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On Mathematics Page 1 you have seen some prime numbers. The list of prime numbers may be viewed in many ways. Here is one view which I like.
Prime numbers:
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2, |
3, |
5, 7, |
11, 13, |
17, 19, |
23, __, |
29, 31, |
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_, 37, |
41, 43, |
47, __, |
53, __, |
59, 61, |
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_, 67, |
71, 73, |
__, 79, |
83, __, |
89, __, |
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_, 97, |
101, 103, |
107, 109, |
113, __, |
__, __, |
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A number of patterns appear in this set-up. In one pattern the primes appear to occur in pairs. This gives the idea of 'twin primes'. Twin primes are pairs of prime numbers which have a difference between them of two. For instance, 13 and 11 are twin primes since 13-11 = 2.
One of the unanswered questions in mathematics is: Will the pairs of primes continue to occur forever?
The number of prime numbers which can be found in a given span of numbers can be counted reasonably accurately and the accuracy gets better the larger the span of numbers. The answer is close to
[This may be improved to 
following Legendre and others]
It has not yet proved possible to count the number of pairs of primes because it is not known if they stop existing or not. There are formulae which can be used to give estimates of how many exist within the span of numbers from 2 to the highest known twin prime.
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