Example #1
0
        mp.append(sum(arr))
    # print(mp)
    for i in range(len(mp)):
        # print(i, mp[i - 1], mp[i])
        for j in range(mp[i - 1], mp[i]):
            out[j] = i
    # out[mp[len(mp) - 1]] = len(mp) - 1
    return tuple([0] + out)


pm = {2: p_to_m(2), 3: p_to_m(3), 5: p_to_m(5), 7: p_to_m(7)}
for x in pm:
    print(x, pm[x], len(pm[x]))

M = 10**8
pp = mylib.primes_from_file(M)

f_cashed = dict()


def get_f(dd):
    if dd in f_cashed:
        return f_cashed[dd]
    # print(' ', dd)
    d = dd[0]
    p = len(dd)
    if d in pm:
        p = pm[d][p]
    f_cashed[dd] = d * p
    return f_cashed[dd]
Example #2
0
If N is admissible, the smallest integer M > 1 such that N+M is prime, will be called the pseudo-Fortunate number for N.

For example, N=630 is admissible since it is even and its distinct prime factors are the consecutive primes 2,3,5 and 7.
The next prime number after 631 is 641; hence, the pseudo-Fortunate number for 630 is M=11.
It can also be seen that the pseudo-Fortunate number for 16 is 3.

Find the sum of all distinct pseudo-Fortunate numbers for admissible numbers N less than 10**9.
"""

import math
import mylib

top = 10 ** 9

pp_100 = sorted(mylib.primes_from_file(100))
bb = []
m = 1
for x in pp_100:
    m *= x
    if m >= top:
        m //= x
        break
    bb.append(x)
print(bb, m)

rrr = [[1]]
for b in bb:
    mm = sorted(rrr[len(rrr) - 1])
    p = math.floor(math.log(top, b))
    nn = [b ** (x + 1) for x in range(p)]
Example #3
0
import mylib
import math

L = 20
r = math.floor(L ** 0.5)
pp = sorted(x for x in mylib.primes_from_file(r) if x <= r)
print(pp)
for m in pp:
    print(m)
Example #4
0
import mylib, math

pp = sorted(mylib.primes_from_file(10 ** 6 + 1))

ends = dict((x, [x * y % 10 for y in range(10)]) for x in [1, 3, 7, 9])
# print(ends)

ends_map = dict()
for p in ends:
    ends_map[p] = [0 for x in range(10)]
    for i in range(len(ends[p])):
        ends_map[p][ends[p][i]] = i
print(ends_map)


def divide(x, y):
    x_str = str(x)
    z = x * 1
    pwr = len(x_str)

    d = 0
    e = y % 10
    print('*' + str(x), '/', y, end=' ')
    for c in range(pwr):
        n = z % 10
        m = ends_map[e][n]
        d += m * 10 ** c
        z = (z - m * y) // 10
        print(' > ', n, m, m * y, end=' ')
    print(' : ', d * y, '/', y, '=', d)
    return d * y
Example #5
0
        mp.append(sum(arr))
    # print(mp)
    for i in range(len(mp)):
        # print(i, mp[i - 1], mp[i])
        for j in range(mp[i - 1], mp[i]):
            out[j] = i
    # out[mp[len(mp) - 1]] = len(mp) - 1
    return tuple([0] + out)


pm = {2: p_to_m(2), 3: p_to_m(3), 5: p_to_m(5), 7: p_to_m(7)}
for x in pm:
    print(x, pm[x], len(pm[x]))

M = 10 ** 8
pp = mylib.primes_from_file(M)

f_cashed = dict()


def get_f(dd):
    if dd in f_cashed:
        return f_cashed[dd]
    # print(' ', dd)
    d = dd[0]
    p = len(dd)
    if d in pm:
        p = pm[d][p]
    f_cashed[dd] = d * p
    return f_cashed[dd]
Example #6
0
import mylib, math

m = 500500507
t = 500500
pp = sorted(mylib.primes_from_file(10**7))[:t]
p_max = max(pp)
p_max_r = math.ceil(p_max**0.5)
print(len(pp), p_max, p_max_r, p_max_r**2)
rr = pp[:t]
qq = [q for q in pp if q <= p_max_r]
print(qq)

for q in qq:
    x = q**2
    while x < p_max:
        print(q, x)
        rr.append(x)
        x = x**2

rr = sorted(rr)[:t]
print(max(rr))
s = 1
for i in range(len(rr)):
    r = rr[i]
    if not i % 10:
        print(i, r)
    s = (s * r) % m
print(s)
Example #7
0
 def init_primes(p):
     mylib.known_primes = mylib.primes_from_file(10 ** math.ceil(p / 2))
     print('primes:', '... ' + ', '.join([str(x) for x in (sorted(mylib.known_primes)[-10:])]))
Example #8
0
import mylib

