A '''long prime''' (as defined here) is a prime number whose reciprocal (in decimal) has
a ''period length'' of one less than the prime number.
'''Long primes''' are also known as:
:::* base ten cyclic numbers
:::* full reptend primes
:::* golden primes
:::* long period primes
:::* maximal period primes
:::* proper primes
Another definition: primes '''p''' such that the decimal expansion of '''1/p''' has period '''p-1''', which is the greatest period possible for any integer.
;Example:
'''7''' is the first long prime, the reciprocal of seven
is '''1''''''/''''''7''', which
is equal to the repeating decimal fraction '''0.142857142857ยทยทยท
The length of the ''repeating'' part of the decimal fraction
is six, (the underlined part) which is one less
than the (decimal) prime number '''7'''.
Thus '''7''' is a long prime.
There are other (more) general definitions of a '''long prime''' which
include wording/verbiage for bases other than ten.
;Task:
:* Show all long primes up to '''500''' (preferably on one line).
:* Show the ''number'' of long primes up to ''' 500'''
:* Show the ''number'' of long primes up to ''' 1,000'''
:* Show the ''number'' of long primes up to ''' 2,000'''
:* Show the ''number'' of long primes up to ''' 4,000'''
:* Show the ''number'' of long primes up to ''' 8,000'''
:* Show the ''number'' of long primes up to '''16,000'''
:* Show the ''number'' of long primes up to '''32,000'''
:* Show the ''number'' of long primes up to '''64,000''' (optional)
:* Show all output here.
;;;Also see:
:* [[wp:Full_reptend_prime|Wikipedia: full reptend prime]]
:* [http://mathworld.wolfram.com/FullReptendPrime.html MathWorld: full reptend prime]
:* [[oeis:A001913|OEIS: A001913]]