

A119449


Primes with even digit sum.


7



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
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OFFSET

1,1


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), 15911646.
ScienceDaily, Sum of Digits of Prime Numbers Is Evenly Distributed: New Mathematical Proof of Hypothesis, May 13, 2010.


MATHEMATICA

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


PROG

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


CROSSREFS

Intersection of A054683 and A000040.
Primes with odd digit sum A119450.
Sequence in context: A241659 A038915 A166849 * A243586 A296923 A243588
Adjacent sequences: A119446 A119447 A119448 * A119450 A119451 A119452


KEYWORD

base,nonn


AUTHOR

Zak Seidov, May 20 2006


STATUS

approved



