import addmath
totient_memo = {}
print("Calculating primes...", end='')
primes = addmath.primes_under(1000000)
print("done.")
for prime in primes:
totient_memo[prime] = prime - 1
def totient(n):
if n in totient_memo:
return totient_memo[n]
i = 0
prime = primes[i]
acc = n
while prime * prime <= n:
prime = primes[i]
if n % prime == 0:
totient_memo[n] = totient(prime) * totient(n // prime)
return totient_memo[n]
i += 1
if (n > 1):
acc = acc * (1 - (1 / (n)))
totient_memo[n] = int(acc)
primes.append(n)
return int(acc)
def is_permutation(n, k):
ind = encountered.index(k)
encountered = encountered[ind:]
for item in encountered:
chain_memo[item] = len(encountered)
return 0
encountered.append(k)
length += 1
k = next(k)
encountered.append(n)
for enc in encountered:
chain_memo[enc] = length
return length
limit = 1000000
primes = addmath.primes_under(limit)
loadMemo()
chain(14316)
print("Done.")
chain(next(14316))
#
# bestVal = 220
# bestLen = 2
# for i in range(1, limit):
# k = chain(i)
# print(i, bestVal, bestLen)
# if k > bestLen:
# bestVal = i
# bestLen = k
import addmath
LIMIT = 1000000
primes = addmath.primes_under(LIMIT)
def sopf(n):
i = 0
tot = 0
prime = primes[i]
while prime <= n:
if n % prime == 0:
tot += prime
i += 1
prime = primes[i]
return tot
kappa_memo = {}
def kappa(n):
if n == 0:
return 0
if n in kappa_memo:
return kappa_memo[n]
acc = sopf(n)
for j in range(1, n):
acc += sopf(j) * kappa(n - j)
acc = acc // n
kappa_memo[n] = acc
import addmath
def quadratic(a, b, n):
return (n**2) + (a * n) + b
primes = addmath.primes_under(87400)
def isPrime(n):
i = 0
while (primes[i] <= n):
if (primes[i] == n):
return True
i += 1
return False
print("produced primes")
aMax = bMax = nMax = 0
for a in range(-1000, 0):
for b in range(-1000, 1000):
n = 0
while (isPrime(abs(quadratic(a, b, n)))):
n += 1
if (n > nMax):
print("n2+" + str(a) + "n+" + str(b))
nMax = n
bMax = b
aMax = a
import addmath
primes=set(addmath.primes_under(9999))
def is_permutation(n1, n2):
n1=str(n1)
n2=str(n2)
if(len(n1)!=len(n2)):
return False
for c in n1:
if c not in n2:
return False
return True
def sequence(n):
cursor=n
for increment in range(3330, 3331):
if(cursor+increment in primes and cursor+(2*increment) in primes):
if(is_permutation(cursor, cursor+increment) and is_permutation(cursor, cursor+(2*increment))):
return (cursor, cursor+increment, cursor+2*increment)
return False
def concat(n):
return str(n[0])+str(n[1])+str(n[2])
for prime in primes:
if(sequence(prime)!=False):
print(concat(sequence(prime)))
import addmath
import numpy
primes = set(addmath.primes_under(2000000))
def truncatable(number):
number = str(number)
for i in range(len(number)):
j = len(number) - i
if (number[i:] == '' or number[:j] == ''):
break
if (not (int(number[i:]) in primes and int(number[:j]) in primes)):
return False
return True
trunc = []
sumall = 0
for i in primes:
if (len(str(i)) == 1):
continue
if (truncatable(i)):
trunc.append(i)
print(trunc)
for element in trunc:
for digit in range(1, 10):
new = str(element) + str(digit)
if (truncatable(int(new)) and int(new) not in trunc):
import addmath
upperbound = int(input("Upperbound: "))
print(sum(addmath.primes_under(upperbound)))
import sys
sys.path.append('../libraries')
import addmath
def pandigital(number, n):
number_set = addmath.get_digits(number)
if (len(number_set) != len(str(number)) or 0 in number_set):
return False
for i in range(1, n):
if i not in number_set:
return False
return True
primes = addmath.primes_under(7654321)
for i in range(len(primes) - 1, -1, -1):
if (pandigital(primes[i], 7)):
print(primes[i])
break