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Sharedsupport / 2015-03-11-102341 prime power.sagewsOpen in CoCalc

Examples for support purposes...

is_prime_power(4)
True
is_prime_power(2)
True
[n for n in [1..100] if is_prime_power(n)]
[1, 2, 3, 4, 5, 7, 8, 9, 11, 13, 16, 17, 19, 23, 25, 27, 29, 31, 32, 37, 41, 43, 47, 49, 53, 59, 61, 64, 67, 71, 73, 79, 81, 83, 89, 97]
is_prime_power?
File: /usr/local/sage/sage-6.5/local/lib/python2.7/site-packages/sage/rings/arith.py
Signature : is_prime_power(n, flag=0)
Docstring :
Returns True if n is a prime power, and False otherwise.  The
result is proven correct - *this is NOT a pseudo-primality test!*.

INPUT:

   * "n" - an integer or rational number

   * "flag (for primality testing)" - int

   * "0" (default): use a combination of algorithms.

   * "1": certify primality using the Pocklington-Lehmer Test.

   * "2": certify primality using the APRCL test.

EXAMPLES:

   sage: is_prime_power(389)
   True
   sage: is_prime_power(2000)
   False
   sage: is_prime_power(2)
   True
   sage: is_prime_power(1024)
   True
   sage: is_prime_power(-1)
   False
   sage: is_prime_power(1)
   True
   sage: is_prime_power(997^100)
   True
   sage: is_prime_power(1/2197)
   True
   sage: is_prime_power(1/100)
   False
   sage: is_prime_power(2/5)
   False