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A119449
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Primes with even digit sum.
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4
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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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. [From Jonathan Vos Post (jvospost3(AT)gmail.com), May 13 2010]
Primes p such that sum of digits + 3 is prime. [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 13 2010]
This last comment is false; the first counterexample is 499, which has digit sum 22.
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REFERENCES
| C. Mauduit and J. Rivat. Sur un probleme de Gelfond: la somme des chiffres des nombres premiers. Annals of Mathematics, 2010; 171 (3): 1591. [From Jonathan Vos Post (jvospost3(AT)gmail.com), May 13 2010]
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LINKS
| T. D. Noe, Table of n, a(n) for n = 1..10000
ScienceDaily, Sum of Digits of Prime Numbers Is Evenly Distributed: New Mathematical Proof of Hypothesis, May 13, 2010.
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CROSSREFS
| Primes with odd digit sum A119450.
Sequence in context: A058048 A038915 A166849 * A137977 A160950 A141168
Adjacent sequences: A119446 A119447 A119448 * A119450 A119451 A119452
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KEYWORD
| base,nonn
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AUTHOR
| Zak Seidov (zakseidov(AT)yahoo.com), May 20 2006
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