CoCalc -- Circular Primes.ipynb

Circular Primes as done at Software Tools For Mathematics Koper 2018

Project: Software Tools For Mathematics

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Kernel: SageMath (stable)

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)

In [0]: