def test_search():
assert 2 in sieve
assert 2.1 not in sieve
assert 1 not in sieve
assert 2**1000 not in sieve
raises(ValueError, lambda: sieve.search(1))
def next_prime(value):
"""Returns the nearest prime at or after value, calculated using the sieve of Erastosthenes."""
return sieve[sieve.search(value)[1]]
from modular_multiplicative_inverse import inverse from sympy import sieve I = inverse() I.inv(3, 4) N = 2028455971 s = 702505371 t = 188270011 print I.gcd(s, N) print I.gcd(t, N) a = I.gcd(s + t, N) b = I.gcd(s - t, N) N / I.gcd(s - t, N) 44027 * 46073 sieve.search(a) sieve.search(b)
def test_search():
assert 2 in sieve
assert 2.1 not in sieve
assert 1 not in sieve
assert 2**1000 not in sieve
raises(ValueError, lambda: sieve.search(1))
print(sieve[10]) # returns n th prime
sieve.extend_to_no(15) # extends upto n th prime
# mobiusrange(a,b) genarates Mobius numbers for the range [a,b), means output will be a list.
Mob_func = sieve.mobiusrange(7, 12)
print('\n Mobius function outputs in the given range:', [i for i in Mob_func])
# primerange(a,b) generates all prime numbers in the range [a,b)
Prime_list = sieve.primerange(1, 5)
print('\n Primes in the given range are :', [i for i in Prime_list])
#search(n) return the indices i, j of the primes that bound n. If n is prime then i == j. Although n can be an expression,
# if ceiling cannot convert it to an integer then an error will be raised.
x, y = sieve.search(25)
print('\n The given input is in between ', '(', x, ',', y, ')', 'th Primes \n')
#totientrange(a, b) generates all totient numbers for the range [a, b). Simply it is a list of outputs
Totient_range = sieve.totientrange(1, 10)
print(' Values of Totient(n):', [i for i in Totient_range])
#sympy.ntheory.generate.prime(nth) return the n th prime number. Logarithmic integral of x is a pretty nice approximation
# for number of primes <= x, i.e. li(x) ~ pi(x)
print('\n', 'See this! The 1000000th prime: ', generate.prime(1000000))
#sympy.ntheory.generate.primepi(n) returns the value of the prime counting function pi(n) = the number of prime numbers
# less than or equal to n.
print('\n', 'There are ', generate.primepi(40),
' primes < or = the given input')