e = 4
ppp = mylib.primes_from_file(10 ** (2 * e))
pp = sorted(p for p in ppp if p < 10 ** e)
ss = [{}]

max_len = 0
for p in pp:
    if p == 2:
        continue
    ss_add = []
    for s in ss:
        if not len(s):
            ss_add.append({p})
            continue
        all_primes = True
        for q in s:
            pq = [str(p), str(q)]
            if int("".join(pq)) not in ppp or int("".join(pq[::-1])) not in ppp:
                all_primes = False
                break
        if all_primes:
            s_new = s | {p}
            if len(s_new) >= max_len:
                max_len = len(s_new)
                print(s_new)
            ss_add.append(s_new)
    ss += ss_add
print([(s, sum(s)) for s in ss if len(s) >= max_len])
Example #9
0
import mylib, math

m = 500500507
t = 500500
pp = sorted(mylib.primes_from_file(10 ** 7))[:t]
p_max = max(pp)
p_max_r = math.ceil(p_max ** 0.5)
print(len(pp), p_max, p_max_r, p_max_r ** 2)
rr = pp[:t]
qq = [q for q in pp if q <= p_max_r]
print(qq)

for q in qq:
    x = q ** 2
    while x < p_max:
        print(q, x)
        rr.append(x)
        x = x ** 2

rr = sorted(rr)[:t]
print(max(rr))
s = 1
for i in range(len(rr)):
    r = rr[i]
    if not i % 10:
        print(i, r)
    s = (s * r) % m
print(s)
Example #10
0
"""
It is possible to write ten as the sum of primes in exactly five different ways:

7 + 3
5 + 5
5 + 3 + 2
3 + 3 + 2 + 2
2 + 2 + 2 + 2 + 2

What is the first value which can be written as the sum of primes in over five thousand different ways?
"""
import mylib

pp = sorted(mylib.primes_from_file(100))


def find_ways(number, max_a=0):
    ways = []
    for a in pp:
        if a > number:
            break
        if max_a and a > max_a:
            break
        if number == a:
            ways.append([a])
            continue
        append_ways = find_ways(number - a, a)
        for w in append_ways:
            ways.append([a] + w)

    return ways
Example #11
0
 def init_primes(p):
     mylib.known_primes = mylib.primes_from_file(10**math.ceil(p / 2))
     print(
         'primes:', '... ' +
         ', '.join([str(x) for x in (sorted(mylib.known_primes)[-10:])]))
Example #12
0
import mylib
import math

L = 20
r = math.floor(L**0.5)
pp = sorted(x for x in mylib.primes_from_file(r) if x <= r)
print(pp)
for m in pp:
    print(m)
Example #13
0
import mylib

e = 4
ppp = mylib.primes_from_file(10**(2 * e))
pp = sorted(p for p in ppp if p < 10**e)
ss = [{}]

max_len = 0
for p in pp:
    if p == 2:
        continue
    ss_add = []
    for s in ss:
        if not len(s):
            ss_add.append({p})
            continue
        all_primes = True
        for q in s:
            pq = [str(p), str(q)]
            if int(''.join(pq)) not in ppp or int(''.join(
                    pq[::-1])) not in ppp:
                all_primes = False
                break
        if all_primes:
            s_new = s | {p}
            if len(s_new) >= max_len:
                max_len = len(s_new)
                print(s_new)
            ss_add.append(s_new)
    ss += ss_add
print([(s, sum(s)) for s in ss if len(s) >= max_len])
Example #14
0
import mylib, math

pp = sorted(mylib.primes_from_file(10**6 + 1))

ends = dict((x, [x * y % 10 for y in range(10)]) for x in [1, 3, 7, 9])
# print(ends)

ends_map = dict()
for p in ends:
    ends_map[p] = [0 for x in range(10)]
    for i in range(len(ends[p])):
        ends_map[p][ends[p][i]] = i
print(ends_map)


def divide(x, y):
    x_str = str(x)
    z = x * 1
    pwr = len(x_str)

    d = 0
    e = y % 10
    print('*' + str(x), '/', y, end=' ')
    for c in range(pwr):
        n = z % 10
        m = ends_map[e][n]
        d += m * 10**c
        z = (z - m * y) // 10
        print(' > ', n, m, m * y, end=' ')
    print(' : ', d * y, '/', y, '=', d)
    return d * y