def m_search(n,k,m=1,phi=1,lowerInd=0):
global primes,mask,pcap
s = 0
if k == 0:
M = m*phi-phi+m
bnd = int(M**.25)
pi = bisect_right(primes,n/m)
if n/m > pcap:
f = shanks_factorize(M,primes[:15])
for d in divisors([[bas,f[bas]] for bas in f]):
q,r = divmod(d-phi,m-phi)
if r == 0 and q > primes[lowerInd] and q*m <= n and is_prime(q,pcap-1,mask):
if (q*m-1) % (q*m - (q-1)*phi) == 0:
s += q*m
else:
for q in primes[lowerInd+1:pi+1]:
if q*m <= n and (q*m-1) % (q*m - (q-1)*phi) == 0:
s+= q*m
# print q*m,q,m
return s
bound = int((n/m)**(1./(k+1)))
i=lowerInd+1
for i,p in enumerate(primes[lowerInd+1:],lowerInd+1):
if p > bound:
break
else:
s += m_search(n,k-1,m*p,phi*(p-1),i)
return s
def find_pairs(n):
global primes,mask
s = 0
pairs = {}
for p in primes[1:]:
num = p**2-p+1
f = shanks_factorize(num,primes[:15])
for k in divisors([[bas,f[bas]] for bas in f] ):
q = num/k - p + 1
if q > 0 and q > p and q*p <= n and is_prime(q,pcap-1,mask):
s += p*q
# print p,q
if p not in pairs:
pairs[p] = [q]
else:
pairs[p].append(q)
print "Sum over semi-primes %d" % s
#now do backtracking pair-combos
for p1 in pairs:
for p2 in pairs[p1]:
s += cores_backtrack(n/p1/p2,pairs,[p1,p2])
return s
def p_sum(d):
s = 0
for i in xrange(3):
s += pe.is_prime(d[i],cap,mask)
return s
pcap = 2*10**5
n = 10**9
mask = pe.mark_primes(pcap)
cache = []
pDivs = {}
i = 1
e1 = 0
while i < cap:
j = 1
e2 = 0
cache.append([])
while j*i < cap:
t = j*i
cache[e1].append(t)
for k in xrange(t,cap,t):
if pe.is_prime(k+1,pcap,mask):
if k+1 not in pDivs:
pDivs[k+1] = [t]
else:
pDivs[k+1].append(t)
j *= 5
e2 += 1
i *= 2
e1 += 1
s = 0
num_found = 0
m = 40
