The (double) Primorial sieve  &  Prime spirals E-mail

In 2016, Standford number theorists, Robert Lemke Oliver and Kannan Soundararajan discovered that
the first hundred million consecutive prime numbers,
e.g.   pi ( m ) = 10^8  with  m = 2 x 10^9 ,
end less frequently with the same digit than other digits.
The last digit gap  (9, 1)  is favored, see table.

This find is exceptional because prime numbers have no known last digit preference.

The graph shows the frequencies of the  Last digit gaps  for several values of  m,  with  m  the number of consecutive natural numbers. The displayed curves stabilize after the erratic behaviour up to around  m = 10^5,  due to the buildup of the Primorial sieves.

It is the conjecture that all curves ultimately converge to the expected value of  6,25%  (e.g. 1/16)  and thus:
        prime numbers have  no  last digit preference.

See also the  (double) primorial sieve.pdf


Double Primorial Sieve: Last digit gap of successive primes