def main(limit):
rv = 0
for p in Primes(limit).gen():
if p > limit:
break
if not isFactor(p):
rv += p
return rv
def main(limit):
primes = Primes(limit)
def circular(p):
d = digits(p)
return all(
primes.isPrime(num(d[i:] + d[:i])) for i in range(1, len(d)))
return sum(map(circular, takewhile(lambda n: n < limit, primes.gen())))
def main(limit=28123):
primes = Primes(limit)
abundant = [n for n in range(limit + 1) if n < primes.sumDivisors(n)]
abundantSet = set(abundant)
def can(n):
for a in abundant:
if 2 * a > n:
break
if n - a in abundantSet:
return True
return False
return sum(n for n in range(limit + 1) if not can(n))
def main(N, solns):
primes = Primes(N)
rv = 0
for n in range(N):
count = 0
for A in primes.divisors(n):
if A * A < 3 * n and (A + n // A) % 4 == 0:
count += 1
if count > solns:
break
if count == solns:
rv += 1
return rv
from lib import Primes primes = Primes() def main(limit): mem = [False] * limit for pa in primes.gen(): sq = pa * pa if sq > limit: break for pb in primes.gen(): cu = pb * pb * pb if sq + cu > limit: break for pc in primes.gen(): fo = pc * pc * pc * pc tot = sq + cu + fo if tot > limit: break mem[tot] = True return sum(mem) if __name__ == '__main__': print(main(50000000)) # 1097343
from lib import Primes
import heapq
primeGen = Primes()
def main(e, m):
factors = list(map(primeGen.get, range(e)))
heapq.heapify(factors)
n = 1
for _ in range(e):
factor = factors[0]
n = n * factor % m
heapq.heappushpop(factors, factor ** 2)
return n
if __name__ == '__main__':
print(main(500500, 500500507)) # 35407281
from lib import numLen, Primes
from collections import defaultdict
prime = Primes()
class chainLenObj():
def __init__(self, limit):
self.limit = limit
self.mem = [None] * limit
self.mem[1] = 1
def get(self, n):
if self.mem[n] == None:
self.mem[n] = 1 + self.get(prime.phi(n))
return self.mem[n]
def gen(self, length):
for p in prime.gen():
if p >= self.limit:
break
print(p)
if self.get(p) == length:
yield p
def main(limit, length):
clo = chainLenObj(limit)
return sum(clo.gen(length))
