So I have a question:
Given an even number (greater than 2), return two prime numbers whose sum will be equal to given number. There are several combinations possible. Print only first such pair
This is for additional reference:
*Input: The first line contains T, the number of test cases. The following T lines consist of a number each, for which we'll find two prime numbers.
Note: The number would always be an even number.
Output: For every test case print two prime numbers space separated, such that the smaller number appears first. Answer for each test case must be in a new line.
Constraints: 1 ≤ T ≤ 70
2 < N ≤ 10000
Example:
Input:
5, 74, 1024, 66, 8, 9990
Output: 3 71, 3 1021, 5 61, 3 5, 17 9973
Here is what I tried:
import math
def prime(n):
for i in range(2, int(math.sqrt(n)) + 1):
if n % i == 0:
return False
return True
T = int(input("No of inputs: ")) #T is the no of test cases
input_num = []
for i in range(0,T):
input_num.append(input())
lst2= []
if T in range(1,71):
for i in input_num:
if (i in range(3,1000)) and (i % 2 == 0):
for j in range(0,i):
if prime(j) == True:
lst2.append(j)
for x in lst2:
for y in lst2:
if x + y == j:
print(x,end = ' ')
print(y)
This is only taking inputs but not returning outputs.
Also my code is currently intended for all the combinations but what I want is only the first pair and I am not able to do that
I found a more elegant solution to this problem here. Java, C, C++ etc versions of solution is also present there. I am going to give the python3 solution.
# Python 3 program to find a prime number
# pair whose sum is equal to given number
# Python 3 program to print super primes
# less than or equal to n.
# Generate all prime numbers less than n.
def SieveOfEratosthenes(n, isPrime):
# Initialize all entries of boolean
# array as True. A value in isPrime[i]
# will finally be False if i is Not a
# prime, else True bool isPrime[n+1]
isPrime[0] = isPrime[1] = False
for i in range(2, n+1):
isPrime[i] = True
p = 2
while(p*p <= n):
# If isPrime[p] is not changed,
# then it is a prime
if (isPrime[p] == True):
# Update all multiples of p
i = p*p
while(i <= n):
isPrime[i] = False
i += p
p += 1
# Prints a prime pair with given sum
def findPrimePair(n):
# Generating primes using Sieve
isPrime = [0] * (n+1)
SieveOfEratosthenes(n, isPrime)
# Traversing all numbers to find
# first pair
for i in range(0, n):
if (isPrime[i] and isPrime[n - i]):
print(i,(n - i))
return
# Driven program
n = 74
findPrimePair(n)
Related
I'm absolutely new to Python and programming in general so it'd be helpful if someone can give very beginner friendly help. I'm trying to get the sum of prime numbers upto say 50.
I used the below code but it adds additional 2 on my sum. for example sum of prime number upto 50 should be 326 but I get 328 as my output
upto = int(input("Find sum of prime numbers upto : "))
sum = 0
for num in range(2, upto + 1):
for i in range(2, num):
if (int(num % i) == 0):
break;
#If the number is prime then add it.
else:
sum += num
print("\nSum of all prime numbers upto", upto, ":", sum)
Your Code is working fine and the answer of " sum of prime numbers from 1 to 50" is 328 not 326, if you still have doubt about it you can check your result with this code below :
Explanation: Given a range [l, r], the task is to find the sum of all the prime numbers within that range.
# from math lib import sqrt method
from math import sqrt
# Function to compute the prime number
def checkPrime(numberToCheck) :
if numberToCheck == 1 :
return False
for i in range(2, int(sqrt(numberToCheck)) + 1) :
if numberToCheck % i == 0 :
return False
return True
# Function to iterate the loop
# from l to r. If the current
# number is prime, sum the value
def primeSum(l, r) :
sum = 0
for i in range(r, (l - 1), -1) :
# Check for prime
isPrime = checkPrime(i)
if (isPrime) :
# Sum the prime number
sum += i
return sum
# Driver code
if __name__ == "__main__" :
l, r = 1, 50
# Call the function with l and r
print(primeSum(l, r))
I set your range in the code above just copy and paste the code in your editor and run the code , you will see the result.
