data = []
P = Primes()
n = P.unrank(2000)
def nextprime(n, P):
for i in range(20):
n = P.next(n + 1)
return n
for i in range(100):
n = nextprime(n, P)
timestart = time.time()
result = check_prime_aks(n)
timeend = time.time()
t = timeend - timestart
x = float(log(n))
y = float(log(t))
print result, x, y
data.append((x, y))
_ = var('k, b, x')
model(x) = k * x + b
sol = find_fit(data, model)
f(x) = model(b=sol[0].rhs(), k=sol[1].rhs())
a = plot([])
a += plot(f(x), x, data[0][0], data[-1][0])
a += points(data, color='darkgreen', pointsize=50, aspect_ratio=1)
show(a)
sqrt(17579)
17579^(1/3)
17579^(1/4)
17579^(1/5)
17579^(1/6)
17579^(1/7)
17579^(1/8)
17579^(1/9)
17579^(1/10)
17579^(1/11)
17579^(1/12)
17579^(1/13)
17579^(1/14)
True 9.7744602868 -0.46220369887
sqrt(17789)
17789^(1/3)
17789^(1/4)
17789^(1/5)
17789^(1/6)
17789^(1/7)
17789^(1/8)
17789^(1/9)
17789^(1/10)
17789^(1/11)
17789^(1/12)
17789^(1/13)
17789^(1/14)
True 9.78633556773 -0.225245690501
sqrt(17977)
17977^(1/3)
17977^(1/4)
17977^(1/5)
17977^(1/6)
17977^(1/7)
17977^(1/8)
17977^(1/9)
17977^(1/10)
17977^(1/11)
17977^(1/12)
17977^(1/13)
17977^(1/14)
True 9.79684844205 -0.418010983057
sqrt(18149)
18149^(1/3)
18149^(1/4)
18149^(1/5)
18149^(1/6)
18149^(1/7)
18149^(1/8)
18149^(1/9)
18149^(1/10)
18149^(1/11)
18149^(1/12)
18149^(1/13)
18149^(1/14)
Error in lines 8-17
Traceback (most recent call last):
File "/cocalc/lib/python2.7/site-packages/smc_sagews/sage_server.py", line 1188, in execute
flags=compile_flags) in namespace, locals
File "", line 4, in <module>
File "", line 16, in check_prime_aks
File "", line 3, in check_comp_aks_test
File "", line 20, in get_aks_poly
File "sage/rings/polynomial/polynomial_template.pxi", line 630, in sage.rings.polynomial.polynomial_zmod_flint.Polynomial_template.__pow__ (build/cythonized/sage/rings/polynomial/polynomial_zmod_flint.cpp:12216)
celement_pow(&r.x, &(<Polynomial_template>self).x, e, NULL, (<Polynomial_template>self)._cparent)
File "./sage/libs/flint/nmod_poly_linkage.pxi", line 529, in sage.rings.polynomial.polynomial_zmod_flint.celement_pow (build/cythonized/sage/rings/polynomial/polynomial_zmod_flint.cpp:5665)
sig_on()
File "src/cysignals/signals.pyx", line 98, in cysignals.signals.sig_raise_exception
KeyboardInterrupt