phil1882 13 Posted August 12, 2013 Report Share Posted August 12, 2013 consider the golden ratio. 1.618.... now, imagine multiplying this by each integer. keep the numbers it truncates to. 1 1.618*2 = 3 1.618*3 = 4 1.618*4 = 6 1.618*5 = 8 1.618*6 = 9 and so on. its a very interesting sequence with some "nice" properties. now here's my question. if you're allowed any irrational number; which one goes through the most primes and fewest composites? Quote Link to post Share on other sites

0 DeGe 9 Posted August 12, 2013 Report Share Posted August 12, 2013 Prime numbers (greater than 3) are of the form 6n+1 or 6n-1 Since approximating 6n+1 using a rational number will be difficult as n increases, lets consider only 6n-1 cases. As we are rounding down the numbers, an expression close to but only just less than 6 that gives all the numbers of form 6n-1, will have almost a third of the numbers prime. Therefore using 5.99999999... we would get all 6n-1 numbers and nearly 1/3 of these numbers would be prime Quote Link to post Share on other sites

0 Anza Power 9 Posted August 13, 2013 Report Share Posted August 13, 2013 ^ 5.999999... (continue forever) is actually 6.And if it doesn't continue forever then at some point you will get 6n-2... Quote Link to post Share on other sites

## Question

## phil1882 13

consider the golden ratio.

1.618....

now, imagine multiplying this by each integer. keep the numbers it truncates to.

1

1.618*2 = 3

1.618*3 = 4

1.618*4 = 6

1.618*5 = 8

1.618*6 = 9

and so on.

its a very interesting sequence with some "nice" properties.

now here's my question. if you're allowed any irrational number;

which one goes through the most primes and fewest composites?

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