##problem2
##since we can buy nuggets in x, x +1, x+5,
##in packs of 6,9,20. Which means that any large enough of ##amounts  of nuggets can be bought with these sizes of ##packs  as long as the first six continuous amount of ##nuggets set are established, as the 7th nugget is just ##6more than the first nugget and the 8th is 6 more than the ##2 nugget of that set
##and so on..... 









##PROBLEM 3




notreachable=[]
counter=0
n=0
for n in range (6,100):
    ans = False
    for s in range (0,n+1):
        for m in range (0,n+1):
            for l in range (0,n+1):
                if (6*s) + (9*m) + (20*l) == n:
                    ans = True
                


    if ans:
        counter +=1
        if counter == 6:
            print ("Largest number of McNuggets that cannot be bought in exact quantity:  ",notreachable[-1])
    else:
        notreachable.append(n)
        counter = 0




##problem 4
package = (13,17,19)
notreachable = 0
counter = 0
n = 0
for n in range (n, 200):
    ans = False
    for s in range (0, n+1):
        for m in range (0, n+1):
            for l in range (0,n+1):
                if ((s*package[0]) + (m*package[1]) + (l*package[2]) == n):
                    ans = True    
                
                    
    


    if ans:
        counter+=1
        if package[0] == counter:
            break;
    else:
        counter = 0
        notreachable = n
print ("Given that sizes %d, %d, and %d, the largest number of McNuggets that cannot be bought in exact quantity is: %d" % (package[0], package[1], package[2], notreachable))

limit = 10000
prime_list = [2]

for n in range (3, limit):
    for m in range(2, n):
        if n%m == 0:
            break
    else:
        prime_list.append(n)



print ("length of list = ",prime_list)
print ("length of list = ", len(prime_list))
print ("thousand'th prime = ", prime_list[999])
print ("last prime = ", prime_list[-1])


##program 2
import math
a = 3
b = 1
c = int (input("Please Enter a Number"))
d = math.log(2)
while a < c:
    v = 3
    while (v < math.sqrt(a) and a%v <= 0):
        v += 2
    if v > math.sqrt(a):
        d +=  math.log(a)
    a += a + 2
print (d)
print (a)
w = d/ a
print (w)

second_name = (input "enter last name:  ")
first_name = (input "enter first name:  ")

print(second_name,first_name)