial divisions. Here we use a 2,3,5-wheel:
def factors(n):
gaps = [1,2,2,4,2,4,2,4,6,2,6]
length, cycle = 11, 3
f, fs, nxt = 2, [], 0
while f * f <= n:
while n % f == 0:
fs.append(f)
n /= f
f += gaps[nxt]
nxt += 1
if nxt == length:
nxt = cycle
if n > 1: fs.append(n)
return fs
Thus, print factors(13290059) will output [3119, 4261]. Factoring wheels have the same O(sqrt(n)) time complexity as normal trial division, but will be two or three times faster in practice.
I've done a lot of work with prime numbers at my blog. Please feel free to visit and study.
def get_prime_factors(number):
"""
Return prime factor list for a given number
number - an integer number
Example: get_prime_factors(8) --> [2, 2, 2].
"""
if number == 1:
return []
# We have to begin with 2 instead of 1 or 0
# to avoid the calls infinite or the division by 0
for i in xrange(2, number):
# Get remainder and quotient
rd, qt = divmod(number, i)
if not qt: # if equal to zero
return [i] + get_prime_factors(rd)
return [number]
Most of the answer are making things too complex. We can do this
def prime_factors(n):
num = []
#add 2 to list or prime factors and remove all even numbers(like sieve of ertosthenes)
while(n%2 == 0):
num.append(2)
n /= 2
#divide by odd numbers and remove all of their multiples increment by 2 if no perfectlly devides add it
for i in xrange(3, int(sqrt(n))+1, 2):
while (n%i == 0):
num.append(i)
n /= i
#if no is > 2 i.e no is a prime number that is only divisible by itself add it
if n>2:
num.append(n)
print (num)
Algorithm from GeeksforGeeks
prime factors of a number:
def primefactors(x):
factorlist=[]
loop=2
while loop<=x:
if x%loop==0:
x//=loop
factorlist.append(loop)
else:
loop+=1
return factorlist
x = int(input())
alist=primefactors(x)
print(alist)
You'll get the list.
If you want to get the pairs of prime factors of a number try this:
http://pythonplanet.blogspot.in/2015/09/list-of-all-unique-pairs-of-prime.html
def factorize(n):
for f in range(2,n//2+1):
while n%f == 0:
n //= f
yield f
It's slow but dead simple. If you want to create a command-line utility, you could do:
import sys
[print(i) for i in factorize(int(sys.argv[1]))]
Here is an efficient way to accomplish what you need:
def prime_factors(n):
l = []
if n < 2: return l
if n&1==0:
l.append(2)
while n&1==0: n>>=1
i = 3
m = int(math.sqrt(n))+1
while i < m:
if n%i==0:
l.append(i)
while n%i==0: n//=i
i+= 2
m = int(math.sqrt(n))+1
if n>2: l.append(n)
return l
prime_factors(198765430488765430290) = [2, 3, 5, 7, 11, 13, 19, 23, 3607, 3803, 52579]
You can use sieve Of Eratosthenes to generate all the primes up to (n/2) + 1 and then use a list comprehension to get all the prime factors:
def rwh_primes2(n):
# http://stackoverflow.com/questions/2068372/fastest-way-to-list-all-primes-below-n-in-python/3035188#3035188
""" Input n>=6, Returns a list of primes, 2 <= p < n """
correction = (n%6>1)
n = {0:n,1:n-1,2:n+4,3:n+3,4:n+2,5:n+1}[n%6]
sieve = [True] * (n/3)
sieve[0] = False
for i in xrange(int(n**0.5)/3+1):
if sieve[i]:
k=3*i+1|1
sieve[ ((k*k)/3) ::2*k]=[False]*((n/6-(k*k)/6-1)/k+1)
sieve[(k*k+4*k-2*k*(i&1))/3::2*k]=[False]*((n/6-(k*k+4*k-2*k*(i&1))/6-1)/k+1)
return [2,3] + [3*i+1|1 for i in xrange(1,n/3-correction) if sieve[i]]
def primeFacs(n):
primes = rwh_primes2((n/2)+1)
return [x for x in primes if n%x == 0]
print primeFacs(99999)
#[3, 41, 271]
from sets import Set
# this function generates all the possible factors of a required number x
def factors_mult(X):
L = []
[L.append(i) for i in range(2,X) if X % i == 0]
return L
# this function generates list containing prime numbers upto the required number x
def prime_range(X):
l = [2]
for i in range(3,X+1):
for j in range(2,i):
if i % j == 0:
break
else:
l.append(i)
return l
# This function computes the intersection of the two lists by invoking Set from the sets module
def prime_factors(X):
y = Set(prime_range(X))
z = Set(factors_mult(X))
k = list(y & z)
k = sorted(k)
print "The prime factors of " + str(X) + " is ", k
# for eg
prime_factors(356)
Simple way to get the desired solution
def Factor(n):
d = 2
factors = []
while n >= d*d:
if n % d == 0:
n//=d
# print(d,end = " ")
factors.append(d)
else:
d = d+1
if n>1:
# print(int(n))
factors.append(n)
return factors
This is the code I made. It works fine for numbers with small primes, but it takes a while for numbers with primes in the millions.
