import PrimeNumber, collections
primes = PrimeNumber.get_primes( 100 )
queues = {}
for p in primes:
queues[p] = collections.deque()
queues[p].append( p )
howmany = 1
while True:
howmany += 1
mini = 0
for p in primes:
if len( queues[p] ) == 0: continue
if mini == 0 or queues[p][0] < queues[mini][0]:
mini = p
top = queues[mini][0]
if howmany % 100 == 0:
print howmany, top
queues[mini].popleft()
if top >= 10 ** 9:
break
for p in primes:
if mini <= p and top * p <= 10 ** 9:
queues[p].append( top * p )
print howmany
def get_numways( n ):
primes = PrimeNumber.get_primes( n )[::-1]
cache = {}
ret = solve( 0, n, primes, cache )
return ret
import PrimeNumber limit = 10**6 primes = PrimeNumber.get_primes( limit ) sieves = PrimeNumber.sieve( limit ) best_length = 0 best_prime = 0 for i in xrange( len(primes) ): cand = 0 for j in xrange( i, len(primes) ): cand += primes[j] if cand >= limit: break if sieves[ cand ]: length = j - i + 1 if best_prime == 0 or best_length < length: best_length = length best_prime = cand print best_prime, 'length is', best_length
import PrimeNumber, math bound = 50 * 10 ** 6 print bound primes = PrimeNumber.get_primes( int( math.sqrt(bound) ) ) s = set( [ p**2 + q**3 + r**4 for p in primes for q in primes if p**2+q**3 <= bound for r in primes if p**2+q**3+r**4 <= bound ] ) """ for sq in [ p**2 for p in primes ]: for cb in [ q**3 for q in primes if sq + q**3 <= bound ]: for qd in [ r**4 for r in primes if sq + cb + r**4 <= bound ]: s.add( sq + cb + qd ) """ print len( s )
