full reptend prime
If for a prime number in a given base such that , the formula
The first few base 10 full reptend primes are given by A001913 of Sloane’s OEIS: 7, 17, 19, 23, 29, 47, 59, 61, 97, 109, 113, 131, 149, 167.
For example, the case , gives the cyclic number 142857, thus, 7 is a full reptend prime.
Not all values of will yield a cyclic number using this formula; for example gives 076923076923. These failed cases will always contain a repetition of digits (possibly several).
The known pattern to this sequence comes from algebraic number theory, specifically, this sequence is the set of primes such that 10 is a primitive root modulo . A conjecture of Emil Artin on primitive roots is that this sequence contains about 37 percent of the primes.
|Title||full reptend prime|
|Date of creation||2013-03-22 16:04:50|
|Last modified on||2013-03-22 16:04:50|
|Last modified by||PrimeFan (13766)|