from utils import primes_below
from fractions import gcd
TOP = 100
primes = primes_below(TOP)
candidates = map(lambda x: x + 1, primes)
candidate_set = set(candidates)
values = []
TESTS = [(2, 5, 11), (2, 11, 47), (5, 11, 23), (5, 17, 53), (7, 11, 17),
(7, 23, 71), (11, 23, 47), (17, 23, 31), (17, 41, 97), (31, 47, 71),
(71, 83, 97)]
for (i, a) in enumerate(candidates):
print(a)
for b in candidates[(i + 1):]:
if ((b * b) % a) != 0:
continue
candidate = (b * b) // a
if candidate >= TOP:
break
if candidate in candidate_set:
values.append((a - 1, b - 1, candidate - 1))
print(sum(map(sum, values)))
from utils import primes_below
from memoizers import key_memoized
TOP = 1000000000
primes = primes_below(100)
@key_memoized
def count_multiplicities(prime_index, top):
global primes
if prime_index >= len(primes):
return 0
p = primes[prime_index]
if p > top:
return 0
v1 = count_multiplicities(prime_index + 1, top)
v2 = count_multiplicities(prime_index, top // p)
return 1 + v1 + v2
print(count_multiplicities(0, TOP)) + 1
from fractions import Fraction
from utils import primes_below
# index: (position, jumps_remaining) => probability of completing the sequence
FIELD = 500
STEPS = 15
primes = set(primes_below(FIELD + 1))
sequence = 'PPPPNNPPPNPPNPN'
def to_letter(n):
return 'P' if n in primes else 'N'
probability_matrix = [[0 for x in range(FIELD + 1)] for y in range(STEPS)]
probability_matrix[0] = [Fraction(1, FIELD)] * (FIELD + 1)
probability_matrix[0][0] = 0
for jump in range(1, STEPS):
probability_matrix[jump][2] = probability_matrix[jump - 1][1]
probability_matrix[jump][FIELD - 1] = probability_matrix[jump - 1][FIELD]
for j in range(2, 500):
probability_matrix[jump][j - 1] += Fraction(
1, 2) * (probability_matrix[jump - 1][j])
probability_matrix[jump][j + 1] += Fraction(
1, 2) * (probability_matrix[jump - 1][j])
hit_all_ps = 1
to_turn_off = len(prev_str) - len(p_str)
m = sum([len(segs[int(i)]) for i in prev_str[:to_turn_off]])
for d in range(len(p_str)):
d_prev = int(prev_str[d + to_turn_off])
d_p = int(p_str[d])
m += transitions[d_prev][d_p]
if (p >= 10):
root = sum(map(int, p_str))
next_m, next_s = clock_counts(root, prev=p)
m, s = m + next_m, s + next_s
else:
m += sum([len(segs[int(i)]) for i in str(p)])
return m, s
for p in primes_below(2 * (10**7)):
if p < 10**7:
continue
m, s = clock_counts(p)
max_count += m
sam_count += s
print(sam_count - max_count)
#!/usr/bin/env python3
from utils import primes_below
TOP = 100000000
total = 0
primes = primes_below(TOP * 1.6)
prime_set = set(primes)
vals = [True] * (TOP + 1)
for p in primes:
if 2 * p > TOP:
break
print(p)
vals[p] = False
for i in range(2, (TOP // p) + 1):
if i + p not in prime_set:
vals[i * p] = False
v = set([i for i in range(1, TOP + 1) if vals[i]])
v2 = set(map(lambda x: x - 1, prime_set))
print(sum(v & v2))