using Python Problem 2: Large Exponents The built-in next_prime function gives t
ID: 3711527 • Letter: U
Question
using Python
Problem 2: Large Exponents The built-in next_prime function gives the next prime after the input. For example, next prime(9)-11 Part A: Let p be the next prime after 10 and q the next prime after p 2.A.1. What are the last 5 digits of p'? 2.A.2. What is p (mod 10)? 2.A.3. How many decimal digits does have? . 2.A.4. What is logo(p")? Part B: Let z be the next prime after 1000 and y the next prime after . .2.B.1. What are the last 5 digits of r? 2.B.2. How many decimal digits does have? Give an integer m such that the number of decimal digits of is between 10 and 10m(Make sure after we run your codes, the variable m contains your answer for m.) 2.B.3. How does the number of decimal digits of r compare to typical estimates for the number of atoms in the universe? (2.B.3 will not be graded, but you should be aware of the comparison.)Explanation / Answer
Large Exponents python program
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2 A) Program
#package for log10 calculation
import math
#Next prime calculation function
def next_prime(val):
for p in range(val+1, 2*(val+1)):
for i in range(2, p):
if p % i == 0:
break
else:
return p
return None
#main method definition
def main():
#call next_prime function to find next prime number after 10^3
p=next_prime(pow(10,3))
#print p
print('Value of P=',p)
#call next_prime function to find next prime number after p
q=next_prime(p)
#print p
print('Value of q=',q)
#find p^q
val=pow(p,q)
#print last 5 digits of p^q
print('Last 5 digits of p^q=',(val % 100000))
#find p^q mod 10^5
print('p^q%10^5=',val%pow(10,5))
#print decimal digits of p^q
print('Decimal digit of p^q=',len(str(abs(val))))
#find log value of p^q
print('log10 of p^q=',math.log10(val))
#main function
if __name__ == '__main__':
main()
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2B) Program
#package for log10 calculation
import math
#Next prime calculation function
def next_prime(val):
for p in range(val+1, 2*(val+1)):
for i in range(2, p):
if p % i == 0:
break
else:
return p
return None
#main method definition
def main():
#call next_prime function to find next prime number after 10^100
x=next_prime(pow(10,100))
#print x
print('Value of x=',x)
#call next_prime function to find next prime number after x
y=next_prime(x)
#print y
print('Value of y=',y)
#find x^y
val=pow(x,y)
#print last 5 digits of x^y
print('Last 5 digits of p^q=',(val % 100000))
#print decimal digits ofx^y
print('Decimal digit of p^q=',len(str(abs(val))))
#main function
if __name__ == '__main__':
main()
-------------------------------------------------------------------------------------
Note:-
I am using python3.6
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