This is Emil Artin's guess for the portion of primes that are long to base 10. It is denoted by C and is defined as:
C = 1/2 x 5/6 x 19/20 x 41/42 x ... = 0.37395581361920228805472805434641641511162924860615...
Each factor is (p² - p - 1) / (p² - p) for each consecutive prime p.
My attempts to write an algorithm to calculate this have been dismally unsuccessful. The terms quickly reach 0.99999999 and then the cumulative rounding errors really start adding up. Let me know if you have any more success.