def pfactor(num):
div = 2
pflist = []
while div <= num:
if num % div == 0:
pflist.append(div)
num /= div
else:
div += 1
# The stuff afterwards is just to convert the list of primes into an expression
pfex = ''
for item in list(set(pflist)):
pfex += str(item) + '^' + str(pflist.count(item)) + ' * '
pfex = pfex[0:-3]
return pfex
I would like to share my code for finding the prime factors of number given input by the user:
a = int(input("Enter a number: "))
def prime(a):
b = list()
i = 1
while i<=a:
if a%i ==0 and i!=1 and i!=a:
b.append(i)
i+=1
return b
c = list()
for x in prime(a):
if len(prime(x)) == 0:
c.append(x)
print(c)
def prime_factors(num, dd=2):
while dd <= num and num>1:
if num % dd == 0:
num //= dd
yield dd
dd +=1
Lot of answers above fail on small primes, e.g. 3, 5 and 7. The above is succinct and fast enough for ordinary use.
print list(prime_factors(3))
[3]
I'm truly a beginner at python so I apologise for the lack of knowledge, but the reason I'm asking is that reading the Python manual and tutorial (http://docs.python.org/2.7/tutorial) I'm not unable to totally grasp how loops work. I've written some simple programs so I think I get the basics but for whatever reason this program that is meant to list all primes less than or equal to n is not working:
n = int(raw_input("What number should I go up to? "))
p = 2
while p <= n:
for i in range(2, p):
if p%i == 0:
p=p+1
print "%s" % p,
p=p+1
print "Done"
The output when I enter 100 for example is:
2 3 5 7 11 13 17 19 23 27 29 31 35 37 41 43 47 53 59 61 67 71 73 79 83 87 89 95 97 101 Done
Which looks almost right but for some reason contains 27, 35, 95, which are composite of course. I've been trying to pick apart the way my loop works but I just don't see where it skips checking for divisibility suddenly. I figured that if someone had a look they could explain to me what about the syntax is causing this. Thanks a bunch!
I would actually restructure the program to look like this:
for p in range(2, n+1):
for i in range(2, p):
if p % i == 0:
break
else:
print p,
print 'Done'
This is perhaps a more idiomatic solution (using a for loop instead of a while loop), and works perfectly.
The outer for loop iterates through all the numbers from 2 to n.
The inner one iterates to all numbers from 2 to p. If it reaches a number that divides evenly into p, then it breaks out of the inner loop.
The else block executes every time the for loop isn't broken out of (printing the prime numbers).
Then the program prints 'Done' after it finishes.
As a side note, you only need to iterate through 2 to the square root of p, since each factor has a pair. If you don't get a match there won't be any other factors after the square root, and the number will be prime.
Your code has two loops, one inside another. It should help you figure out the code if you replace the inner loop with a function. Then make sure the function is correct and can stand on its own (separate from the outer loop).
Here is my rewrite of your original code. This rewrite works perfectly.
def is_prime(n):
i = 2
while i < n:
if n%i == 0:
return False
i += 1
return True
n = int(raw_input("What number should I go up to? "))
p = 2
while p <= n:
if is_prime(p):
print p,
p=p+1
print "Done"
Note that is_prime() doesn't touch the loop index of the outer loop. It is a stand-alone pure function. Incrementing p inside the inner loop was the problem, and this decomposed version doesn't have the problem.
Now we can easily rewrite using for loops and I think the code gets improved:
def is_prime(n):
for i in range(2, n):
if n%i == 0:
return False
return True
n = int(raw_input("What number should I go up to? "))
for p in range(2, n+1):
if is_prime(p):
print p,
print "Done"
Note that in Python, range() never includes the upper bound that you pass in. So the inner loop, which checks for < n, we can simply call range(2, n) but for the outer loop, where we want <= n, we need to add one to n so that n will be included: range(2, n+1)
Python has some built-in stuff that is fun. You don't need to learn all these tricks right away, but here is another way you can write is_prime():
def is_prime(n):
return not any(n%i == 0 for i in range(2, n))
This works just like the for loop version of is_prime(). It sets i to values from range(2, n) and checks each one, and if a test ever fails it stops checking and returns. If it checks n against every number in the range and not any of them divide n evenly, then the number is prime.
Again, you don't need to learn all these tricks right away, but I think they are kind of fun when you do learn them.
