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 July 25, 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 July 25, 2014).

Share This




More Computers & Math News

Friday, July 25, 2014

Featured Research

from universities, journals, and other organizations


Featured Videos

from AP, Reuters, AFP, and other news services

Bill Gates: Health, Agriculture Key to Africa's Development

Bill Gates: Health, Agriculture Key to Africa's Development

AFP (July 24, 2014) — Health and agriculture development are key if African countries are to overcome poverty and grow, US software billionaire Bill Gates said Thursday, as he received an honourary degree in Ethiopia. Duration: 00:36 Video provided by AFP
Powered by NewsLook.com
Creative Makeovers for Ugly Cellphone Towers

Creative Makeovers for Ugly Cellphone Towers

AP (July 24, 2014) — Mobile phone companies and communities across the country are going to new lengths to disguise those unsightly cellphone towers. From a church bell tower to a flagpole, even a pencil, some towers are trying to make a point. (July 24) Video provided by AP
Powered by NewsLook.com
Robot Parking Valet Creates Stress-Free Travel

Robot Parking Valet Creates Stress-Free Travel

AP (July 23, 2014) — 'Ray' the robotic parking valet at Dusseldorf Airport in Germany lets travelers to avoid the hassle of finding a parking spot before heading to the check-in desk. (July 23) Video provided by AP
Powered by NewsLook.com
Facebook Earnings Put Smile on Investors Faces

Facebook Earnings Put Smile on Investors Faces

Reuters - Business Video Online (July 23, 2014) — Facebook earnings beat forecasts- with revenue climbing 61 percent. Bobbi Rebell reports. Video provided by Reuters
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