View Single Post 2006-09-20, 12:26 #1 AntonVrba   Jun 2005 2·72 Posts Sum of all integer digits of all primes between 1 an n With the discovery of M44 (congratulations GIMPS) I pondered over the thought if it is possible to count/calculate all the ones of all the primes between 2 and M44. It is a bit off-topic but the result is interesting. To calculate or estimate the number of ones, I set about as follows. Define as the sum of all base-b integer digits between 1 and n and can be expressed as. Above has the spot values Now assume to be large then and proportioning to the number of primes between and which is approximated in the Prime Number Theorem as we obtain the unexpected result that the cumulative sum of all base-b integer digits of all the primes between and prime approximates to Conjecture The ratio defined as "the sum of all base-b digits of all the primes between 1 and n" to "n", converges to the constant for increasing n. and A computation check confirms above tendency already at relatively small values of n. Is above already known or have I introduced a new constant? In parctice how will the constant depart from above definition? Regards Anton Vrba  