This should work and is bit more optimized
import math
for i in range(2, 99):
is_prime = True
for j in range(2, int(math.sqrt(i)+1)):
if i % j == 0:
is_prime = False
if is_prime:
print(i)
Please compare your snippet with the one pasted below and you will notice where you were wrong.
n = int(raw_input("What number should I go up to? "))
p = 2
while p <= n:
is_prime=True
for i in range(2, p):
if p%i == 0:
is_prime=False
break;
if is_prime==True:
print "%d is a Prime Number\n" % p
p=p+1
you do not re-start the i loop after you find a non-prime
p = i = 2
while p <= n:
i = 2
while i < p:
if p%i == 0:
p += 1
i = 1
i += 1
print p,
p += 1
print "Done"
A while loop executes the body, and then checks if the condition at the top is True, if it is true, it does the body again. A for loop executes the body once for each item in the iterator.
def is_prime(n):
if n>=2:
for i in range(2, n):
if n%i == 0:
return False
return True
else:
return False
To find PRIME NUMBER
Let's do a couple more improvements.
You know 2 is the only even prime number, so you add 2 in your list and start from 3 incrementing your number to be checked by 2.
Once you are past the half-way point (see above sqrt and * examples), you don't need to test for a prime number.
If you use a list to keep track of the prime numbers, all you need to do is to divide by those prime numbers.
I wrote my code and each of the above items would improve my code execution time by about 500%.
prime_list=[2]
def is_prime(a_num):
for i in prime_list:
div, rem = divmod(a_num, i)
if rem == 0:
return False
elif div < i:
break;
prime_list.append(a_num)
return True
This in my opinion is a more optimised way. This finds all the prime numbers up to 1,000,000 in less than 8 seconds on my setup.
It is also one of my very first attempts at python, so I stand to be corrected
class prime:
def finder (self):
import math
n = long(raw_input("What number should I go up to? "))
for i in range(2, n):
is_prime = True
if i % 2 == 0:
is_prime = False
for j in range(3, long(math.sqrt(i) + 1), 2):
if i % j == 0:
is_prime = False
break
if is_prime:
print(i)
prime().finder()
print('Enter a Number: ')
number=abs(int(input()))
my_List=[0,1]
def is_prime(n):
if n in my_List:
return True
elif n>=2:
for i in range(2, n):
if n%i == 0:
return False
return True
else:
return False
if is_prime(number):
print("%d is Prime!"%number)
else:
print(number,'is not prime')
for i in range(2, p):
if p%i == 0:
p=p+1
print "%s" % p,
p=p+1
I am going to tell your error only,in line 3 you are incrimenting p but actually what you are missing is your i if your i in previous case is let say 13 then it will check your loop after 13 but it is leaving 2,3,5,7,11 so its an error .that is what happening in case of 27 your i before 27 is 13 and now it will check from 14.and I don't think u need an solution.
def findprime(num):
count = 0
for i in range(1,num+1):
list1 = []
for ch in range(1,i+1):
if i%1==0 and i%ch==0:
list1.append(ch)
if len(list1)==2:
count += 1
print(i,end=", ")
print()
return count
num2 = int(input("enter a number: "))
result=findprime(num2)
print("prime numbers between 1 and",num2,"are",result)
Here's a more extensive example with optimization in mind for Python 3.
import sys
inner_loop_iterations: int = 0
def is_prime(n):
a: int = 2
global inner_loop_iterations
if n == 1:
return("Not prime")
elif n == 2:
return("Prime")
while a * a <= n + 1:
inner_loop_iterations += 1
# This if statement reduces the number of inner loop iterations by roughy 50%
# just weeding out the even numbers.
if a % 2 == 0:
a += 1
else:
a += 2
if n % 2 == 0 or n % a == 0:
return ("Not prime")
else:
return ("Prime")
while True:
sys.stdout.write("Enter number to see if it's prime ('q' to quit): ")
n = input()
if not n:
continue
if n == 'q':
break
try:
n = int(n)
except ValueError:
print("Please enter a valid number")
if n < 1:
print("Please enter a valid number")
continue
sys.stdout.write("{}\n".format(is_prime(n)))
sys.stderr.write("Inner loops: {}\n\n".format(inner_loop_iterations))
inner_loop_iterations=0
This program has two main optimizations, first it only iterates from 2 to the square root of n and it only iterates through odd numbers. Using these optimizations I was able to find out that the number 1000000007 is prime in only 15811 loop iterations.
My fast implementation returning the first 25 primes:
#!/usr/bin/env python3
from math import sqrt
def _is_prime(_num: int = None):
if _num < 2:
return False
if _num > 3 and not (_num % 2 and _num % 3):
return False
return not any(_num % _ == 0 for _ in range(3, int(sqrt(_num) + 1), 2))
_cnt = 0
for _ in range(1, 1000):
if _is_prime(_):
_cnt += 1
print(f"Prime N°: {_:,} | Count: {_cnt:,}")
Better use
for i in range(2, p//2 + 1):