There are two parts you need to handle. One is to check if the number is a prime number or not. Second is to iterate through the range of numbers. Refer to the code below,
from math import sqrt
sum = 0
#some explanation here we are iterating from 50 all the way to 1. So you can indicate your range here. -1 is the step value which tells the difference between each iteration.
for i in range(50, 0, -1):
# Check whether it is a prime number here
bPrime = True #initialize a boolean here to be indicated by the loop below
for a in range(2, int(sqrt(i)) + 1):
if i % a == 0:
bPrime = False #definitely not a prime,break the loop and set boolean to false
break
bPrime = True #not ==0 so it is a prime, set boolean to true
if (bPrime) :
# Add up if it is a prime number
sum += i
#view the results
print(sum)
It should get you 328
Hi Sumit firstly Welcome to Stackoverflow :)
Now as per your question the sum of prime numbers upto range 50 is 328 only, not 326.
But if you want the sum of first 50 odd prime numbers then you can make minor change in your code as below which will give you 326 [which is the sum of odd prime nos till range 50]
upto = int(input("Find sum of prime numbers upto : "))
sum = 0
for num in range(3, upto+1):
for i in range(2, num):
if (int(num % i) == 0):
break;
#If the number is prime then add it.
else:
sum += num
print("\nSum of all prime numbers upto", upto, ":", sum)
I need to write a Python program that determines whether a given integer input is is a twin prime number or not. If the input number is a twin prime, the program must output true. Otherwise, it must output false.
Please may someone guide me with how this program should be written in Python?
This is what I have done so far. I am stuck at the is_twin_prime function part.
def is_prime(x):
for i in range(2, x):
if x % i == 0:
return False
return True
def is_twin_prime(x):
if is_prime(x) = True:
N = int(input())
for i in range(N):
p = int(input())
if is_twin_prime(p):
print("true")
else:
print("false")
Based on the assumption, that you are trying to determine if N & p are twin primes of one another, I found several issues with your code as follows:
the is_twin_prime function has no False return
the is_prime function always starts with 2 and iteratively checks for prime, this is very inefficient.
To provide an answer, I started with the following factoids about twin_primes:
both numbers must be prime
abs(n-p) == 2
n and p must each have a units digit in [0, 2, 3, 5, 7, 8]
To make the function testing for twin primes as efficient as possible, I eliminated any numbers not meeting the last two cases first, and only if necessary did I generate a list of primes. Also, when generating the primes, I only did it once for the largest number since, once I have the list or the largest both numbers must be in the list.
To make searching for primes more efficient I employed itertools, although this could be done with slightly less efficiency without it's use.
import itertools
def erat2():
D = { }
yield 2
for q in itertools.islice(itertools.count(3), 0, None, 2):
p = D.pop(q, None)
if p is None:
D[q*q] = q
yield q
else:
x = p + q
while x in D or not (x&1):
x += p
D[x] = p
def generatePrimes(given_number):
"""
Returns the prime number <= given_number using
an adaptive sieve of estraothenes approach
"""
return list(itertools.islice(erat2(), given_number))
def is_twinPrime(n, p):
accepted_digits = [0, 2, 3, 5, 7, 8]
if abs(n-p) != 2:
return False
elif n%10 not in accepted_digits and p%10 not in accepted_digits:
return False
else:
primes = generatePrimes(max(n, p))
if n in primes and p in primes:
return True
return False
N = int(input("Enter first number"))
P = int(input(Enter second number"))
print(istwinPrime(N, P)
I am working on a python program where I want to find the minimum number of steps needed to reach a top floor such that the count of steps should be divisible by given number say m
Here is my program taken from here:
# A program to count the number of ways to reach n'th stair
# Recurssive program to find n'th fibonacci number
def fib(n):
if n <= 1:
return n
return fib(n-1) + fib(n-2)
# returns no. of ways to reach s'th stair
def countWays(s):
return fib(s + 1)
# Driver program
s = 10
print("Number of ways = ", countWays(s) )
Here I am getting the total number of ways, but I want to filter them by those divisible by a given number say m, how to do this?
