Featured Research

from universities, journals, and other organizations

Sum of digits of prime numbers is evenly distributed: New mathematical proof of hypothesis

Date:
May 13, 2010
Source:
CNRS (Délégation Paris Michel-Ange)
Summary:
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. This hypothesis, first made in 1968, has recently been proven by mathematics researchers in France.

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. This hypothesis, first made in 1968, has recently been proven by researchers from the Institut de Mathématiques de Luminy (CNRS/Université de la Méditerranée).

A prime number is an integer greater than or equal to 2 that has exactly two distinct natural number divisors, 1 and itself. For example, 2, 3, 5, 7, 11,..., 1789, etc. are prime numbers, whereas 9, divisible by 3, is not a prime number.

Numerous arithmetical problems concern prime numbers and most of them still remain unresolved, sometimes even after several centuries. For example, it has been known since Euclid that the sequence of prime numbers is infinite, but it is still not known if an infinity of prime numbers p exists such that p+2 is also a prime number (problem of twin prime numbers). In the same way, it is not known if there exists an infinity of prime numbers, the decimal representation of which does not use the digit 7.

Two researchers from the Institut de Mathématiques de Luminy (CNRS/Université de la Méditerranée) have recently made an important breakthrough regarding a conjecture formulated in 1968 by the Russian mathematician Alexandre Gelfond concerning the sum of digits of prime numbers. In particular, they have demonstrated that, 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.

The methods employed to arrive at this result, derived from combinatorial mathematics, the analytical theory of numbers and harmonic analysis, are highly groundbreaking and should pave the way to the resolution of other difficult questions concerning the representation of certain sequences of integers.

Quite apart from their theoretical interest, these questions are directly linked to the construction of sequences of pseudo-random numbers and have important applications in digital simulation and cryptography.


Story Source:

The above story is based on materials provided by CNRS (Délégation Paris Michel-Ange). Note: Materials may be edited for content and length.


Journal Reference:

  1. Christian Mauduit, Joël Rivat. Sur un problème de Gelfond: la somme des chiffres des nombres premiers. Annals of Mathematics, 2010; 171 (3): 1591 DOI: 10.4007/annals.2010.171.1591

Cite This Page:

CNRS (Délégation Paris Michel-Ange). "Sum of digits of prime numbers is evenly distributed: New mathematical proof of hypothesis." ScienceDaily. ScienceDaily, 13 May 2010. <www.sciencedaily.com/releases/2010/05/100512172533.htm>.
CNRS (Délégation Paris Michel-Ange). (2010, May 13). Sum of digits of prime numbers is evenly distributed: New mathematical proof of hypothesis. ScienceDaily. Retrieved August 28, 2014 from www.sciencedaily.com/releases/2010/05/100512172533.htm
CNRS (Délégation Paris Michel-Ange). "Sum of digits of prime numbers is evenly distributed: New mathematical proof of hypothesis." ScienceDaily. www.sciencedaily.com/releases/2010/05/100512172533.htm (accessed August 28, 2014).

Share This




More Computers & Math News

Thursday, August 28, 2014

Featured Research

from universities, journals, and other organizations


Featured Videos

from AP, Reuters, AFP, and other news services

JPMorgan Chase Confirms Possible Cyber Attack

JPMorgan Chase Confirms Possible Cyber Attack

Reuters - US Online Video (Aug. 28, 2014) — Attackers stole checking and savings account information and lots of other data from JPMorgan Chase, according to the New York Times. Other banks are believed to be victims as well. Fred Katayama reports. Video provided by Reuters
Powered by NewsLook.com
Spend 2 Minutes Watching This Smartwatch Roundup

Spend 2 Minutes Watching This Smartwatch Roundup

Newsy (Aug. 28, 2014) — LG announces a round-faced smartwatch, Samsung adds 3G connectivity to its latest wearable, and Apple will reportedly announce the iWatch on Sept. 9. Video provided by Newsy
Powered by NewsLook.com
Why Apple Might Add Mobile Payment Options To iPhone 6

Why Apple Might Add Mobile Payment Options To iPhone 6

Newsy (Aug. 28, 2014) — A report by Wired suggests Apple's next iPhone will feature a mobile payment system and near-field communication. Video provided by Newsy
Powered by NewsLook.com
Hackerspace Provides Hackers Creative Haven

Hackerspace Provides Hackers Creative Haven

AP (Aug. 27, 2014) — HeatSync Labs, a so-called hackerspace in Mesa, Arizona provides members and the public alike a space to allow their creative juices to flow and make their tech dreams into a reality. (Aug 27) Video provided by AP
Powered by NewsLook.com

Search ScienceDaily

Number of stories in archives: 140,361

Find with keyword(s):
 
Enter a keyword or phrase to search ScienceDaily for related topics and research stories.

Save/Print:
Share:  

Breaking News:
from the past week

In Other News

... from NewsDaily.com

Science News

Health News

Environment News

Technology News



Save/Print:
Share:  

Free Subscriptions


Get the latest science news with ScienceDaily's free email newsletters, updated daily and weekly. Or view hourly updated newsfeeds in your RSS reader:

Get Social & Mobile


Keep up to date with the latest news from ScienceDaily via social networks and mobile apps:

Have Feedback?


Tell us what you think of ScienceDaily -- we welcome both positive and negative comments. Have any problems using the site? Questions?
Mobile iPhone Android Web
Follow Facebook Twitter Google+
Subscribe RSS Feeds Email Newsletters
Latest Headlines Health & Medicine Mind & Brain Space & Time Matter & Energy Computers & Math Plants & Animals Earth & Climate Fossils & Ruins