--- Juan Ignacio Casaubon <

jicasaubon@...> wrote:

>

> Hi,

>

> A result of Juan Pablo Cosentino juancosentino@...

>

> From 10 to 20 the primes are 11, 13, 17, 19

>

> he puts 101000101 where 1 indicate prime

>

> From 20 to 30 the primes are 23, 29

>

> he puts 1000001

>

> AND SO ON...

>

> Now he transform these 16 possible binary numbers

Modulo 10, there are phi(2)*Phi(5) = 1*4 = 4 possible non-zero-divisors (or

units, or numbers coprime to 10).

1, 3, 7, 9

Therefore the 16 possible numbers are

{0,2^8}+{0,2^6}+{0,2^2}+{0,2^0}

> in arabic, he found four WELL SEPARATED bands

>

> of exactly 5 numbers (width)

>

> 0-5

>

> 64-69

>

> 256-261

>

> 320-325

My expresion above is equivalent to

{0,2^6,2^8,2^8+2^6} + {0,2^0,2^2,2^2+2^0}

or

{0, 64, 256, 320} + {0, 1, 4, 5}

There're the 4 bands, and here are the "5" numbers.

> Take this into account: Do not steal this result, Juan Pablo is a student

> in Engineering.

>

> My students are ever very inteligent!

As were Eratosthenes and many others. However, they got to the topic

2 millennia ago.

Phil

=====

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