Finding Carmichael Numbers
I cant seem to figure out why my python code is telling me wrong carmichael numbers. Thanks in advance. I just cant see the error in the algorithm.
def isCarmichaelNumber( x ):
for y in range(2,x):
#check if prime
if math.gcd (x, y) == 1:
if pow(y, x-1, x) != 1:
return False
return True
print(isCarmichaelNumber(1847))
python algorithm
asked Nov 20 at 6:21
ShelbyJ
183
add a comment |
I cant seem to figure out why my python code is telling me wrong carmichael numbers. Thanks in advance. I just cant see the error in the algorithm.
def isCarmichaelNumber( x ):
for y in range(2,x):
#check if prime
if math.gcd (x, y) == 1:
if pow(y, x-1, x) != 1:
return False
return True
print(isCarmichaelNumber(1847))
python algorithm
asked Nov 20 at 6:21
ShelbyJ
183
add a comment |
I cant seem to figure out why my python code is telling me wrong carmichael numbers. Thanks in advance. I just cant see the error in the algorithm.
def isCarmichaelNumber( x ):
for y in range(2,x):
#check if prime
if math.gcd (x, y) == 1:
if pow(y, x-1, x) != 1:
return False
return True
print(isCarmichaelNumber(1847))
python algorithm
asked Nov 20 at 6:21
ShelbyJ
183
I cant seem to figure out why my python code is telling me wrong carmichael numbers. Thanks in advance. I just cant see the error in the algorithm.
def isCarmichaelNumber( x ):
for y in range(2,x):
#check if prime
if math.gcd (x, y) == 1:
if pow(y, x-1, x) != 1:
return False
return True
print(isCarmichaelNumber(1847))
python algorithm
python algorithm
asked Nov 20 at 6:21
ShelbyJ
183
asked Nov 20 at 6:21
ShelbyJ
183
asked Nov 20 at 6:21
ShelbyJ
183
asked Nov 20 at 6:21
ShelbyJ
183
asked Nov 20 at 6:21
ShelbyJ
183
183
add a comment |
add a comment |
1 Answer
1
active
oldest
votes
You're not checking to see whether x is prime. By definition, a Carmichael number must be composite. For any prime x, pow(y, x-1, x) == 1 for all y in range(2, x), so will incorrectly return True. 1847 is prime, which is why your function claims it's a Carmichael number.
One way to fix it:
def isCarmichaelNumber(x):
import math
isprime = True
for y in range(2,x):
if math.gcd(x, y) == 1:
if pow(y, x-1, x) != 1:
return False
else:
isprime = False
return not isprime
answered Nov 20 at 6:39
Tim Peters
41.8k67293
add a comment |
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
You're not checking to see whether x is prime. By definition, a Carmichael number must be composite. For any prime x, pow(y, x-1, x) == 1 for all y in range(2, x), so will incorrectly return True. 1847 is prime, which is why your function claims it's a Carmichael number.
One way to fix it:
def isCarmichaelNumber(x):
import math
isprime = True
for y in range(2,x):
if math.gcd(x, y) == 1:
if pow(y, x-1, x) != 1:
return False
else:
isprime = False
return not isprime
answered Nov 20 at 6:39
Tim Peters
41.8k67293
add a comment |
You're not checking to see whether x is prime. By definition, a Carmichael number must be composite. For any prime x, pow(y, x-1, x) == 1 for all y in range(2, x), so will incorrectly return True. 1847 is prime, which is why your function claims it's a Carmichael number.
One way to fix it:
def isCarmichaelNumber(x):
import math
isprime = True
for y in range(2,x):
if math.gcd(x, y) == 1:
if pow(y, x-1, x) != 1:
return False
else:
isprime = False
return not isprime
answered Nov 20 at 6:39
Tim Peters
41.8k67293
add a comment |
You're not checking to see whether x is prime. By definition, a Carmichael number must be composite. For any prime x, pow(y, x-1, x) == 1 for all y in range(2, x), so will incorrectly return True. 1847 is prime, which is why your function claims it's a Carmichael number.
One way to fix it:
def isCarmichaelNumber(x):
import math
isprime = True
for y in range(2,x):
if math.gcd(x, y) == 1:
if pow(y, x-1, x) != 1:
return False
else:
isprime = False
return not isprime
answered Nov 20 at 6:39
Tim Peters
41.8k67293
You're not checking to see whether x is prime. By definition, a Carmichael number must be composite. For any prime x, pow(y, x-1, x) == 1 for all y in range(2, x), so will incorrectly return True. 1847 is prime, which is why your function claims it's a Carmichael number.
One way to fix it:
def isCarmichaelNumber(x):
import math
isprime = True
for y in range(2,x):
if math.gcd(x, y) == 1:
if pow(y, x-1, x) != 1:
return False
else:
isprime = False
return not isprime
answered Nov 20 at 6:39
Tim Peters
41.8k67293
answered Nov 20 at 6:39
Tim Peters
41.8k67293
answered Nov 20 at 6:39
Tim Peters
41.8k67293
answered Nov 20 at 6:39
Tim Peters
41.8k67293
41.8k67293
add a comment |
add a comment |
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