7^100
|
|
|
|
def pisano(m):
a=1 # second Fib number
b=1 # first Fib number
counter = 1
while [b,a] != [0,1]:
a,b=a+b,a
a=a%m
b=b%m
counter+=1
return(counter)
|
|
pisano(3)
8 8 |
pisano(10)
60 60 |
pisano(10^2)
300 300 |
pisano(10^3)
1500 1500 |
pisano(10^4)
15000 15000 |
pisano(10^5)
150000 150000 |
pisano(10^6)
1500000 1500000 |
pisano(10^7)
15000000 15000000 |
pisano(10^8)
|
|
t=cputime()
print(pisano(10^7))
print(cputime()-t)
15000000 10.902355 15000000 10.902355 |
prime_pisano_periods=[]
N=20000
p=2
while p<N:
pip=pisano(p)
prime_pisano_periods.append([p,pisano(p)])
p=p.next_prime()
list_plot(prime_pisano_periods)
|
print(prime_pisano_periods)
|
|
prime_pisano_periods=[]
N=20000
p=2
while p<N:
pip=pisano(p)
if pip>3*p/2:
prime_pisano_periods.append([p,pisano(p)])
p=p.next_prime()
list_plot(prime_pisano_periods)
|
len(prime_pisano_periods)
907 907 |
print(prime_pisano_periods[:20])
[[3, 8], [5, 20], [7, 16], [13, 28], [17, 36], [23, 48], [37, 76], [43, 88], [53, 108], [67, 136], [73, 148], [83, 168], [97, 196], [103, 208], [127, 256], [137, 276], [157, 316], [163, 328], [167, 336], [173, 348]] [[3, 8], [5, 20], [7, 16], [13, 28], [17, 36], [23, 48], [37, 76], [43, 88], [53, 108], [67, 136], [73, 148], [83, 168], [97, 196], [103, 208], [127, 256], [137, 276], [157, 316], [163, 328], [167, 336], [173, 348]] |
prime_pisano_periods=[]
N=2000
p=2
while p<N:
pip=pisano(p)
if pip<3*p/2 and pip>9*p/10:
prime_pisano_periods.append([p,pisano(p)])
p=p.next_prime()
list_plot(prime_pisano_periods)
Graphics object consisting of 1 graphics primitive Graphics object consisting of 1 graphics primitive |
print(prime_pisano_periods[:20])
[[11, 10], [19, 18], [31, 30], [41, 40], [59, 58], [61, 60], [71, 70], [79, 78], [109, 108], [131, 130], [149, 148], [179, 178], [191, 190], [239, 238], [241, 240], [251, 250], [269, 268], [271, 270], [311, 310], [359, 358]] [[11, 10], [19, 18], [31, 30], [41, 40], [59, 58], [61, 60], [71, 70], [79, 78], [109, 108], [131, 130], [149, 148], [179, 178], [191, 190], [239, 238], [241, 240], [251, 250], [269, 268], [271, 270], [311, 310], [359, 358]] |
prime_pisano_periods=[]
N=2000
p=2
while p<N:
pip=pisano(p)
if pip<3*p/4 and pip>3*p/5:
prime_pisano_periods.append([p,pisano(p)])
p=p.next_prime()
show(list_plot(prime_pisano_periods))
|
print(prime_pisano_periods[:20])
[[47, 32], [107, 72], [113, 76], [263, 176], [347, 232], [353, 236], [563, 376], [677, 452], [743, 496], [977, 652], [1097, 732], [1217, 812], [1223, 816], [1277, 852], [1307, 872], [1523, 1016], [1553, 1036], [1733, 1156], [1823, 1216], [1877, 1252]] [[47, 32], [107, 72], [113, 76], [263, 176], [347, 232], [353, 236], [563, 376], [677, 452], [743, 496], [977, 652], [1097, 732], [1217, 812], [1223, 816], [1277, 852], [1307, 872], [1523, 1016], [1553, 1036], [1733, 1156], [1823, 1216], [1877, 1252]] |
plot(sin(x),x,0,10)
Graphics object consisting of 1 graphics primitive Graphics object consisting of 1 graphics primitive |
prime_pisano_periods=[]
N=2000
p=2
while p<N:
pip=pisano(p)
if pip<3*p/5 and pip>2*p/5:
prime_pisano_periods.append([p,pisano(p)])
p=p.next_prime()
show(list_plot(prime_pisano_periods))
|
print(prime_pisano_periods[:20])
[[29, 14], [89, 44], [101, 50], [181, 90], [229, 114], [349, 174], [401, 200], [509, 254], [761, 380], [941, 470], [1021, 510], [1061, 530], [1109, 554], [1229, 614], [1249, 624], [1361, 680], [1409, 704], [1549, 774], [1621, 810], [1669, 834]] [[29, 14], [89, 44], [101, 50], [181, 90], [229, 114], [349, 174], [401, 200], [509, 254], [761, 380], [941, 470], [1021, 510], [1061, 530], [1109, 554], [1229, 614], [1249, 624], [1361, 680], [1409, 704], [1549, 774], [1621, 810], [1669, 834]] |
prime_pisano_periods_ratio=[]
N=20000
p=2
while p<N:
pip=pisano(p)
if p%5==2 or p%5==3:
prime_pisano_periods_ratio.append([p,2*(p+1)/pisano(p)])
else:
prime_pisano_periods_ratio.append([p,(p-1)/pisano(p)])
p=p.next_prime()
show(list_plot(prime_pisano_periods_ratio))
|
print(prime_pisano_periods_ratio[:20])
[[2, 2], [3, 1], [5, 1/5], [7, 1], [11, 1], [13, 1], [17, 1], [19, 1], [23, 1], [29, 2], [31, 1], [37, 1], [41, 1], [43, 1], [47, 3], [53, 1], [59, 1], [61, 1], [67, 1], [71, 1]] [[2, 2], [3, 1], [5, 1/5], [7, 1], [11, 1], [13, 1], [17, 1], [19, 1], [23, 1], [29, 2], [31, 1], [37, 1], [41, 1], [43, 1], [47, 3], [53, 1], [59, 1], [61, 1], [67, 1], [71, 1]] |
def is_5_square(p):
for i in srange(1,p):
if (i^2 %p) ==5:
return(i)
return(False)
|
|
for i in srange(2,100):
if is_prime(i):
print(i,is_5_square(i))
(2, False) (3, False) (5, False) (7, False) (11, 4) (13, False) (17, False) (19, 9) (23, False) (29, 11) (31, 6) (37, False) (41, 13) (43, False) (47, False) (53, False) (59, 8) (61, 26) (67, False) (71, 17) (73, False) (79, 20) (83, False) (89, 19) (97, False) (2, False) (3, False) (5, False) (7, False) (11, 4) (13, False) (17, False) (19, 9) (23, False) (29, 11) (31, 6) (37, False) (41, 13) (43, False) (47, False) (53, False) (59, 8) (61, 26) (67, False) (71, 17) (73, False) (79, 20) (83, False) (89, 19) (97, False) |
|
|