import brandonsEP
import math
primes = brandonsEP.sieve(10**6)
oneDPrimes = [2,3,5,7]
del primes[:4]
primesofDigit = [[]] * 7
primesofDigit[1] = oneDPrimes
digits = 1
beginIndex = 0
for i in range(len(primes)):
if int(math.log10(primes[i]))>digits:
digits +=1
primesofDigit[digits] = primes[beginIndex:i]
beginIndex = i
primesofDigit[digits+1] = primes[beginIndex:]
reducedPrimes = primes[:]
def valid(num, digits):
rightTrunc = False
leftTrunc = num%(10**digits) in primesofDigit[digits]
if leftTrunc:
rightTrunc = num//10**(int(math.log10(num))-digits+1) in primesofDigit[digits]
return rightTrunc and leftTrunc
winers = []
for x in range(1,6):
reducedPrimes = [p for p in reducedPrimes if valid(p,x)]
import brandonsEP
import itertools
p = brandonsEP.sieve(100)
bsi = brandonsEP.binary_search_index
def pslice(min, max):
return p[bsi(p,min):bsi(p,max)+1]
def addto(n, min = 1):
if n<=0: return not n
total = 0
for part in pslice(min,n):
total += addto(n-part, min=part)
return total
for n in itertools.count(start=11):
if addto(n)>5000:
print n
break
[3373, 3631, 8923, 14083], [2687, 3023, 8069, 14447],
[11527, 12073, 12703, 14737], [4201, 4759, 14797, 16729],
[6323, 6491, 8237, 17333], [659, 947, 5009, 18233],
[5209, 5419, 9241, 18427], [6047, 6203, 7643, 19727],
[373, 661, 1237, 20011], [15359, 15737, 18401, 20333]]
fours.sort(key=sum)
isP = brandonsEP.isPrime
cc = brandonsEP.concatNums
def doubleCC(a, b):
return isP(cc(a, b)) and isP(cc(b, a))
p = brandonsEP.sieve(10**6)
def search(four):
print four
for a in p:
#if all(doubleCC(a,b) for a,b in combinations(four+[num],2)):
# print num, sum(four)+num
for b in four:
if not doubleCC(a, b): break
else:
print a, sum(four) + a
search([5197, 5701, 6733, 8389])
#for x in fours: search(x)
import math, brandonsEP
from collections import defaultdict
import itertools
def nlen(x):
return int(math.log10(x)) + 1
fourDPs = brandonsEP.sieve(10**4)
fourDPs = [x for x in fourDPs if nlen(x) == 4]
print len(fourDPs)
sets = defaultdict(list)
for p in fourDPs:
l = sets[brandonsEP.lsToNum(sorted(brandonsEP.digits(p), reverse=True))]
l.append(p)
#{brandonsEP.lsToNum(sorted(brandonsEP.digits(d), reverse=True)):d for d in fourDPs}
for k, v in sets.items():
if len(v) < 3: del sets[k]
#print sets, len(sets)
def search(Ps):
for num in Ps:
from brandonsEP import sieve
import timeit
timein = timeit.time.time()
LIMIT = 10**6
primes = sieve(LIMIT)
pset = set(primes)
#0.264675140381 seconds
def search1(sliceSize):
#search from 0-s to n-s to n
for i in range(len(primes) - sliceSize + 1):
s = sum(primes[i:i + sliceSize])
if s > primes[-1]: return None
if s in pset: return s
return None
# 0.128955125809 seconds
def search2(sliceSize):
s = sum(primes[:sliceSize])
for i in range(len(primes) - sliceSize + 1):
if s > primes[-1]: return None
if s in pset: return s
s = s - primes[i] + primes[i + sliceSize]
return None