SharedExploration 2 / 2018-03-06-132538.sagewsOpen in CoCalc
#Problem 1
def OneN(n):
n = input('N is')
if mod(n,4) == 1:
print 'This number is 1 modulo 4'
else:
print 'This number is not 1 modulo 4'

OneN(n)


N is
This number is not 1 modulo 4
#Problem 2
def PrimeOneN(n):
list = []
n = input('N is')
while n not in list:
for i in range (1,n):
if is_prime(i) == True and mod(i,4) == 1:
list.append(n)
length = len(list)
return length

PrimeOneN(n)


N is
6
#Problem 3
from sage.plot.line import Line
prime1 = []
prime3 = []
lengthprime1 = []
lengthprime3 = []
array = []
n = 0
i = 2
while n<50000:
while i <= n:
if is_prime(i) == True and i%4==3:
prime3.append(i)
if is_prime(i) == True and i%4==1:
prime1.append(i)
i += 1
lengthprime3.append(len(prime3))
lengthprime1.append(len(prime1))
array.append(n)
n+=1

array1 = zip(array, lengthprime1)
array3 = zip(array, lengthprime3)
#print array1
#print array3

line(array1, rgbcolor='red')+line(array3)


#Problem 5
from sage.plot.line import Line
prime51 = []
prime52 = []
prime53 = []
prime54 = []
prime50 = []
lengthprime51 = []
lengthprime52 = []
lengthprime53 = []
lengthprime54 = []
lengthprime50 = []
array = []
n = 0
i = 2
while n<1000:
while i <= n:
if is_prime(i) == True and i%5==1:
prime51.append(i)
if is_prime(i) == True and i%5==2:
prime52.append(i)
if is_prime(i) == True and i%5==3:
prime53.append(i)
if is_prime(i) == True and i%5==4:
prime54.append(i)
if is_prime(i) == True and i%5==0:
prime50.append(i)
i += 1
lengthprime51.append(len(prime51))
lengthprime52.append(len(prime52))
lengthprime53.append(len(prime53))
lengthprime54.append(len(prime54))
lengthprime50.append(len(prime50))
array.append(n)
n+=1

array51 = zip(array, lengthprime51)
array52 = zip(array, lengthprime52)
array53 = zip(array, lengthprime53)
array54 = zip(array, lengthprime54)
array50 = zip(array, lengthprime50)
#print array1
#print array3

line(array51, rgbcolor='red')+line(array52, rgbcolor='blue')+line(array53, rgbcolor='green')+line(array54, rgbcolor='orange')+line(array50, rgbcolor='yellow')