## The New Encyclopędia Britannica, Volume 30Encyclopędia Britannica, 1992 - Encyclopedias and dictionaries |

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Page 15

The distribution of primes appears to be more regular if they are counted in large

blocks , say in groups of 1,000 where p , q , ... are the distinct

and consecutive integers . The first six blocks of length 1,000 the exponents A , B

...

The distribution of primes appears to be more regular if they are counted in large

blocks , say in groups of 1,000 where p , q , ... are the distinct

**prime**factors of n ,and consecutive integers . The first six blocks of length 1,000 the exponents A , B

...

Page 31

It has been conjectured that the inequality | M ( n ) / < nl / 2 + holds for every e > 0.

If this were true it would have important implications concerning the distribution of

primes . It is known that M ( n ) / n → as n , a result equivalent to the

It has been conjectured that the inequality | M ( n ) / < nl / 2 + holds for every e > 0.

If this were true it would have important implications concerning the distribution of

primes . It is known that M ( n ) / n → as n , a result equivalent to the

**prime**...Page 32

psx k = 1 k = 1 Dirichlet L - functions Š ns n = 1 ns n = 1 deduced from ( 2 ) , so

the two statements are equivalent . Σ 1 Each of the following statements involving

the Möbius log ( log x ) + O ( 1 ) , р function is also equivalent to the

number ...

psx k = 1 k = 1 Dirichlet L - functions Š ns n = 1 ns n = 1 deduced from ( 2 ) , so

the two statements are equivalent . Σ 1 Each of the following statements involving

the Möbius log ( log x ) + O ( 1 ) , р function is also equivalent to the

**prime**number ...

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### Contents

NUMBER GAMES and Other Mathematical Recreations | 1 |

NUMBER THEORY | 14 |

NUMERICAL ANALYSIS | 38 |

Copyright | |

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