This is a Number Theory problem. My professor wants us to use Python coding to a

Question

This is a Number Theory problem.
My professor wants us to use Python coding to answer. I have got a little bit of the coding down, but it would be greatly appreciated if I could get some extra help! Coding Exercise. (1) The year 2017 had the following property: 2017 is prime, 2018 is two times a prime number (2018 2 1009), and p + 2 is three times a prime number (2019-3 673). Call such a year a triple prime year. Find five triple prime years after 2017. (2) Define a and b to be a5666668532329037424074138019351214527900, and b 30650433630342066289005004723923980642610. Let d- ged(a, b). Count how many solutions (x, y) there are to the linear Diophantine equation ax + by d satisfying the condition 0

Explanation / Answer

import itertools

import math

# function to check if the number is prime or not

def is_prime(n):

if n % 2 == 0 and n > 2:

return False

for i in range(3, int(math.sqrt(n)) + 1, 2):

if n % i == 0:

return False

return True

count = 0

# this runs the for loop infinitly until the count condition is complete

for x in itertools.count(2016,1):

if count == 5:

break

else:

a=x+1

# a%2 return the remainder after dividing

if is_prime(x)==True and (a)%2==0 and (a)%3==0:

print(x, " is a triple prime number")

count = count + 1

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