Answer:
In Python:
low = int(input("Low: "))
high = int(input("High: "))
if low >= 1000000000 or high >=1000000000:
print("Out of range")
else:
mylist = []
for num in range(low,high+1):
flag = False
if num > 1:
for i in range(2, num):
if (num % i) == 0:
flag = True
break
if not flag:
mylist.append(num)
print(num, end = " ")
print()
print("The twin primes are: ",end="")
count = 0
for i in range(1,len(mylist)):
if mylist[i] - mylist[i-1] == 2:
print(str(mylist[i])+" & "+str(mylist[i-1]),end=", ")
count+=1
print()
print("There are "+str(count)+" twin primes")
Explanation:
See attachment for complete program where comments were used to explain each line
Answer:
A collating machine is used to gather or arrange in their proper sequence.
Explanation:
Let P(n) be "a postage of n cents can be formed using 5-cent and 17-cent stamps if n is greater than 63".Basis step: P(64) is true since 64 cents postage can be formed with one 5-cent and one 17-cent stamp.Inductive step: Assume that P(n) is true, that is, postage of n cents can be formed using 5-cent and 17-cent stamps. We will show how to form postage of n + 1 cents. By the inductive hypothesis postage of n cents can be formed using 5-cent and 17-cent stamps. If this included a 17-cent stamp, replace this 17-cent stamp with two 5-cent stamps to obtain n + 1 cents postage. Otherwise, only 5-cent stamps were used and n 65. Hence there are at least three 5-cent stamps forming n cents. Remove three of these 5-cent stamps and replace them with two 17-cent stamps to obtain n + 1 cents postage.Hence P(n + 1) is true.
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