It's All True: The Sum of Digits of Prime Numbers Is Evenly Distributed

May 14, 2010 

Researchers from the Institut de Mathématiques de Luminy (CNRS/Université de la Méditerranée) have demonstrated that, on average, there are as many prime numbers for which the sum of decimal digits is even as there are prime numbers for which the sum is odd.

The conjecture on the sum of digits of prime numbers had been formulated by Russian mathematician Alexandre Gelfond in 1968. Its solution, which made use of combinatorial mathematics, analytical number theory, and harmonic analysis, may have implications for the the construction of sequences of pseudorandom numbers, which may impact digital simulation and cryptography.

C. Mauduit, J. Rivat summed it up in "Sur un problème de Gelfond: la somme des chiffres des nombres premiers" ("On a Gelfond Problem: the Sum of Digits of Prime Numbers"), which appeared in Annals of Mathematics (May 2010).

Source: CRNS (May 12, 2010)