Example:
1) s = 10 and m = 2, output should be 6, as the steps are {2,2,2,2,1,1}
2) s = 3 and m = 5 output should be -1 as the possible steps are {1,1,1}, {2,1}, {1,2}
--> here none of them (means 3 steps, 2 steps, 2 steps) are divible by 5.
s = 10
m = 2
if s % m == 0:
print(s)
outputs: 10
Using % is a modulo operation. This provides a "remainder" after division. So if your item has no remainder, it is divisible by the selected number.
# A program to count the number of ways to reach n'th stair
# Recursive function used by countWays
def countWaysUtil(n,m):
res = [0 for x in range(n)] # Creates list res witth all elements 0
res[0],res[1] = 1,1
for i in range(2,n):
j = 1
while j<=m and j<=i:
res[i] = res[i] + res[i-j]
j = j + 1
return res[n-1]
# Returns number of ways to reach s'th stair
def countWays(s,m):
return countWaysUtil(s+1, m)
# Driver Program
s,m = 4,2
print "Number of ways =",countWays(s,m)
# Contributed by Harshit Agrawal
You can use this:
# A program to count the number of ways to reach n'th stair
# Recurssive program to find n'th fibonacci number
def fib(n):
if n <= 1:
return n
return fib(n-1) + fib(n-2)
# returns no. of ways to reach s'th stair
def countWays(s, m):
# Add in a division by m, which you pass to the function
# Cast it as an int to return a whole # and not decimal
return int(fib(s + 1) / m)
# Driver program
s = 10
# Set this to whatever
m = 3
print("Number of ways = ", countWays(s, m) )
Im a newbie at python and i have a task. Given a number as input, i have to print the prime that belongs in the number/position on a list of primes starting from position 1 and not 0, until the input is 'END'. For example, if the input is 1, output should be the first prime which is 2, if the input is 5, output should be the 5th prime which is 11 and so. It works fine but after 3/4-digit numbers the output has a delay until i get the Error: Time limit exceeded. How can i make it run faster? Here's the code:
def primes_function(n):
primes = []
num = 2
while len(primes) <= n:
x = num // 2
while x > 1:
if num % x == 0:
break
x -= 1
else:
primes.append(num)
num += 1
return primes[n - 1]
#main
while True:
n = input()
if n == 'END':
break
elif n > '0':
n = int(n)
value = primes_function(n)
print(value)
Sorry if i made any mistakes in the description
enter image description here
I combined this answer (1) and this answer (2) to speed up the function. The two key ideas are: When testing primality of a candidate ...
... do not divide by every number (2, 3, 4, 5, 6, ...) but only by the preceding prime numbers (2, 3, 5, ...). Every non-prime number > 2 is has to have some prime factor.
... divide only by numbers that are ≤ sqrt(candidate).
import math
def nth_prime(n):
prime_list = [2]
candidate = 3
while len(prime_list) < n:
max_factor = math.sqrt(candidate)
is_prime = True
for p in prime_list:
if p > max_factor:
break
elif candidate % p == 0:
is_prime = False
break
if is_prime:
prime_list.append(candidate)
candidate += 2
return prime_list[-1]
Benchmark of different solutions:
n=9000 n=15000 n=25000 n=75000
your solution 1m38.455s - - -
linked answer (1) 0m 2.954s 8.291s 22.482s -
linked answer (2) 0m 0.352s 0.776s 1.685s 9.567s
this answer 0m 0.120s 0.228s 0.410s 1.857s
Brij's answer 0m 0.315s 0.340s 0.317s 0.318s
For every n the programs where started from scratch.
