## Re: [PrimeNumbers] On the 1, 3, 7, 9

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• ... 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
Message 1 of 2 , Nov 28, 2002
--- 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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