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Quasi-primes and the Goldbach conjecture

Published online by Cambridge University Press:  01 August 2016

Nick MacKinnon
Nick MacKinnon*
Affiliation:
Winchester College
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Extract

In 1742 Goldbach sent a letter to Euler which contained the conjecture that:

Every even number greater than 2 is the sum of two prime numbers.

It is easy to verify Goldbach's conjecture numerically up to some quite high limits but no proof has yet been found. I have long had the uneasy feeling that the conjecture is not about the prime numbers at all but would equally apply to any ‘sufficiently dense’ sequence of odd numbers. However a recent attempt to generalise the sieve of Eratosthenes has led me to regard Goldbach's conjecture with a good deal more respect.

Type
Research Article
Information
The Mathematical Gazette , Volume 72 , Issue 460 , June 1988 , pp. 103 - 108
Copyright
Copyright © The Mathematical Association 1988

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