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Runs of composite integers and the Chinese Remainder Theorem

Published online by Cambridge University Press:  01 August 2016

Rex Watson
Rex Watson*
Affiliation:
Homerton College, Hills Rd., Cambridge CB2 2PH
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Extract

The distribution of the prime numbers is of course a well-trodden path. The casual enquirer, working with small numbers, soon finds that the distribution has no obvious regularities, and sees that the primes thin out. The Prime number theorem (which is not elementary) helps to firm up this observation:

Prime number theorem: If π(n) is the number of primes no greater than n, then i.e. π(n)/(n/ln(n)) → 1 as n → ∞. Thus for the proportion of prime numbers upto to n, π(n)/n, we have that which tends slowly to 0.

Type
Research Article
Information
The Mathematical Gazette , Volume 78 , Issue 482 , July 1994 , pp. 167 - 173
Copyright
Copyright © The Mathematical Association 1994

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References

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