A119449 Primes with even digit sum.

2, 11, 13, 17, 19, 31, 37, 53, 59, 71, 73, 79, 97, 101, 103, 107, 109, 127, 149, 163, 167, 181, 211, 233, 239, 251, 257, 271, 277, 293, 307, 347, 349, 367, 383, 389, 419, 431, 433, 439, 457, 479, 491, 499, 503, 509, 521, 523, 541, 547, 563, 569, 587, 613, 617

Offset: 1

Author

Zak Seidov, May 20 2006

Keywords

• base
• nonn

Comments

On average, there are as many prime numbers for which the sum of decimal digits is even as prime numbers for which it is odd [A119450]. This hypothesis, first made in 1968, has recently been proved by researchers from the Institut de Mathematiques de Luminy. - Jonathan Vos Post, May 13 2010

Also primes such that absolute value of difference between largest digit and the sum of all the other digits is an even integer. This is in accordance with hypothesis of Alexandre Gelfond, proved by C. Mauduit and J. Rivat, see the link below. - Osama Abuajamieh, Feb 10 2017.

Links

• T. D. Noe, Table of n, a(n) for n = 1..10000
• Christian Mauduit and Joël Rivat, Sur un problème de Gelfond: la somme des chiffres des nombres premiers, Annals Math., 171 (2010), 1591-1646.
• ScienceDaily, Sum of Digits of Prime Numbers Is Evenly Distributed: New Mathematical Proof of Hypothesis, May 13, 2010.

Crossrefs

Intersection of A054683 and A000040.

Primes with odd digit sum A119450.

Programs

Mathematica

Select[Prime@ Range@ 113, EvenQ@ Total@ IntegerDigits@ # &] (* Michael De Vlieger, Feb 11 2017 *)

PARI

isok(n) = isprime(n) && (sumdigits(n) % 2 == 0); \\ Michel Marcus, Oct 10 2013