CoCalc Public FilesCircular Primes.ipynb
Authors: Samuel Lelièvre, Julian Rüth
Views : 53
Description: Circular Primes as done at Software Tools For Mathematics Koper 2018
Compute Environment: Ubuntu 18.04 (Deprecated)

## Circular Primes

In [1]:
p = 19937
p.is_prime()

True
In [2]:
print(19937.is_prime())
print(71993.is_prime())
print(37199.is_prime())
print(93719.is_prime())
print(99371.is_prime())

True True True True True
In [3]:
print(Primes())
print(Primes()[:100])

Set of all prime numbers: 2, 3, 5, 7, ... [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541]
In [4]:
def rotate(s):
return s[1:] + s[0]

def is_circular(p):
pstring = str(p)
for i in range(len(pstring)):
pstring = rotate(pstring)
q = ZZ(pstring, base=10)
if not q.is_prime():
return False
return True

for p in Primes()[:100000]:
if is_circular(p):
print(p)

2 3 5 7 11 13 17 31 37 71 73 79 97 113 131 197 199 311 337 373 719 733 919 971 991 1193 1931 3119 3779 7793 7937 9311 9377 11939 19391 19937 37199 39119 71993 91193 93719 93911 99371 193939 199933 319993 331999 391939 393919 919393 933199 939193 939391 993319 999331
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