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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.

Read more at The Science Daily:

http://www.sciencedaily.com/releases/2010/05/100512172533.htm