Nicholas123

###PS2a###

n = 1					#The desired total number of nuggets, starting with 1
maxTest = 20		#the largest polynomial coefficient to test
cantObtain = 0  	#last found number can't be obtained by combo of 6, 9, 20
consecutive = 0 	#number of consecutive combinations found
found = False		#have we found a valid combination?

while consecutive < 6:
	found = False
	#these for loops try every combination of coefficients up to maxTest
	for a in range(maxTest):
		for b in range(maxTest):
			for c in range(maxTest):
				#print 'a:{0:2d} b:{1:2d} c:{2:2d} -> {3:4d}'.format(a, b, c, 6*a+9*b+20*c)
				if 6*a+9*b+20*c == n:
					print 'Found a combination for', n
					found = True					
	if found == False:
		cantObtain = n
		consecutive = 0
	elif found == True:
		consecutive += 1
	n += 1
	
print 'The last unobtainable number was', cantObtain



###PS2b###

n = 1					#The desired total number of nuggets, starting with 1
maxTest = 40		#the largest polynomial coefficient to test
cantObtain = 0  	#last found number can't be obtained by combo of tuple box
consecutive = 0 	#number of consecutive combinations found
found = False		#have we found a valid combination?

#box = (1, 2, 3)
#box = (6, 9, 20)
#box = (3, 10, 12)
#box = (4, 6, 9)
#box = (2, 4, 6)
box = (7, 9, 11)

while consecutive < 6:
	found = False
	#these for loops try every combination of coefficients up to maxTest
	for a in range(maxTest):
		for b in range(maxTest):
			for c in range(maxTest):
				#print 'a:{0:2d} b:{1:2d} c:{2:2d} -> {3:4d}'.format(a, b, c, 6*a+9*b+20*c)
				if box[0]*a+box[1]*b+box[2]*c == n:
					print 'Found a combination for', n
					found = True					
	if found == False:
		cantObtain = n
		consecutive = 0
	elif found == True:
		consecutive += 1
		if n >= 200: 
			print 'Limit exceeded, probably no answer'
			break
	n += 1

print "Given package sizes " + str(box[0]) + ", " + str(box[1]) + " and " + str(box[2]) + " the largest number of McNuggets that cannot be bought in exact quantity is: " + str(cantObtain)

###PS1a###

#print 2, because it is exceptional in being the only even (non-odd) prime
print '{0:4d} {1:4d}'.format(1, 2)

numPrimesCalcd = 1 		#because we already printed '2'
candidate = 3				#the first number to test
divTest = 3					#the minimum number a given prime might divide by					

while numPrimesCalcd < 1000 :
	while divTest <= candidate :
		if divTest == candidate :
			# It's a prime, because it hasn't divided by anything until it divided by itself
			numPrimesCalcd += 1
			print '{0:4d} {1:4d}'.format(numPrimesCalcd, candidate)
			divTest = 3		#reset divTest to lowest possible divisor
			candidate += 2 #skip even numbers
		elif candidate%divTest == 0 :
		 	# Not a prime, because it divides by a number other than itself
			divTest = 3 	#reset divTest to lowest possible divisor
			candidate += 2 #skip even numbers
			break 			#break out of the while loop, start testing a new candidate
		else :
			# Haven't proved or disproved, test with the next odd number
			divTest += 2




###PS1b###

from math import *

numPrimesCalcd = 1 		#because we include '2' manually
candidate = 3				#the first number to test
divTest = 3					#the minimum number a given prime might divide by					
sumOfPrimesLog = log(2)	#b/c we already counted 2 manually		

while numPrimesCalcd < 1000 :
	while divTest <= candidate :
		if divTest == candidate :
			# It's a prime, because it hasn't divided by anything until it divided by itself
			numPrimesCalcd += 1
			print sumOfPrimesLog/candidate
			sumOfPrimesLog += log(candidate)
			divTest = 3
			candidate += 2 #skip even numbers
		elif candidate%divTest == 0 :
		 	# Not a prime, because it divides by a number other than itself
			divTest = 3 	#reset divTest to lowest possible divisor
			candidate += 2 #skip even numbers
			break 			#break out of the while loop, start testing a new candidate
		else :
			divTest += 2

last = raw_input('Enter your last name: ')
first = raw_input('Enter your first name: ')
print first + ' ' + last