#Week 10 projects:
#Patterns in primes

import matplotlib.pyplot as plt

n = 100
#1)
#a)
def primelist(n):
    prime_list = list(range(2,n+1))
    for i in prime_list:
        j=2
        while i*j <= prime_list[-1]:
            if i*j in prime_list:
                prime_list.remove(i*j)
            j = j+1
    return prime_list

#primes = primelist(N)

#b)
def prime_test(n):
   for i in range(2, n):
      if n % i == 0:
         return False
   return True

#c)
def twinprimes(n):
    twinprimes_list = []
    for i in range(2,n):
        j = i+2
        if(prime_test(i) and prime_test(j)):
            twinprimes_list.append((i,j))
    return twinprimes_list

def twinprimes_sing(n):
    twinprimes_sing_list = []
    for i in range(2,n):
        j = i+2
        if(prime_test(i) and prime_test(j)):
            twinprimes_sing_list.append(j)
    return twinprimes_sing_list

#d)
def sgprimes(n):
    sgprimes_list = []
    for i in range(2,n):
        j = 2*i+1
        if(prime_test(i) and prime_test(j)):
            sgprimes_list.append(i)
    return sgprimes_list

#e)
#Non Logarithmic Plots:
a = 20000
fig1, ax1 = plt.subplots()

x = primelist(a)
y = [i+1 for i in range(len(primelist(a)))]
ax1.plot(x,y, '-b', label = 'Primes')
ax1.legend(loc = 'upper left')

x = twinprimes_sing(a)
y = [i+1 for i in range(len(twinprimes_sing(a)))]
ax1.plot(x,y, '-r', label = 'Twin Primes')
ax1.legend(loc = 'upper left')

x = sgprimes(a)
y = [i+1 for i in range(len(sgprimes(a)))]
ax1.plot(x,y, '-', color = 'orange', label = 'Sophie Germain Primes')
ax1.legend(loc = 'upper left')

plt.xlabel('n')
plt.ylabel('Respective Prime Counts')
plt.title('Prime/Twin Prime/SG Prime Counts')
fig1.show()


#Logarithmic Plots:
fig2, ax2 = plt.subplots()

x = primelist(a)
y = [i+1 for i in range(len(primelist(a)))]
ax2.loglog(x,y, '-b', label = 'Primes')
ax2.legend(loc = 'upper left')

x = twinprimes_sing(a)
y = [i+1 for i in range(len(twinprimes_sing(a)))]
ax2.loglog(x,y, '-r', label = 'Twin Primes')
ax2.legend(loc = 'upper left')

x = sgprimes(a)
y = [i+1 for i in range(len(sgprimes(a)))]
ax2.loglog(x,y, '-', color = 'orange', label = 'Sophie Germain Primes')
ax2.legend(loc = 'upper left')

plt.xlabel('log(n)')
plt.ylabel('Respective Prime Counts')
plt.title('Prime/Twin Prime/SG Prime Counts (Logarithmic)')
fig2.show()


#2
#a)
def sexyprimes(n):
    sexyprimes_list = []
    for i in range(2,n):
        j = i+6
        if(prime_test(i) and prime_test(j)):
            sexyprimes_list.append((i,j))
    return sexyprimes_list

#b)
def tripletprimes(n):
    tripletprimes_list = []
    for i in range(2,n):
        j,k,l = i+2,i+4,i+6
        if(prime_test(i) and prime_test(j) and prime_test(l)):
            tripletprimes_list.append((i,j,l))
        if(prime_test(i) and prime_test(k) and prime_test(l)):
            tripletprimes_list.append((i,k,l))
    return tripletprimes_list

#c)
def tripletprimes_count(n): return len(tripletprimes(n))
def sexyprimes_count(n): return len(sexyprimes(n))
def twinprimes_count(n): return len(twinprimes(n))

def S(n):
    if sexyprimes_count(n) != 0:
        return tripletprimes_count(n)/sexyprimes_count(n)
def T(n):
    if twinprimes_count(n) != 0:
        return tripletprimes_count(n)/twinprimes_count(n)

def S_output(n):
    listy = []
    for i in range(1,n):
        x = S(i)
        if S(i) != S(i-1):
            listy.append(x)
    return listy

def S_list(n):
    listx = []
    for i in range(1,n):
        if S(i) != S(i-1):
            listx.append(i)
    return listx

def T_output(n):
    listy = []
    for i in range(1,n):
        x = T(i)
        if T(i) != T(i-1):
            listy.append(x)
    return listy

def T_list(n):
    listx = []
    for i in range(1,n):
        if T(i) != T(i-1):
            listx.append(i)
    return listx
'''
fig3, ax3 = plt.subplots()
fig4, ax4 = plt.subplots()

S_T_value

x_2 = T_list(200)
y_2 = T_output(200)
plot_c = ax3.plot(x_2,y_2,label = 'T(n) against n.')

x_1 = S_list(500)
y_1 = S_output(500)
plot_d = ax4.plot(x_1,y_1,label = 'S(n) against n.')

fig3.show()
fig4.show()
'''