tkmharris

tkmharris

{--
We provide a function 'nextPrimeBias' that when called as
  nextPrimeBias a b n r
returns the probability that, among the first r primes, a prime that is equivalent to a mod n is followed by a prime that is equivalent to b mod n.

We see that these probabilities are not evenly distributed among equivalence classes, as described in https://arxiv.org/abs/1603.03720 :
nextPrimeBias 7 1 10 100000 = 0.25736558
nextPrimeBias 7 3 10 100000 = 0.27695382
nextPrimeBias 7 7 10 100000 = 0.144993
nextPrimeBias 7 9 10 100000 = 0.3206876

tkmharris

## Mordell's equation

'''
Get integer solutions of the Mordell equation
y^2 = x^3 - d
for certain special values of d.
See mordell.txt for details.
'''

def mordell_test(d, x,y):

tkmharris

def hurwitz_radon(n):
    '''Takes a positve integer n; returns the Hurwitz-Radon number p(n).
    p(n) defined as follows:
    Let n = (2^v)m with m odd and write v = 4a + b, 0<= b < 4.
    Then p(n) = 8a + 2^b.'''
    if not isinstance(n, int):
        raise TypeError("hurwitz_radon only defined for positive integers")
    if n <= 0:
        raise ValueError("hurwitz_radon only defined for positive integers")
    # helper to get largest power of 2 divinding n