def testWithinGroup(n, p, prime_sieve, certain = False):
if n < 2: return n
# Always do at least one test
num_tests = 1
# Only test further if the first test comes up positive. This gives the
# probability of needing to do further tests
master_mult = (1-(1-p)**n)
master_mult = (1-(1-p)**n)
if certain:
num_tests = 0
master_mult = 1
# If the number of sheep is prime, we just have to check a single group
if prime_sieve.isPrime(n):
# If positive, we test all but one sheep in group
num_tests += master_mult*(n-1)
# Finally, if at least one of the (n-1) tests is positive, test the
# final sheep
num_tests += master_mult*(1-(1-p)**(n-1))
else:
# If we have a non-prime number of sheep, we make smaller groups
num_grps = primes_pp.getPrimeFactors(n, prime_sieve)[0]
num_per_grp = n/num_grps
twg = testWithinGroup(num_per_grp, p, prime_sieve)
twg_certain = testWithinGroup(num_per_grp, p, prime_sieve, True)
# First, fully test all but one group
num_tests += master_mult * ((num_grps-1) * twg)
# If any of those groups is positive, test final group
mult = master_mult * (1 - (1-p)**((num_grps-1)*num_per_grp))
num_tests += mult * twg
# If none of the groups were positive, we know the final group has an
# infected sheep
mult = master_mult * (1-p)**((num_grps-1)*num_per_grp)
num_tests += mult * twg_certain
return num_tests
def findConsecutiveIntegers(num_integers, num_primes, terminal = None):
# - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
# if terminal == None: terminal = int(1e7)
if terminal == None: terminal = int(10**(2+num_primes))
print 'Generating primes from 2-%d' % terminal
prime_seive = primes_pp.primeSeive(terminal)
consecutive_integers = []
print 'Primes successfully generated'
for cand in xrange(terminal):
prime_factors = set(primes_pp.getPrimeFactors(cand, prime_seive))
if len(prime_factors) == num_primes:
consecutive_integers.append(cand)
else:
del consecutive_integers[:]
if len(consecutive_integers) == num_integers:
break
return consecutive_integers