As we can see, Brij's Sieve Of Eratosthenes takes a fairly low constant amount of time. If you want to find big prime numbers below a fixed limit then that's the best solution (here n < 78499, as the 78499-th prime number is 1 000 003 which is bigger than the sieve list).
If you also want to find a lot of smaller or medium sized prime numbers or cannot accept a fixed limit then go with this solution.
def SieveOfEratosthenes():
n = 1000000
prime = [True for i in range(n+1)]
p = 2
count = 0
while (p * p <= n):
if (prime[p] == True):
count = count + 1
for i in range(p * p, n+1, p):
prime[i] = False
p += 1
seive = []
for p in range(2, n):
if prime[p]:
seive.append(p)
return seive
def primes_function(n , seive):
return seive[n - 1]
#main
seive = SieveOfEratosthenes()
while True:
n = input()
if n == 'END':
break
elif n > '0':
n = int(n)
value = primes_function(n,seive)
print(value)
Full working : https://ide.geeksforgeeks.org/QTSGQfhFV3
I have precomputed the primes below 10^6 and made a list of primes and accessed the nth prime number by the index.
I have obtained input from user and put its factors to a new list.How do i check for prime numbers in the list.
a=int(input())
b=[]
for x in range(2,a):
if(a%x)==0:
b.append(x)
print(b)
Here you can print the list of factors and then iterate through the list of factors and this program will print out the ones that are prime. Instead of printing it you could also append it to another list by replace the print(n) with something else.
import math
a=int(input())
b=[]
for x in range(2,a):
if(a%x)==0:
b.append(x)
print(b)
def is_prime(n): #calling a function
if n == 2:
print(n) #if one of the factors is 2 it prints it because it is a prime number
if n % 2 == 0 or n <= 1: # if it is less than one or is a factor of 2 it returns false and does nothing
return False
sqr = int(math.sqrt(n)) + 1
for divisor in range(3, sqr, 2): #checks for other divisors
if n % divisor == 0:
return False
print(n) #otherwise it prints out the number since it is a prime number
for n in b: #iterates through the list of factors and checks if they are prime
is_prime(n)
If we run this and I input 10 it returns this :
[2, 5]
2
5
EDIT :
When you input a prime number it returns a blank array. So i edited the code to be :
import math
values = []
def is_prime(n): #calling a function
if n == 2:
values.append(n)
#print(n) #if one of the factors is 2 it prints it because it is a prime number
return True
if n % 2 == 0 or n <= 1: # if it is less than one or is a factor of 2 it returns false and does nothing
return False
sqr = int(math.sqrt(n)) + 1
for divisor in range(3, sqr, 2): #checks for other divisors
if n % divisor == 0:
return False
#print(n) #otherwise it prints out the number since it is a prime number
values.append(n)
return True
a=int(input())
b=[]
for x in range(2,a):
if(a%x)==0:
b.append(x)
if is_prime(a)==True: #if the inputted number is prime it automatically appends that number to the list and breaks since prime numbers don't have any other factors
b.append(a)
break;
print(b)
for n in b: #iterates through the list of factors and checks if they are prime
is_prime(n)
def remove_duplicates(values): #here it checks for duplicates
output = []
seen = set()
for value in values:
# If value has not been encountered yet,
# ... add it to both list and set.
if value not in seen:
output.append(value)
seen.add(value)
return output
# Remove duplicates from this list.
values = remove_duplicates(values)
print("Here are the prime factors :")
print(values) #prints out the values
Now if you input a prime number it returns :
[7]
Here are the prime factors :
[7]
And any other number such as 20 :
[2, 4, 5, 10]
Here are the prime factors :
[2, 5]
will still run.
Note : I changed it from printing out just the numbers to appending the numbers to an array and then printing out the array.
Here is a one liner, you can change lower and upper limit by changing 1 and 150. Assign this to a variable. Not as fast as SoA though
[i for i in range(1,150) if all(i%j for j in range(2,int(i**(1/2))+1)) and i != 1]