The (double) Primorial sieve & Prime spirals |
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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.

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.

prime numbers have no last digit preference.

See also the (double) primorial sieve.pdf.

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Double Primorial Sieve: Last digit gap of successive primes